From 903fb508ffdb4c4561589772ce4db963e87e4db2 Mon Sep 17 00:00:00 2001 From: schochastics Date: Tue, 19 Sep 2017 17:12:54 +0200 Subject: [PATCH] added --- _pkgdown.yaml | 4 +- docs/LICENSE.html | 159 +++ docs/articles/benchmarks.html | 220 ++++ docs/articles/centrality_indices.html | 256 ++++ docs/articles/index.html | 169 +++ docs/articles/indirect_relations.html | 197 +++ docs/articles/mcmc_samples_exp.png | Bin 0 -> 22842 bytes docs/articles/mcmc_samples_rel.png | Bin 0 -> 23144 bytes docs/articles/neighborhood_inclusion.html | 259 ++++ .../figure-html/dominance_graph-1.png | Bin 0 -> 14081 bytes .../figure-html/simple_graph-1.png | Bin 0 -> 9914 bytes docs/articles/partial_centrality.html | 228 ++++ .../figure-html/tg_ri-1.png | Bin 0 -> 12055 bytes .../figure-html/tg_ri_cent-1.png | Bin 0 -> 20577 bytes .../figure-html/vis_intervals-1.png | Bin 0 -> 14101 bytes .../figure-html/vis_intervals_cent-1.png | Bin 0 -> 22942 bytes .../figure-html/vis_intervals_names-1.png | Bin 0 -> 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mode 100644 docs/reference/approx_rank_relative.html create mode 100644 docs/reference/comparable_pairs.html create mode 100644 docs/reference/compare_ranks.html create mode 100644 docs/reference/dominance_graph.html create mode 100644 docs/reference/exact_rank_prob.html create mode 100644 docs/reference/florentine_m.html create mode 100644 docs/reference/get_rankings.html create mode 100644 docs/reference/hyperbolic_index.html create mode 100644 docs/reference/index.html create mode 100644 docs/reference/indirect_relations.html create mode 100644 docs/reference/is_preserved.html create mode 100644 docs/reference/majorization_gap.html create mode 100644 docs/reference/mcmc_rank_prob.html create mode 100644 docs/reference/neighborhood_inclusion.html create mode 100644 docs/reference/netrankr.html create mode 100644 docs/reference/plot_rank_intervals.html create mode 100644 docs/reference/positional_dominance.html create mode 100644 docs/reference/rank_intervals.html create mode 100644 docs/reference/spectral_gap.html create mode 100644 docs/reference/threshold_graph.html create mode 100644 docs/reference/transform_relations.html create mode 100644 docs/reference/transitive_reduction.html create mode 100644 index.Rmd create mode 100644 index.md diff --git a/_pkgdown.yaml b/_pkgdown.yaml index 40cee82..97651ee 100644 --- a/_pkgdown.yaml +++ b/_pkgdown.yaml @@ -1,5 +1,5 @@ title: netrankr -url: https://github.com/schochastics/netrankr +url: https://schochastics.github.io/netrankr template: params: bootswatch: sandstone @@ -27,6 +27,8 @@ navbar: href: articles/use_case.html - text: "Benchmarks" href: articles/benchmarks.html + - text: "Periodic Table" + href: http://schochastics.net/sna/periodic.html right: - icon: fa-newspaper-o text: "news" diff --git a/docs/LICENSE.html b/docs/LICENSE.html new file mode 100644 index 0000000..8a1efef --- /dev/null +++ b/docs/LICENSE.html @@ -0,0 +1,159 @@ + + + + + + + + +License • netrankr + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ +
+
+
+

License

+
+ +
YEAR: 2017
+COPYRIGHT HOLDER: David Schoch
+
+ +
+ +
+ + +
+
+

Developed by David Schoch.

+
+ +
+

Site built with pkgdown.

+
+ +
+
+ + + diff --git a/docs/articles/benchmarks.html b/docs/articles/benchmarks.html new file mode 100644 index 0000000..4e18b46 --- /dev/null +++ b/docs/articles/benchmarks.html @@ -0,0 +1,220 @@ + + + + + + + +Benchmark Results • netrankr + + + + + + +
+
+ + + +
+
+
+

Benchmark Results

+ +
+ + + +
+

Some of the methods provided in netrankr are computationally very expensive. Computing all rankings of a partial ranking, for instance, is a NP-hard problem such that using the function exact_rank_prob() quickly becomes infeasible. This article provides some guidelines for when the use of this function is possible. Additionally, the quality of the approximation functions approx_* and sampling rankings with mcmc_rank_prob() for expected ranks and relative rank probabilities are assessed.

+
+
+

+Runtimes exact probabilities

+

The below figure shows the runtime of exact_rank_prob() for a sample of 13,000 partial rankings with 10 to 30 nodes and varying degree of completeness.

+

+

Not surprisingly, the runtime increases quickly with the number of nodes and the number of incomparable pairs in the partial ranking. As a very crude rule of thumb: As long as a partial ranking has less than 30 elements, it is always save to run exact_rank_prob(). Beyond 30 elements, it is advisable to only use the function if a high fraction of pairs of elements is already comparable. The more elements, the higher this fraction should be.

+
+
+
+

+Approximating expected ranks

+

netrankr implements five methods to approximate expected ranks which are given by the functions approx_rank_expected() and mcmc_rank_prob(). The four methods implemented in the former are only based on structural features of the partial ranking, while the latter is based on sampling rankings (almost) uniformly at random from the set of all rankings. Consult the help files for a more detailed description and references. The below figure shows the (averaged) mean absolute error compared to the exact expected ranks of the five methods on the set of 13000 partial rankings from above. The number of drawn samples for the mcmc function is set to \(n^4\), where \(n\) is the number of elements in the partial ranking.

+

+

The basic local partial order model performs considerably worse than the other methods on almost all partial rankings. Its generalized version outperforms the methods based on the relative rank probabilities (loof1 and loof2) if the number of incomparable pairs is high. The mcmc method generally yields the best approximations, especially with increasing number of elements. However, its performance seems to get worse when almost none of the elements are comparable. This issue is discussed in the section on choosing the number of samples further down.

+
+
+
+

+Approximating relative ranks

+

Relative ranks can either be approximated with the iterative function approx_rank_relative() or again via sampling rankings (almost) uniformly at random with mcmc_rank_prob(). The below figure shows the (averaged) mean absolute error compared to the exact relative rank probabilities on the set of 13000 partial rankings from above. The number of drawn samples for the mcmc function is set to \(n^4\), where \(n\) is the number of elements in the partial ranking. The number of iterative steps in approx_rank_relative() is set to 1 (no iteration), 5, 10 and 15 respectively.

+

Clearly, the non-iterative approximation performs worse on all partial rankings. The more iterations the better the approximation quality seems to be, yet the gain in quality going from 10 to 15 iterations seems negligible. The function based on random samples again performs better except in the region of low comparability.

+
+
+
+

+MCMC sampling of rankings

+

The results above have shown that approximating expected ranks and relative rank probabilities on the basis of a random sample generally give the best results, except in the region of low comparability. This problem can be mitigated by increasing the number of samples. The below boxplot shows the mean absolute error for the expected ranks of an empty partial ranking with 10 elements, when the number of samples is increased. For each sample size, 100 repetition were done.

+

The same procedure is carried out for the relative ranks below.

+

+

That is, increasing the number of samples (quite naturally) leads to better approximations, but of course also comes with an increase in running time, especially for larger partial rankings.

+
+
+
+

+Runtimes of approximation

+

The function mcmc_rank_prob() generally gives the best approximations. The larger the number of samples, the better. Since the number of samples should be at least cubic in the number of elements, it is limited to partial rankings with a couple of hundred elements.

+

Although the function approx_rank_expected() and approx_rank_relative() performed the worst in the above tests, they are computationally the least expensive with a time complexity of \(\mathcal{O}(n^2)\). Thus, they are able to at least give a rough approximation also for partial rankings beyond a 1000 elements.

+
+
+
+

+Session info

+
## R version 3.4.1 (2017-06-30)
+## Platform: x86_64-pc-linux-gnu (64-bit)
+## Running under: Ubuntu 16.04.3 LTS
+## 
+## Matrix products: default
+## BLAS: /usr/lib/libblas/libblas.so.3.6.0
+## LAPACK: /usr/lib/lapack/liblapack.so.3.6.0
+## 
+## locale:
+##  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
+##  [3] LC_TIME=de_DE.UTF-8        LC_COLLATE=en_US.UTF-8    
+##  [5] LC_MONETARY=de_DE.UTF-8    LC_MESSAGES=en_US.UTF-8   
+##  [7] LC_PAPER=de_DE.UTF-8       LC_NAME=C                 
+##  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
+## [11] LC_MEASUREMENT=de_DE.UTF-8 LC_IDENTIFICATION=C       
+## 
+## attached base packages:
+## [1] stats     graphics  grDevices utils     datasets  methods   base     
+## 
+## loaded via a namespace (and not attached):
+##  [1] compiler_3.4.1  backports_1.1.0 magrittr_1.5    rprojroot_1.2  
+##  [5] tools_3.4.1     htmltools_0.3.6 yaml_2.1.14     Rcpp_0.12.11   
+##  [9] stringi_1.1.5   rmarkdown_1.6   knitr_1.16      stringr_1.2.0  
+## [13] digest_0.6.12   evaluate_0.10.1
+
+
+
+ + + +
+ + +
+

Developed by David Schoch.

+
+ +
+

Site built with pkgdown.

+
+ +
+
+ + + diff --git a/docs/articles/centrality_indices.html b/docs/articles/centrality_indices.html new file mode 100644 index 0000000..a9d929d --- /dev/null +++ b/docs/articles/centrality_indices.html @@ -0,0 +1,256 @@ + + + + + + + +Centrality indices • netrankr + + + + + + +
+
+ + + +
+
+
+

Centrality indices

+ +
+ + + +
+

This vignette describes how to build different centrality indices on the basis of indirect relations as described in this vignette. Note, however, that the primary purpose of the netrankr package is not to provide a great variety of indices, but to offer alternative methods for centrality assessment. Consult the tutorial and this vignette, before starting trial-and-error usage of indices.

+
+
+

+Theoretical Background

+

A one-mode network can be described as a dyadic variable \(x\in \mathcal{W}^\mathcal{D}\), where \(\mathcal{W}\) is the value range of the network (in the simple case of unweighted networks \(\mathcal{W}=\{0,1\}\)) and \(\mathcal{D}=\mathcal{N}\times\mathcal{N}\) describes the dyadic domain of actors \(\mathcal{N}\).

+Observed presence or absence of ties (the value range is binary) is usually not the relation of interest for network analytic tasks. Instead, mostly implicitly, relations are transformed into a new set of indirect relations on the basis of the observed relations. As an example, consider (geodesic) distances in the underlying graph. While they are fairly easy to derive from an observed network of contacts, it is impossible for actors in a network to answer the question “How far away are you from others you are not connected with?”. We denote generic transformed networks from an observed network \(x\) as \(\tau(x)\).

+With this notion of indirect relations, we can express all centrality indices in a common framework as \[ +c_\tau(i)=\sum\limits_{t \in \mathcal{N}} \tau(x)_{it} +\] Degree and closeness centrality, for instance, can be obtained by setting \(\tau=id\) and \(\tau=dist\), respectively. Others need several additional specifications which can be found in Brandes (2016) or Schoch & Brandes (2016).
+With this framework, all centrality indices can be characterized as degree-like measures in a suitably transformed network \(\tau(x)\). To build specific indices, we follow the analytic pipeline for centrality assessment: \[ +\text{Observed network}\;(x) \longrightarrow +\text{transformation}\;(\tau(x)) \longrightarrow +\text{aggregation}\;(e.g. \sum_j \tau(x)_{ij}) +\]

+
+
+
+

+Building indices with the netrankr package

+
library(netrankr)
+library(igraph)
+library(magrittr)
+

The netrankr does, by design, not explicitly implement any centrality index. It does, however, provide a large set of components to create indices. Building an index based on an indirect relation, computed with indirect_relations(), is done with the function aggregate_positions().

+The usual workflow is as follows:
g %>% indirect_relations() %>% aggregate_positions()
+which is equivalent to aggregate_positions(indirect_relations(g)).
+The former, however, comes with enhanced readability and is in accordance with the proposed analytic pipeline (see above).

aggregate_position() has a parameter type which is used to choose an appropriate aggregation method. Commonly, this is simply the sum operation.

+
g <- graph.empty(n=11,directed = FALSE)
+g <- add_edges(g,c(1,11,2,4,3,5,3,11,4,8,5,9,5,11,6,7,6,8,
+                   6,10,6,11,7,9,7,10,7,11,8,9,8,10,9,10))
+V(g)$name <- 1:11
+
+#Degree
+g %>% 
+  indirect_relations(type="identity") %>% 
+  aggregate_positions(type="sum")
+#Closeness
+g %>% 
+  indirect_relations(type="geodesic") %>% 
+  aggregate_positions(type="invsum")
+#Betweenness Centrality
+g %>% 
+  indirect_relations(type="dependencies") %>% 
+  aggregate_positions(type="sum")
+#Eigenvector Centrality
+g %>% 
+  indirect_relations(type="walks",FUN=walks_limit_prop) %>% 
+  aggregate_positions(type="sum")
+

For closeness type="invsum" is used since traditional closeness is defined as \[ +c_c(i)=\frac{1}{\sum_t dist(i,t)}. +\] To obtain a slight variant of closeness, i.e. \[ +c_c(i)=\sum_t \frac{1}{dist(i,t)}, +\] the following code can be used:

+
#harmonic closeness
+g %>% 
+  indirect_relations(type="geodesic",FUN=dist_inv) %>% 
+  aggregate_positions(type="sum")
+

The distance based indices constitute one of the biggest groups of indices in the netrankr package.

+
#residual closeness (Dangalchev,2006)
+g %>% 
+  indirect_relations(type="geodesic",FUN=dist_2pow) %>% 
+  aggregate_positions(type="sum")
+
+#generalized closeness (Agneessens et al.,2017) (alpha>0)
+g %>% 
+  indirect_relations(type="geodesic",FUN=dist_dpow,alpha=2) %>% 
+  aggregate_positions(type="sum")
+
+#decay centrality (Jackson, 2010) (alpha in [0,1])
+g %>% 
+  indirect_relations(type="geodesic",FUN=dist_powd,alpha=0.7) %>% 
+  aggregate_positions(type="sum")
+
+#integration centrality (Valente & Foreman, 1998)
+dist_integration <- function(x){
+  x <- 1 - (x - 1)/max(x)
+}
+g %>% 
+  indirect_relations(type="geodesic",FUN=dist_integration) %>% 
+  aggregate_positions(type="sum")
+

Another large group of indices is based on counting walks

+
#subgraph centrality
+g %>% 
+  indirect_relations(type="walks",FUN=walks_exp) %>% 
+  aggregate_positions(type="self")
+#communicability centrality
+g %>% 
+  indirect_relations(type="walks",FUN=walks_exp) %>% 
+  aggregate_positions(type="sum")
+#odd subgraph centrality
+g %>% 
+  indirect_relations(type="walks",FUN=walks_exp_odd) %>% 
+  aggregate_positions(type="self")
+#even subgraph centrality
+g %>% 
+  indirect_relations(type="walks",FUN=walks_exp_even) %>% 
+  aggregate_positions(type="self")
+#katz status
+g %>% 
+  indirect_relations(type="walks",FUN=walks_attenuated) %>% 
+  aggregate_positions(type="sum")
+

Note: The analytic pipeline can of course be wrapped into a function.

+
degree_centrality <- function(g){
+  DC <- g %>% 
+    indirect_relations(type="identity") %>% 
+    aggregate_positions(type="sum")
+  return(DC)
+}
+
+
+
+ + + +
+ + +
+

Developed by David Schoch.

+
+ +
+

Site built with pkgdown.

+
+ +
+
+ + + diff --git a/docs/articles/index.html b/docs/articles/index.html new file mode 100644 index 0000000..805cf99 --- /dev/null +++ b/docs/articles/index.html @@ -0,0 +1,169 @@ + + + + + + + + +Articles • netrankr + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ +
+

Articles version 0.1.0

+
+ +
+
+
+

All vignettes

+

+ + +
+
+
+ +
+
+

Developed by David Schoch.

+
+ +
+

Site built with pkgdown.

+
+ +
+
+ + + diff --git a/docs/articles/indirect_relations.html b/docs/articles/indirect_relations.html new file mode 100644 index 0000000..23c3444 --- /dev/null +++ b/docs/articles/indirect_relations.html @@ -0,0 +1,197 @@ + + + + + + + +Indirect relations in networks • netrankr + + + + + + +
+
+ + + +
+
+
+

Indirect relations in networks

+ +
+ + + +
+

This vignette describes the importance of indirect relations on networks, how they are used in centrality indices and how they are implemented in the netrankr package.

+
+
+

+Theoretical Background

+

A one-mode network can be described as a dyadic variable \(x\in \mathcal{W}^\mathcal{D}\), where \(\mathcal{W}\) is the value range of the network (in the simple case of unweighted networks \(\mathcal{W}=\{0,1\}\)) and \(\mathcal{D}=\mathcal{N}\times\mathcal{N}\) describes the dyadic domain of actors \(\mathcal{N}\).

+Observed presence or absence of ties (the value range is binary) is usually not the relation of interest for network analytic tasks. Instead, mostly implicitly, relations are transformed into a new set of indirect relations on the basis of the observed relations. As an example, consider (geodesic) distances in the underlying graph. While they are fairly easy to derive from an observed network of contacts, it is impossible for actors in a network to answer the question “How far away are you from others you are not connected with?”. We denote generic transformed networks from an observed network \(x\) as \(\tau(x)\).

+With this notion of indirect relations, we can express all centrality indices in a common framework as \[ +c_\tau(i)=\sum\limits_{t \in \mathcal{N}} \tau(x)_{it} +\] Degree and closeness centrality, for instance, can be obtained by setting \(\tau=id\) and \(\tau=dist\), respectively. Others need several additional specifications which can be found in Brandes (2016) or Schoch & Brandes (2016).
+With this framework, all centrality indices can be characterized as degree-like measures in a suitably transformed network \(\tau(x)\).

+
+
+
+

+Indirect relations in the netrankr package

+
library(netrankr)
+library(igraph)
+

The netrankr package implements a great variety of indirect relations that are (or could be) used for centrality related considerations in a network. All indirect relations can be computed with the indirect_relations() function, by specifying the type parameter.

+
g <- graph.empty(n=11,directed = FALSE)
+g <- add_edges(g,c(1,11,2,4,3,5,3,11,4,8,5,9,5,11,6,7,6,8,
+                   6,10,6,11,7,9,7,10,7,11,8,9,8,10,9,10))
+V(g)$name <- 1:11
+
+#adjacency
+A <- indirect_relations(g,type="identity")
+#geodesic distances
+D <- indirect_relations(g,type="geodesic")
+#dyadic dependencies (as used in betweenness centrality)
+B <- indirect_relations(g,type="dependencies")
+#resistance distance (as used in information centrality)
+R <- indirect_relations(g,type="resistance")
+

The function takes an additional parameter FUN which passes an additional function to further specify the transformation. The main use is to obtain walk based indirect relations

+
#count the limit proportion of walks (used for eigenvector centrality)
+W <-  indirect_relations(g,type="walks",FUN=walks_limit_prop)
+#count the number of walks of arbitrary length between nodes, weighted by 
+#the inverse factorial of their length (used for subgraph centrality)
+S <-  indirect_relations(g,type="walks",FUN=walks_exp)
+

Additional parameters can also be passed to calculate parameterized versions of relations.

+
#Calculate dist(s,t)^-alpha
+D <- indirect_relations(g,type="geodesic",FUN=dist_dpow,alpha=2)
+

To view all predefined transformation functions type ?transform_relations. The predefined functions follow the naming scheme <relation>_<transformation>. The functions dist_ are thus only meaningful for type="geodesic" or type="resistance" and walks_ for type="walks". The predefined functions are not exhaustive and just constitute the most common transformations. It is, however, straightforward to pass your own transformation function.

+
dist_integration <- function(x){
+  x <- 1 - (x - 1)/max(x)
+}
+D <- indirect_relations(g,type="geodesic",FUN=dist_integration)
+

The function dist_integration() computes \[ +\tau(x)_{ij}=1-\frac{dist(i,j)-1}{max_{i,j}\; dist(i,j)} +\] which is used in the centrality index integration defined by Valente and Foreman (1998)

+
+
+
+ + + +
+ + +
+

Developed by David Schoch.

+
+ +
+

Site built with pkgdown.

+
+ +
+
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b/docs/articles/neighborhood_inclusion.html new file mode 100644 index 0000000..bafdd70 --- /dev/null +++ b/docs/articles/neighborhood_inclusion.html @@ -0,0 +1,259 @@ + + + + + + + +Neighborhood-inclusion in networks • netrankr + + + + + + +
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+ + + +
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+

Neighborhood-inclusion in networks

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+ + + +
+

This vignette describes the concept of neighborhood-inclusion, its connection with network centrality and gives some example use cases with the netrankr package. The partial ranking induced by neighborhood-inclusion can be used to assess partial centrality or compute probabilistic centrality.

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+
+

+Theoretical Background

+

In an undirected graph \(G=(V,E)\), the neighborhood of a node \(u \in V\) is defined as \[N(u)=\lbrace w : \lbrace u,w \rbrace \in E \rbrace\] and its closed neighborhood as \(N[v]=N(v) \cup \lbrace v \rbrace\). If the neighborhood of a node \(u\) is a subset of the closed neighborhood of a node \(v\), \(N(u)\subseteq N[v]\), we speak of neighborhood inclusion. This concept defines a dominance relation among nodes in a network. We say that \(u\) is dominated by \(v\) if \(N(u)\subseteq N[v]\). Neighborhood-inclusion induces a partial ranking on the vertices of a network. That is, (usually) some pairs of vertices are incomparable, such that neither \(N(u)\subseteq N[v]\) nor \(N(v)\subseteq N[u]\) holds. There is, however, a special graph class where all pairs are comparable (found in this vignette).

+

The importance of neighborhood-inclusion is given by the following result:

+

\[ +N(u)\subseteq N[v] \implies c(u)\leq c(v), +\] where \(c\) is a centrality index.

+

Very informally, if \(u\) is dominated by \(v\), then u is always less central than \(v\) no matter which centrality index is used. While this is the key result, this short description leaves out many theoretical considerations. These and more can be found in

+
+

Schoch, David & Brandes, Ulrik. (2016). Re-conceptualizing centrality in social networks. European Journal of Appplied Mathematics, 27(6), 971–985. (link)

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+

+Neighborhood-inclusion in the netrankr Package

+
library(netrankr)
+library(igraph)
+set.seed(1886) #for reproducibility
+

We work with the following simple graph.

+
g <- graph.empty(n=11,directed = FALSE)
+g <- add_edges(g,c(1,11,2,4,3,5,3,11,4,8,5,9,5,11,6,7,6,8,
+                   6,10,6,11,7,9,7,10,7,11,8,9,8,10,9,10))
+V(g)$name <- 1:11
+
+plot(g,
+     vertex.color="black",vertex.label.color="white", vertex.size=16,vertex.label.cex=0.75,
+     edge.color="black",
+     margin=0,asp=0.5)
+

+

We can compare neighborhoods manually with the neighborhood function of the igraph package. Note the mindist parameter to distinguish between open and closed neighborhood.

+
u <- 3
+v <- 5
+Nu <- neighborhood(g,order=1,nodes=u,mindist = 1)[[1]] #N(u) 
+Nv <- neighborhood(g,order=1,nodes=v,mindist = 0)[[1]] #N[v] 
+
+Nu
+
## + 2/11 vertices, named, from 727f78f:
+## [1] 5  11
+
Nv
+
## + 4/11 vertices, named, from 727f78f:
+## [1] 5  3  9  11
+

Although it is obvious that Nu is a subset of Nv, we can verify it with R.

+
all(Nu%in%Nv)
+
## [1] TRUE
+

Checking all pairs of nodes can efficiently be done with the neighborhood_inclusion() function from the netrankr package.

+
P <- neighborhood_inclusion(g)
+P
+
##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11]
+##  [1,]    0    0    1    0    1    1    1    0    0     0     1
+##  [2,]    0    0    0    1    0    0    0    1    0     0     0
+##  [3,]    0    0    0    0    1    0    0    0    0     0     1
+##  [4,]    0    0    0    0    0    0    0    0    0     0     0
+##  [5,]    0    0    0    0    0    0    0    0    0     0     0
+##  [6,]    0    0    0    0    0    0    0    0    0     0     0
+##  [7,]    0    0    0    0    0    0    0    0    0     0     0
+##  [8,]    0    0    0    0    0    0    0    0    0     0     0
+##  [9,]    0    0    0    0    0    0    0    0    0     0     0
+## [10,]    0    0    0    0    0    0    0    0    0     0     0
+## [11,]    0    0    0    0    0    0    0    0    0     0     0
+

If an entry P[u,v] is equal to one, we have \(N(u)\subseteq N[v]\).

+

The function dominance_graph() can alternatively be used to visualize the neighborhood inclusion as a directed graph.

+
g.dom <- dominance_graph(P)
+
+plot(g.dom,
+     vertex.color="black",vertex.label.color="white", vertex.size=16, vertex.label.cex=0.75,
+     edge.color="black", edge.arrow.size=0.5,margin=0,asp=0.5)
+

+
+

+Centrality and Neighborhood-inclusion

+

We start by calculating some standard measures of centrality found in the ìgraph package for our example network. Note that the netrankr package also implements a great variety of indices, but they need further specifications described in this vignette.

+
cent.df <- data.frame(
+  vertex=1:11,
+  degree=degree(g),
+  betweenness=betweenness(g),
+  closeness=closeness(g),
+  eigenvector=eigen_centrality(g)$vector,
+  subgraph=subgraph_centrality(g)
+)
+
+#rounding for better readability
+cent.df.rounded <- round(cent.df,4) 
+cent.df.rounded
+
##    vertex degree betweenness closeness eigenvector subgraph
+## 1       1      1      0.0000    0.0370      0.2260   1.8251
+## 2       2      1      0.0000    0.0294      0.0646   1.5954
+## 3       3      2      0.0000    0.0400      0.3786   3.1486
+## 4       4      2      9.0000    0.0400      0.2415   2.4231
+## 5       5      3      3.8333    0.0500      0.5709   4.3871
+## 6       6      4      9.8333    0.0588      0.9847   7.8073
+## 7       7      4      2.6667    0.0526      1.0000   7.9394
+## 8       8      4     16.3333    0.0556      0.8386   6.6728
+## 9       9      4      7.3333    0.0556      0.9114   7.0327
+## 10     10      4      1.3333    0.0526      0.9986   8.2421
+## 11     11      5     14.6667    0.0556      0.8450   7.3896
+

Notice how for each centrality index, different vertices are considered to be the most central node. The most central from degree to subgraph centrality are \(11\), \(8\), \(6\), \(7\) and \(10\). Note that only undominated vertices can achieve the highest score for any reasonable index. As soon as a vertex is dominated by at least one other, it will always be ranked below the dominator. We can check for undominated vertices simply by forming the row Sums in P.

+
which(rowSums(P)==0)
+
## [1]  4  5  6  7  8  9 10 11
+

8 nodes are undominated in the graph. It is thus entirely possible to find indices that would also rank \(4, 5\) and \(9\) on top.

+

Besides the top ranked nodes, we can check if the entire partial ranking P is preserved in each centrality ranking. If there exists a pair \(u\) and \(v\) and index \(c()\) such that \(N(u)\subseteq N[v]\) but \(c(v)>c(u)\), we do not consider \(c\) to be a valid index.

+

In our example, we considered vertex \(3\) and \(5\), where \(3\) was dominated by \(5\). It is easy to verify that all centrality scores of \(5\) are in fact greater than the ones of \(3\) by inspecting the respective rows in the table. To check all pairs, we use the function is_preserved. The function takes a partial ranking, as induced by neighborhood inclusion, and a score vector of a centrality index and checks if P[i,j]==1 & scores[i]>scores[j] is FALSE for all pairs i and j.

+
apply(cent.df[,2:6],2,function(x) is_preserved(P,x))
+
##      degree betweenness   closeness eigenvector    subgraph 
+##        TRUE        TRUE        TRUE        TRUE        TRUE
+

All considered indices preserve the neighborhood inclusion preorder on the example network.

+

NOTE: Preserving neighborhood inclusion on one network does not guarantee that an index preserves it on all networks. For more details refer to the paper cited in the first section.

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+ + +
+

Developed by David Schoch.

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+ +
+

Site built with pkgdown.

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+
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  • i70mLw>;6>DyELIL=T7s#Y|T2r&wpfG{M?im@#t?fc-)yZHS#K2 zT?xGYaWme~daS6Q$knxszZt|RXtvqpw(pOaIao97g1ctR-*gmU&n9a*qX_C@2C+YW z_1@6=XFCt#P0e2uqTQQ6mOYk_ZNs1#9zgd8ADe3jc+N+a>QRerQv5e+Z+Pr$`X3bU z4E87O3<<-e#g?80H`zlP2hV;uK$p1W6o<^ole@(CxuhI@$jHfTZs&E-?87CYml6}a zNzquH$igwIswk9CU$wI4i2xWpAIAL0?@Gy^ciKS*LlgPfX3fU>!xl_j!tro3pza#2 zb?vx!fDY)~#so$-Ab|CYrH;5T;LfXvsr|G|QC!p2&aE#$Z$#;QnN%zL%Mz+LfB3!c zRKLctne(O}EB5unV#t)H=tYo|BPm*^H<}3%j)Lffwpo#|h z7|iHamul*Km*H#YSsBnQWI!tv2 zE=3hv=~Jd>V3j%vG9S?lwsTUVw_W10c^VYf@i6Gjb$PWD64?6I+c*jT4!86j`oBvk zm0(jF`9Ysp*_Em;(%h+B{iTBWzk36Sx2Bll(`aOW44R>0T5-AACtu>%lyYS>ny+~$ zr}miE6;3qodaeZ@+6>g4PWDZx8G5uO+r2io+A_5^Zxd}1oz#ESH%b?byAS50G4})v zk`|hbBZ)wM + + + + + + +Partial Centrality • netrankr + + + + + + +
    +
    + + + +
    +
    +
    +

    Partial Centrality

    + +
    + + + +
    +

    This vignette describes some methods to analyse partial rankings as obtained from neighborhood-inclusion or, more general, positional dominance. More on the topic of partial rankings can be found in the following literature.

    +
    +

    Schoch, David. (2017). Centrality without Indices: Partial Rankings and Rank Probabilities in Networks. submitted

    +
    +
    +

    Patil, G.P. & Taillie, C. (2004). Multiple Indicators, partially ordered sets, and linear extensions: Multi-criterion ranking and prioritization. Environmental and Ecological Statistics, 11, 199-228 (link)

    +
    +
    +
    +

    +Rank intervals

    +
    library(netrankr)
+library(igraph)
+library(magrittr)
    +

    The function rank_intervals() is used to calculate the maximal and minimal possible rank for each node in any ranking that is in accordance with a given partial ranking.

    +
    g <- graph.empty(n=11,directed = FALSE)
+g <- add_edges(g,c(1,11,2,4,3,5,3,11,4,8,5,9,5,11,6,7,6,8,
+                   6,10,6,11,7,9,7,10,7,11,8,9,8,10,9,10))
+V(g)$name <- LETTERS[1:11]
+
+#neighborhood inclusion 
+P <- g %>% neighborhood_inclusion()
+
+#without %>% operator:
+# P <- neighborhood_inclusion(g)
+
+rank_intervals(P)
    +
    ##    min_rank max_rank mid_point
+## 1         1        6       3.5
+## 2         1        9       5.0
+## 3         2        9       5.5
+## 4         2       11       6.5
+## 5         3       11       7.0
+## 6         2       11       6.5
+## 7         2       11       6.5
+## 8         2       11       6.5
+## 9         1       11       6.0
+## 10        1       11       6.0
+## 11        3       11       7.0
    +

    The package uses the convention, that higher numerical ranks correspond to top ranked position. The lowest possible rank is thus 1. The column mid_point should not be confused with the expected rank of nodes, which is calculated with the function exact_rank_prob(). See this vignette for more details.

    +Rank intervals are useful to assess the ambiguity of ranking nodes. The bigger the intervals are, the more freedom exists, e.g. for centrality indices, to rank nodes differently.

    +The intervals can be visualized with the function plot_rank_intervals(). Note that the package ggplot2 is required to use the function properly. The function takes a partial ranking as input and not already calculated rank intervals. These are calculated internally.

    +
    plot_rank_intervals(P)
    +

    +

    Nodes are ordered according to the mid point for better readability. If the nodes of the input network are named, the parameter names can be set accordingly.

    +
    plot_rank_intervals(P,names=V(g)$name)
    +

    +

    The function can take a data frame of centrality scores as an additional parameter cent.df. The ranks of each node for each index are then plotted within each interval. Again, the higher the numerical rank the higher ranked the node is according to the index.

    +
    cent_scores <- data.frame(
+   degree=degree(g),
+   betweenness=round(betweenness(g),4),
+   closeness=round(closeness(g),4),
+   eigenvector=round(eigen_centrality(g)$vector,4))
+
+plot_rank_intervals(P,names=V(g)$name,cent.df = cent_scores)
    +

    +

    A small jitter effect is added to the points to reduce over-plotting.

    +Observe the inconsistency of betweenness for node \(C\). Betweenness centrality is, so far, the only index that does not strictly preserve neighborhood-inclusion. That is, while \[ +N(u)\subseteq N[v] \text{ and } N(v)\not\subseteq N[u] \implies c(u)<c(v) +\] holds for most indices, betweenness fails to fulfill this property.

    +The intervals reduce to single points for threshold graphs, since all nodes are pairwise comparable by neighborhood-inclusion.

    +
    set.seed(123)
+tg <- threshold_graph(20,0.2)
+
+#neighborhood inclusion 
+P <- tg %>% neighborhood_inclusion()
+
+#without %>% operator:
+# P <- neighborhood_inclusion(tg)
+plot_rank_intervals(P)
    +

    +

    The described betweenness inconsistancy is most evident for threshold graphs as shown in the rank intervals below.

    +
    cent_scores <- data.frame(
+   degree=degree(tg),
+   betweenness=round(betweenness(tg),4),
+   closeness=round(closeness(tg),4),
+   eigenvector=round(eigen_centrality(tg)$vector,4))
+
+
+plot_rank_intervals(P,cent.df=cent_scores)
    +

    +
    +
    +
    + + + +
    + + +
    +

    Developed by David Schoch.

    +
    + +
    +

    Site built with pkgdown.

    +
    + +
    +
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z2Ub!y?6*(NcVX{;Oo$d8oc-c{oZRW|Wzx~!c}*1QH$Lq!2zSWZg6@zq6o=Rw2WL$_ zdvi>N*6%9__VozBfsAY+yVfuG27Lj&3N6;kso7397cC2%F!C-HYOVm3b{pb@99Qf%^N;{qT@)TDHD(gDX=qtW)&1|#+8BS)*1 z$4ZgIV}qm(C0`HQR|TWX+8?5+l<6i!LUMf9LcBzNElkYK4_Dvyc-C%0Aeo^zkm`YL z4yYD1={7{S(8-@xpSG_+Z$t-@K$5Wgllb?O%vqb*A(8aaMArLVDqFJ1vbDsqZkbJq zQac(k4_1h70Y9&e=+^KWqn+)}>9SriZF`!<^mN_4@fLRWJPD_Xp**o2;32GckJVI8an zY5AaIl2%;Dlc#ND85MrwC;!i5=kofoi@yq}77dmVO + + + + + + +Positional dominance in networks • netrankr + + + + + + +
    +
    + + + +
    +
    +
    +

    Positional dominance in networks

    + +
    + + + +
    +

    This vignette describes the concept of positional dominance, the generalization of neighborhood-inclusion for arbitrary network and attribute data. Additionally, some use cases with the netrankr package are given. The partial ranking induced by positional dominance can be used to assess partial centrality or compute probabilistic centrality.

    +
    +
    +

    +Theoretical Background

    +

    A network can be described as a dyadic variable \(x\in \mathcal{W}^\mathcal{D}\), where \(\mathcal{W}\) is the value range of the network (in the simple case of unweighted networks \(\mathcal{W}=\{0,1\}\)) and \(\mathcal{D}=\mathcal{N}\times\mathcal{A}\) describes the dyadic domain of actors \(\mathcal{N}\) and affiliations \(\mathcal{A}\). If \(\mathcal{A}\neq\mathcal{N}\), we obtain a two-mode network and if \(\mathcal{A}=\mathcal{N}\) a one-mode network consisting of relations among actors.


    Definition

    +

    Let \(x\in \mathcal{W}^\mathcal{D}\) be a network and \(i,j \in \mathcal{N}\). We say that \(i\) is dominated by \(j\) under the total homogeneity assumption, denoted by \(i \leq j\) if \[ +x_{it}\leq x_{jt} \quad \forall t \in \mathcal{N}. +\] If there exists a permutation \(\pi: \mathcal{N} \to \mathcal{N}\) such that \[ +x_{it}\leq x_{j\pi(t)} \quad \forall t \in \mathcal{N}, +\] we say that \(i\) is dominated by \(j\) under the total heterogeneity assumption, denoted by \(i ⪯ j\).
    +It holds that \(i\leq j \implies i ⪯ j\) but not vice versa.


    +More about the positional dominance and the positional approach to network analysis can be found in

    +
    +

    Brandes, Ulrik. (2016). Network Positions. Methodological Innovations, 9, 2059799116630650. (link)

    +
    +
    +
    +
    +

    +Positional Dominance in the netrankr Package

    +
    library(netrankr)
+library(igraph)
+library(magrittr)
+set.seed(1886) #for reproducibility
    +

    The function positional_dominance can be used to check both, dominance under homogeneity and heterogeneity. In accordance with the analytic pipeline of centrality (consult the tutorial REFREF) we use the %>% operator from the magrittr package.

    +
    g <- graph.empty(n=11,directed = FALSE)
+g <- add_edges(g,c(1,11,2,4,3,5,3,11,4,8,5,9,5,11,6,7,6,8,
+                   6,10,6,11,7,9,7,10,7,11,8,9,8,10,9,10))
+V(g)$name <- 1:11
+
+#neighborhood inclusion can be expressed with the analytic pipeline
+D <- g %>% indirect_relations(type="identity") %>% positional_dominance()
+
+#without %>% operator:
+# rel <- indirect_relations(g,type="identity")
+# D <- positional_dominance(rel)
+
+#check if identical to neighborhood-inclusion
+identical(D,neighborhood_inclusion(g))
    +
    ## [1] TRUE
    +

    More on the indirect_relations() function can be found in this vignette.

    +

    The map parameter of positional_dominance allows to distinguish between dominance under total heterogeneity (map=FALSE) and total homogeneity (map=TRUE). In the later case, all relations can be ordered non-decreasingly (or non-increasingly if the relation describes costs, such as distances) and afterwards checked front to back. Dominance under total homogeneity yields a ranking, if the relation is binary (e.g. adjacent or not).

    +
    D <- g %>% 
+  indirect_relations(type="identity") %>% 
+  positional_dominance(map=TRUE)
+
+comparable_pairs(D)
    +
    ## [1] 1
    +

    For cost variables like geodesic distances, the benefit parameter is set to FALSE.

    +
    D1 <- g %>% 
+  indirect_relations(type="geodesic") %>% 
+  positional_dominance(map=FALSE,benefit=FALSE)
    +

    From the definition given in the first section, it is clear that there are always at least as many comparable pairs under the total homogeneity assumption as under total heterogeneity.

    +
    D1 <- g %>% 
+  indirect_relations(type="geodesic") %>% 
+  positional_dominance(map=FALSE,benefit=FALSE)
+
+D2 <- g %>% 
+  indirect_relations(type="geodesic") %>% 
+  positional_dominance(map=TRUE,benefit=FALSE)
+
+c("heterogeneity"=comparable_pairs(D1),
+  "homogeneity"=comparable_pairs(D2))
    +
    ## heterogeneity   homogeneity 
+##     0.1636364     0.8727273
    +

    Additionally, all dominance relations from the heterogeneity assumption are preserved under total homogeneity. (Note: \(A\implies B\) is equivalent to \(\neg A \lor B\))

    +
    all(D1!=1 | D2==1)
    +
    ## [1] TRUE
    +
    +
    +
    + + + +
    + + +
    +

    Developed by David Schoch.

    +
    + +
    +

    Site built with pkgdown.

    +
    + +
    +
    + + + diff --git a/docs/articles/probabilistic_cent.html b/docs/articles/probabilistic_cent.html new file mode 100644 index 0000000..f522b6f --- /dev/null +++ b/docs/articles/probabilistic_cent.html @@ -0,0 +1,266 @@ + + + + + + + +Probabilistic Centrality • netrankr + + + + + + +
    +
    + + + +
    +
    +
    +

    Probabilistic Centrality

    + +
    + + + +
    +

    This vignette describes methods to analyse all possible centrality rankings of a network at once. To do so, a partial rankings as computed from neighborhood-inclusion or, more general, positional dominance is needed. In this vignette we focus on neighborhood-inclusion but note that all considered methods are readily applicable for positional dominance. For more examples consult the tutorial.

    +
    +
    +

    +Theoretical Background

    +

    Neighborhood-inclusion or induces a partial ranking on the vertices of a graph \(G=(V,E)\). We write \(u\leq v\) if \(N(u)\subseteq N[v]\) holds for two vertices \(u,v \in V\). From the fact that \[ +u\leq v \implies c(u) \leq c(v) +\] holds for any centrality index \(c:V\to \mathbb{R}\), we can characterize the set of all possible centrality based node rankings. Namely as the set of rankings that extend the partial ranking “\(\leq\)” to a (complete) ranking.

    +A node ranking can be defined as a mapping \[rk: V \to \{1,\ldots,n\},\] where we use the convention that \(u\) is the top ranked node if \(rk(u)=n\) and the bottom ranked one if \(rk(u)=1\). The set of all possible rankings can then be characterized as \[ +\mathcal{R}(\leq)=\{rk:V \to \{1,\ldots,n\}\; : \; u\leq v \implies rk(u)\leq rk(v)\}. +\] This set contains all rankings that could be obtained with a centrality index.

    +Once \(\mathcal{R}(\leq)\) is calculated, it can be used for a probabilistic assessment of centrality, analyzing all possible rankings at once. Examples include relative rank probabilities (How likely is it, that a node \(u\) is more central than another node \(v\)?) or expected ranks (How central do we expect a node \(u\) to be).

    +It most be noted though, that deriving the set \(\mathcal{R}(\leq)\) quickly becomes infeasible for larger networks, and one has to resort to approximation methods. These and more theoretical details can be found in

    +
    +

    Schoch, David. (2017). Centrality without Indices: Partial Rankings and Rank Probabilities in Networks. submitted

    +
    +
    +
    +
    +

    +Exact Probabilities in the netrankr Package

    +
    library(netrankr)
+library(igraph)
+library(magrittr)
    +

    Before calculating any probabilities consider the following example graph and the rankings induced by various centrality indices, shown as rank intervals (consult this vignette for details).

    +
    g <- graph.empty(n=11,directed = FALSE)
+g <- add_edges(g,c(1,11,2,4,3,5,3,11,4,8,5,9,5,11,6,7,6,8,
+                   6,10,6,11,7,9,7,10,7,11,8,9,8,10,9,10))
+V(g)$name <- LETTERS[1:11]
+
+#neighborhood inclusion 
+P <- g %>% neighborhood_inclusion()
+
+#without %>% operator:
+# P <- neighborhood_inclusion(g)
+
+cent_scores <- data.frame(
+   degree=degree(g),
+   betweenness=round(betweenness(g),4),
+   closeness=round(closeness(g),4),
+   eigenvector=round(eigen_centrality(g)$vector,4),
+   subgraph=round(subgraph_centrality(g),4))
+
+plot_rank_intervals(P,cent.df = cent_scores)
    +

    +

    Notice how all five centrality rank a different vertex as the most central one.

    +In the following subsections the output of the function exact_rank_probabilities() are described which may help to circumvent the potential arbitrariness of index induced rankings. But first, let us briefly look at all the return values.

    +
    res <- exact_rank_prob(P)
+str(res)
    +
    ## List of 7
+##  $ lin.ext      : num 739200
+##  $ names        : chr [1:11] "1" "2" "3" "4" ...
+##  $ mse          : int [1:11] 1 2 3 4 5 6 7 8 9 10 ...
+##  $ rank.prob    : num [1:11, 1:11] 0.545 0.273 0 0 0 ...
+##  $ relative.rank: num [1:11, 1:11] 0 0.3333 0 0.0476 0 ...
+##  $ expected.rank: num [1:11] 1.71 3 4.29 7.5 8.14 ...
+##  $ rank.spread  : num [1:11] 0.958 1.897 1.725 2.54 2.16 ...
    +

    The return value lin.ext gives the number of possible rankings that are in accordance with the partial ranking P. The names vector returns the names of nodes if they were supplied with the names parameter. Otherwise, node ids are returned as a character vector. The vector mse returns the equivalence classes of P. Nodes \(u\) and \(v\) are equivalent if \(N(u)\subseteq N[v]\) and \(N(v)\subseteq N[u]\) holds. The remaining return values are discussed in the following.

    +
    +

    +Rank Probabilities

    +

    Instead of insisting on fixed ranks of nodes as given by indices, we can use rank probabilities to assess the likelihood of certain rank. Formally, rank probabilities are simply defined as \[ +P(rk(u)=k)=\frac{\lvert \{rk \in \mathcal{R}(\leq) \; : \; rk(u)=k\} \rvert}{\lvert \mathcal{R}(\leq) \rvert}. +\] Rank probabilities are given by the return value rank.prob of the exact_rank_prob() function.

    +
    rp <- round(res$rank.prob,2)
+rp
    +
    ##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11]
+##  [1,] 0.55 0.27 0.12 0.05 0.01 0.00 0.00 0.00 0.00  0.00  0.00
+##  [2,] 0.27 0.22 0.17 0.13 0.09 0.06 0.04 0.02 0.01  0.00  0.00
+##  [3,] 0.00 0.16 0.22 0.21 0.17 0.12 0.07 0.04 0.01  0.00  0.00
+##  [4,] 0.00 0.03 0.05 0.07 0.09 0.11 0.12 0.13 0.13  0.14  0.14
+##  [5,] 0.00 0.00 0.02 0.05 0.08 0.10 0.13 0.15 0.16  0.16  0.16
+##  [6,] 0.00 0.05 0.08 0.10 0.11 0.11 0.11 0.11 0.11  0.11  0.11
+##  [7,] 0.00 0.05 0.08 0.10 0.11 0.11 0.11 0.11 0.11  0.11  0.11
+##  [8,] 0.00 0.03 0.05 0.07 0.09 0.11 0.12 0.13 0.13  0.14  0.14
+##  [9,] 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09  0.09  0.09
+## [10,] 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09  0.09  0.09
+## [11,] 0.00 0.00 0.02 0.05 0.08 0.10 0.13 0.15 0.16  0.16  0.16
    +

    Entries rp[u,k] correspond to \(P(rk(u)=k)\).

    +The most interesting probabilities are certainly \(P(rk(u)=n)\), that is how likely is it for a node to be the most central.

    +
    rp[,11]
    +
    ##  [1] 0.00 0.00 0.00 0.14 0.16 0.11 0.11 0.14 0.09 0.09 0.16
    +

    Recall from the previous section that we found five indices that ranked \(6,7,8,10\) and \(11\) on top. The probability tell us now, how likely it is to find an index that rank these nodes on top. In this case, node \(11\) has the highest probability to be the most central node.

    +
    +
    +

    +Relative Rank Probabilities

    +

    In some cases, we might not necessarily be interested in a complete ranking of nodes, but only in the relative position of a subset of nodes. This idea leads to relative rank probabilities, that is formally defined as \[ +P(rk(u)\leq rk(v))=\frac{\lvert \{rk \in \mathcal{R}(\leq) \; : \; rk(u)\leq rk(v)\} \rvert}{\lvert \mathcal{R}(\leq) \rvert}. +\] Relative rank probabilities are given by the return value relative.rank of the exact_rank_prob() function.

    +
    rrp <- round(res$relative.rank,2)
+rrp
    +
    ##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11]
+##  [1,] 0.00 0.67 1.00 0.95 1.00 1.00 1.00 0.95 0.86  0.86  1.00
+##  [2,] 0.33 0.00 0.67 1.00 0.92 0.83 0.83 1.00 0.75  0.75  0.92
+##  [3,] 0.00 0.33 0.00 0.80 1.00 0.75 0.75 0.80 0.64  0.64  1.00
+##  [4,] 0.05 0.00 0.20 0.00 0.56 0.44 0.44 0.50 0.38  0.38  0.56
+##  [5,] 0.00 0.08 0.00 0.44 0.00 0.38 0.38 0.44 0.32  0.32  0.50
+##  [6,] 0.00 0.17 0.25 0.56 0.62 0.00 0.50 0.56 0.43  0.43  0.62
+##  [7,] 0.00 0.17 0.25 0.56 0.62 0.50 0.00 0.56 0.43  0.43  0.62
+##  [8,] 0.05 0.00 0.20 0.50 0.56 0.44 0.44 0.00 0.38  0.38  0.56
+##  [9,] 0.14 0.25 0.36 0.62 0.68 0.57 0.57 0.62 0.00  0.50  0.68
+## [10,] 0.14 0.25 0.36 0.62 0.68 0.57 0.57 0.62 0.50  0.00  0.68
+## [11,] 0.00 0.08 0.00 0.44 0.50 0.37 0.37 0.44 0.32  0.32  0.00
    +

    Entries rrp[u,v] correspond to \(P(rk(u)\leq rk(v))\).

    +The more a value rrp[u,v] deviates from \(0.5\) towards \(1\), the more confidence we gain that a node \(v\) is more central than a node \(u\).

    +
    +
    +

    +Expected Ranks

    +

    The expected rank of a node in centrality rankings is defined as the expected value of the rank probability distribution. That is, \[ +\rho(u)=\sum_{k=1}^n k\cdot P(rk(u)=k). +\] Expected ranks are given by the return value expected.rank of the exact_rank_prob() function.

    +
    ex_rk <- round(res$expected.rank,2)
+ex_rk
    +
    ##  [1] 1.71 3.00 4.29 7.50 8.14 6.86 6.86 7.50 6.00 6.00 8.14
    +

    As a reminder, the higher the numeric rank, the more central a node is. In this case, node \(11\) has the highest expected rank in any centrality ranking.

    +
    +
    +
    +
    + + + +
    + + +
    +

    Developed by David Schoch.

    +
    + +
    +

    Site built with pkgdown.

    +
    + +
    +
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z{{B4;PYgiJcy&FjX+?NO?8t-F(}2}{zJ9Hd_awk_M9Ak=^jo)rCCo(PfM5_N@b}XWCjKe0&rB{V?cTwc&-8f*n0=kKyh=DB75ZME&=I7&c0~oiJNnckdoN2p^bV1YG1kCg56@C+Fg)G-BU0hZ{ zml1P~AroXfCk;MWtH73u7bnK6K^0&ObQPBAqXGiqP^~~M*tT0#L_`-f8xD52dmhIM z4b28MLJI&-NBdwh(l6`?mE1JW@tNqj&2K!A6BN`03i;)_uk&qI8jmHht){r?jD-%df%+J@^!I~jKS S%{LK8M_x|pe2VN%xBmjQ`IbQd literal 0 HcmV?d00001 diff --git a/docs/articles/threshold_graph.html b/docs/articles/threshold_graph.html new file mode 100644 index 0000000..242d998 --- /dev/null +++ b/docs/articles/threshold_graph.html @@ -0,0 +1,267 @@ + + + + + + + +Uniquely ranked graphs • netrankr + + + + + + +

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    + + + +
    +
    +
    +

    Uniquely ranked graphs

    + +
    + + + +
    +

    This vignette introduces threshold graphs, a class of graphs with a unique centrality ranking and relevant functions from the netrankr package to work with this class of graphs.

    +
    +
    +

    +Theoretical Background

    +

    A threshold graph is a graph, where all nodes are pairwise comparable by neighborhood inclusion. Formally, \[ +\forall u,v \in V: N(u) \subseteq N[v] \; \lor \; N(v) \subseteq N[u]. +\]

    +

    According to this vignette, it is thus clear that all centrality indices induce the same ranking on a threshold graph. More technical details on threshold graphs and results related to centrality can be found in

    +
    +

    Schoch, David & Valente, Thomas W., & Brandes, Ulrik. (2017). Correlations among centrality indices and a class of uniquely ranked graphs. Social Networks, 50, 46-54.(link)

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    +
    +
    +

    +Uniquely Ranked Graphs in the netrankr Package

    +
    library(netrankr)
+library(igraph)
+set.seed(1886) #for reproducibility
    +

    Threshold graphs on \(n\) vertices can be constructed iteratively with a sequence of \(0\)’s and \(1\)’s. For each \(0\), an isolated vertex is inserted and for each \(1\) a vertex that connects to all previously inserted one’s. This iterative process is implemented in the threshold_graph function. The parameter n is used to set the desired number of vertices. The parameter p is the probability that a dominated vertex is inserted in each step. This parameter roughly equates to the density of the network.

    +
     g1 <- threshold_graph(500,0.4)
+ g2 <- threshold_graph(500,0.05)
+ 
+ c(round(graph.density(g1),2), round(graph.density(g2),2))
    +
    ## [1] 0.41 0.03
    +

    The class of threshold graphs includes various well-known graphs, for instance star shaped and complete networks. This graphs can be constructed with p=0 and p=1 respectively.

    +
    star <- threshold_graph(6,0) 
+complete <- threshold_graph(6,1)
+plot(star,vertex.label=NA,vertex.color="black")
+plot(complete,vertex.label=NA,vertex.color="black")
    +

    +

    To check that all pairs are comparable by neighborhood inclusion, we can use the function comparable_pairs. The function computes the density of the underlying undirected graph induced by the neighborhood-inclusion relation.

    +
    g <- threshold_graph(10,0.4)
+P <- neighborhood_inclusion(g)
+comparable_pairs(P)
    +
    ## [1] 1
    +
    +
    +

    +Correlation and Threshold Graphs

    +

    We construct a random threshold graph and calculate some standard measures of centrality that are included in the igraph package.

    +
    g <- threshold_graph(100,0.1)
+
+cent.df <- data.frame(
+  degree=degree(g),
+  betweenness=betweenness(g),
+  closeness=closeness(g),
+  eigenvector=round(eigen_centrality(g)$vector,8),
+  subgraph=subgraph_centrality(g)
+)
    +

    We expect, that all indices are perfectly rank correlated since all pairs of nodes are comparable by neighborhood-inclusion.

    +
    cor.mat <- cor(round(cent.df,8),method="kendall")
+cor.mat <- round(cor.mat,2)
+cor.mat
    +
    ##             degree betweenness closeness eigenvector subgraph
+## degree        1.00        0.52      1.00        1.00     0.96
+## betweenness   0.52        1.00      0.52        0.52     0.50
+## closeness     1.00        0.52      1.00        1.00     0.96
+## eigenvector   1.00        0.52      1.00        1.00     0.96
+## subgraph      0.96        0.50      0.96        0.96     1.00
    +

    We, however, obtain correlations that are not equal to one. This is due to the definition of Kendall’s (tie corrected) \(\tau\). Before going into detail, consider the following cases which can arise when comparing two scores of indices x and y.

    +
      +
    • concordant: x[i]>x[j] & y[i]>y[j] or x[i]<x[j] & y[i]<y[j] +
      • +
    • discordant: x[i]>x[j] & y[i]<y[j] or x[i]>x[j] & y[i]<y[j] +
      • +
    • tied: x[i]=x[j] & y[i]=y[j] +
      • +
    • left/right ties: x[i]=x[j] & y[i]!=y[j] or x[i]!=x[j] & y[i]=y[j] +
      • +
    +

    Kendall’s \(\tau\) considers left and right ties as correlation reducing. That is if two vertices are tied in one ranking, but not the other, the correlations is weakened. Left and right ties are, however, not forbidden according to the neighborhood inclusion property. The only forbidden case are discordant pairs. That is, \(N(u)\subseteq N[v]\) can not result in \(c(u)>c(v)\) but it may result in \(c(u)=c(v)\). Also, one can argue that left and right ties distinguish between fine/coarse grained indices.

    +

    netrankr comes with a function called compare_ranks which calculates all occurrences of the above cases. Simply counting the cases instead of aggregating them will help circumvent the problem of possibly misinterpreting correlation measures.

    +
    comp <- compare_ranks(cent.df$degree,cent.df$betweenness)
+unlist(comp)
    +
    ## concordant discordant       ties       left      right 
+##       1209          0        464          0       3277
    +

    Notice that there is a high number of right ties which influences the correlation if measured with Kendall’s \(\tau\). However, there do not exist any discordant pairs for any pair of indices.

    +
    dis.pairs <- matrix(0,5,5)
+dis.pairs[1,] <- apply(cent.df,2,
+                       function(x)compare_ranks(cent.df$degree,x)$discordant)
+dis.pairs[2,] <- apply(cent.df,2,
+                       function(x)compare_ranks(cent.df$betweenness,x)$discordant)
+dis.pairs[3,] <- apply(cent.df,2,
+                       function(x)compare_ranks(cent.df$closeness,x)$discordant)
+dis.pairs[4,] <- apply(cent.df,2,
+                       function(x)compare_ranks(cent.df$eigenvector,x)$discordant)
+dis.pairs[5,] <- apply(cent.df,2,
+                       function(x)compare_ranks(cent.df$subgraph,x)$discordant)
+dis.pairs
    +
    ##      [,1] [,2] [,3] [,4] [,5]
+## [1,]    0    0    0    0    0
+## [2,]    0    0    0    0    0
+## [3,]    0    0    0    0    0
+## [4,]    0    0    0    0    0
+## [5,]    0    0    0    0    0
    +

    Although Kendall’s \(\tau\) suggests that the correlations among indices can be low, we see that there do not exist any discordant pairs on threshold graphs.

    +
    +
    +

    +Distances from a threshold graph

    +

    As it is always the case with artificial graph structures, it is rather unlikely to encounter threshold graphs in the wild. The best we can hope for is to be close to a threshold graph. This is based on the intuition that the closer a graph is to be a threshold graph, the more of its properties resemble one. The closer we are, the more correlated we assume centrality indices to be. The further away we are, the more disagreement we will find among indices. The problematic point is: how do we define being close to a threshold graph. An in depth discussion of possible measures can be found in the paper mentioned at the beginning of this vignette.

    +

    netrankr implements one function that can be used to assess the distance of arbitrary graphs to threshold graphs. The so called majorization gap operates solely on the degree sequence and determines the number of entries that have to be changed in order to obtain the degree sequence of a threshold graph. Changing can, however, not be done arbitrarily. The only allowed operation is to lower the degree of one vertex and simultaneously increase the degree of another. For threshold graphs, this measure is obviously zero.

    +
    tg <- threshold_graph(200,0.2)
+majorization_gap(g)
    +
    ## [1] 0
    +

    By default, majorization_gap is normalized by the number of edges.

    +
    g <- graph.empty(n=11,directed = FALSE)
+g <- add_edges(g,c(1,11,2,4,3,5,3,11,4,8,5,9,5,11,6,7,6,8,
+                   6,10,6,11,7,9,7,10,7,11,8,9,8,10,9,10))
+majorization_gap(g)
    +
    ## [1] 0.3529412
    +

    In this example, around 35% of all entries have to be changed in order to obtain a threshold graph. The normalization is done to compare the majorization gap across networks with different sizes. To obtain the raw number of changes, set norm=FALSE.

    +
    majorization_gap(g,norm = FALSE)
    +
    ## [1] 6
    +

    The majorization gap serves as an indicator for how much variance we can expect in the rankings of different centrality indices. The lower it is, the closer we are to a threshold graph where only one ranking is possible. The further away we are, the more degrees of freedom exist to rank nodes differently and we will generally observe lower correlations. For more details, again, refer to the mentioned paper at the beginning.

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    +
    +
    + + + +
    + + +
    +

    Developed by David Schoch.

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    + +
    +

    Site built with pkgdown.

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    +
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    Use Case: Florentine Families

    + +
    + + + +
    +

    This vignette describes a typical use case of the netrankr packages. It contrasts the usual centrality analysis based on indices with the dominance based assessment. It is advisable to read the other vignettes before going through this example.

    +
    +
    library(igraph)
+library(netrankr)
+library(magrittr)
+library(ggplot2)
    +
    +

    +Data

    +

    For this tutorial, we use the famous florentine families dataset (Padget & Ansell, 1993). The marriage links of families together with the wealth attribute are included in the netrankr package.

    +
    data("florentine_m")
+#Delete Pucci family (isolated)
+florentine_m <- delete_vertices(florentine_m,which(degree(florentine_m)==0))
+
+#plot the graph (label size proportional to wealth)
+set.seed(111)
+plot(florentine_m,
+     vertex.label.cex=V(florentine_m)$wealth*0.01, 
+     vertex.label.color="black",
+     vertex.color="white",
+     vertex.frame.color="gray")
    +

    +

    We use this dataset below to illustrate how a dominance based assessment of centrality offers an alternative approach to centrality in two ways:

    +
      +
    • Are the Medici universally the most central family?
      • +
    • Using centrality as explanatory variable (Can centrality explain the wealth attribute?)
      • +
    +
    +
    +
    +

    +Most central family (Index approach)

    +

    The network is often used to benchmark new centrality indices. The premise is that the Medici should always emerge as one of the most central once (if not the most central).

    +

    We start by applying some of the standard centrality indices given in the igraph package.

    +
    cent.df <- data.frame(
+  degree = degree(florentine_m),
+  betweenness = betweenness(florentine_m),
+  closeness = closeness(florentine_m),
+  eigenvector = eigen_centrality(florentine_m)$vector,
+  subgraph = subgraph_centrality(florentine_m))
+
+# most central family according to the 5 indices
+V(florentine_m)$name[apply(cent.df,2,which.max)]
    +
    ## [1] "Medici" "Medici" "Medici" "Medici" "Medici"
    +

    In all cases, the Medici are considered to be the most central family. However, it is possible to find indices that rank other families on top. An example is odd subgraph centrality, which can be assembled with the netrankr package.

    +
    #odd subgraph centrality
+sc_odd <- florentine_m %>% 
+  indirect_relations(type = "walks",FUN = walks_exp_odd) %>% 
+  aggregate_positions(type = "self")
+
+#family with highest score 
+V(florentine_m)$name[which.max(sc_odd)]
    +
    ## [1] "Strozzi"
    +

    In this example, the Strozzi family are considered to be the most central family and the Medici are ranked third.

    +

    Although we have found \(5\) indices that consider the Medici the most central family, we can not guarantee, that there do not exist hundreds (or thousands?) of indices that would give an entirely different result.

    +
    +
    +
    +

    +Most central family (Dominance approach)

    +

    We start by calculating the neighborhood-inclusion preorder, the most general requirement for any centrality index.

    +
    P <- neighborhood_inclusion(florentine_m)
    +

    With the function comparable_pairs() we can assess how many pairs of families are already ordered, before applying any index.

    +
    comparable_pairs(P)
    +
    ## [1] 0.1523809
    +

    Only around 15% of pairs of families are comparable, leaving 85% of pairs of families that could be ordered (basically) arbitrarily.

    +

    If we want to visually assess the dominance relations we can use the function dominance_graph().

    +
    d <- dominance_graph(P)
+V(d)$name <- V(florentine_m)$name
+set.seed(113)
+plot(d,vertex.label.color="black",
+     vertex.color="white",
+     vertex.frame.color="gray",
+     edge.arrow.size=0.5)
    +

    +

    The Castellan family neither dominates nor is dominated by any other family. This means, that we can find indices that potentially rank them on top or on the bottom, or anything in between.

    +

    To better assess the potential ranks of nodes, we can plot the rank intervals with plot_rank_intervals()

    +
    plot_rank_intervals(P,names=V(florentine_m)$name)
    +

    +

    Observe how big the intervals are, indicating that there is ample scope to rank the families differently. These intervals, however, only give us a rough estimate of this arbitrariness and not any rank probabilities. To get all exact probabilities, we use the function exact_rank_prob().

    +
    res <- exact_rank_prob(P,names=V(florentine_m)$name)
    +

    There are 3,972,630,480 different possibilities to rank the families! (the value is stored in res$lin.ext. ). This means that theoretically, we can find almost 4 Billion indices that rank the families differently.

    +

    The rank probabilities of families can be found in res$rank.prob. They are returned as a matrix where rows are families and columns are ranks. That is, an entry in row \(u\) and column \(k\) gives the probability that \(u\) has rank \(k\) (larger \(k\) indicate higher ranks) Mostly, you will be interested in the probability to be the most central node of a network. Below, we calculate these probability for all families and return the one’s that have a higher probability than \(0.1\).

    +
    top_rank_prob <- res$rank.prob[,15]
+names(top_rank_prob) <- V(florentine_m)$name
+round(top_rank_prob[top_rank_prob>0.1],3)
    +
    ##  Albizzi Guadagni   Medici Salviati  Strozzi 
+##    0.109    0.106    0.123    0.111    0.133
    +

    The Strozzi family, with \(0.13\), has the highest probability to be top ranked, followed by the Medici with \(0.12\).

    +

    If we are only interested in a subset of nodes, in our case maybe the Strozzi and Medici, we can assess the relative rank probabilities in res$relative.rank. Again, probabilities are returned as matrix objects, where an entry in row \(u\) and column \(v\) gives the probability that \(u\) is ranked below \(v\). Below we calculate this probability for the Strozzi and Medici.

    +
    id_strozzi <- which(V(florentine_m)$name=="Strozzi") 
+id_medici  <- which(V(florentine_m)$name=="Medici")
+res$relative.rank[id_strozzi,id_medici]
    +
    ## [1] 0.5219845
    +

    The probability that the Strozzi are less central than the Medici is 0.52 and thus very close to a “fifty-fifty” chance.

    +

    The last result of interest returned by exact_rank_prob() are the expected ranks in res$expected.rank. The expected ranks, as the name indicates, returns the ranks that we expect families to have in a centrality ranking.

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    NameExpected
    Medici11.09
    Albizzi10.72
    Strozzi10.67
    Salviati10.60
    Guadagni10.51
    Tornabuon10.11
    Bischeri9.64
    Barbadori9.37
    Ridolfi9.37
    Castellan8.00
    Peruzzi5.33
    Pazzi4.54
    Ginori4.01
    Lambertes3.28
    Acciaiuol2.74
    +

    Although the Strozzi have a higher probability to be the most central family, over all we still expect the Medici to be the most central.

    +

    This very general assessment gives us a general idea of the scope of potential centrality analyses. The more possible rankings we have (as in this case!) the more unreliable an index driven approach can be. We will explore this in more detail in the following section.

    +
    +
    +
    +

    +Centrality as explanatory variable (Index approach)

    +

    Usually, we are not simply interested in a ranking of nodes, but we rather would like to use centrality to explain certain node attributes. In our case, we might be interested in the question: “can an index explain the wealth of families?”, or if we already have a more concrete idea “can proximity to other families explain the wealth attribute?”

    +

    “Proximity” can be translated to the graph-theoretic concept of geodesic distances, such that closeness centrality would be an adequate candidate as an index. We here use the pipeline approach of the netrankr package instead of the closeness() function of igraph. The reasons will become evident in the next section.

    +
    #Closeness
+c_C <- florentine_m %>% 
+  indirect_relations(type="geodesic") %>% 
+  aggregate_positions(type="invsum")
+
+cor(c_C,V(florentine_m)$wealth,method="kendall")
    +
    ## [1] 0.08823953
    +

    The correlation between closeness and wealth (0.0882) is far to low to constitute that “proximity” is related to wealth. However, there exist various other indices, that are based on the geodesic distances in a graph. Refer to the literature for more details on these indices.

    +
    #harmonic closeness
+c_HC <- florentine_m %>% 
+  indirect_relations(type="geodesic",FUN=dist_inv) %>% 
+  aggregate_positions(type="sum")
+#residual closeness (Dangalchev,2006)
+c_RC <- florentine_m %>% 
+  indirect_relations(type="geodesic",FUN=dist_2pow) %>% 
+  aggregate_positions(type="sum")
+
+#integration centrality (Valente & Foreman, 1998)
+dist_integration <- function(x){
+  x <- 1 - (x - 1)/max(x)
+}
+c_IN <- florentine_m %>% 
+  indirect_relations(type="geodesic",FUN=dist_integration) %>% 
+  aggregate_positions(type="sum")
+
+c(cor(c_HC,V(florentine_m)$wealth,method="kendall"),
+cor(c_RC,V(florentine_m)$wealth,method="kendall"),
+cor(c_IN,V(florentine_m)$wealth,method="kendall")
+)
    +
    ## [1] 0.09756214 0.11594338 0.08823953
    +

    The highest correlation (0.1159) is achieved for residual closeness, however, this is still too low to conclude that proximity is related to wealth.

    +

    Besides the already considered indices, there exist further one’s that include a free parameter. The idea is that the parameter can be tuned to maximize the correlation between the index and the attribute under consideration. Again, the mathematical details can be found in the respective literature.

    +
    #generalized closeness (Agneessens et al.,2017) (alpha>0) sum(dist^-alpha)
+alpha <- c(seq(0.01,0.99,0.01),seq(1,10,0.1))
+scores <- 
+sapply(alpha,function(x)
+    florentine_m %>% 
+      indirect_relations(type="geodesic",FUN=dist_dpow,alpha=x) %>% 
+      aggregate_positions(type="sum")
+)
+cors_gc <- apply(scores,2,
+              function(x)cor(x,V(florentine_m)$wealth,method="kendall"))
+
+res_gc <- c(max(cors_gc),alpha[which.max(cors_gc)])
+
+#decay centrality (Jackson, 2010) (alpha in [0,1]) sum(alpha^dist)
+alpha <- seq(0.01,0.99,0.01)
+scores <- 
+sapply(alpha,function(x)
+  florentine_m %>% 
+    indirect_relations(type="geodesic",FUN=dist_powd,alpha=x) %>% 
+    aggregate_positions(type="sum")
+)
+cors_dc <- apply(scores,2,
+              function(x)cor(x,V(florentine_m)$wealth,method="kendall"))
+
+res_dc <- c(max(cors_dc),alpha[which.max(cors_dc)])
    +

    The highest correlation for generalized closeness is 0.1159434 achieved for \(\alpha\)= 0.51

    +

    The highest correlation for decay centrality is 0.1159434 achieved for \(\alpha\)=0.26

    +

    We could know accept that there is no index based on geodesic distances that could explain wealth. Or, we could start to craft new indices that might yield a better correlation with wealth. However, we then enter the dilemma that was mentioned at the end of the last section. If we find one, we can not be certain that there might not even be a better one out there. In contrast, if we do not succeed, we can not guarantee that there does not exist an index with a higher correlation.

    +
    +
    +
    +

    +Centrality as explanatory variable (Dominance approach)

    +

    Since we are postulating a connection between proximity and wealth, we compute the pairwise geodesic distances as our indirect relation of interest and calculate the positional dominance relations.

    +
    D <- florentine_m %>% 
+  indirect_relations(type="geodesic") %>% 
+  positional_dominance(benefit=F)
+
+comparable_pairs(D)
    +
    ## [1] 0.1523809
    +

    Note that exactly the same pairs are comparable as for neighborhood-inclusion. However, with one additional assumption, we will be able to increase the number of comparable pairs significantly (and thus reduce the space of potential rankings). By summing up distances in various ways, as done by the indices above, we assume families to be homogeneous. It doesn’t matter to whom we have a small distance, it just matters that they are small.

    +

    If we can safely comply with this assumption, we can use positional dominance under total homogeneity. It is important to note, that if a family is dominated by another under this premise, it will have a lower score in any distance based centrality index.

    +
    D <- florentine_m %>% 
+  indirect_relations(type="geodesic") %>% 
+  positional_dominance(benefit=F,map=T)
+
+comparable_pairs(D)
    +
    ## [1] 0.8190476
    +

    The number of comparable pairs increased from \(0.15\) to \(0.82\), thus reducing the space of potential centrality rankings based on distances significantly.

    +

    We proceed to explore if there is potential for a distance based ranking to explain wealth perfectly. This is only possible, if families with lower wealth do not dominate wealthier family. Otherwise they would always be ranked higher, prohibiting a perfect correlation.

    +

    The figure below shows the dominance relations as a directed graph, where the x coordinate of nodes is proportional to the wealth attribute and the y coordinate to the number of dominated families. Any edge pointing to the left (shown in red) denotes a pair of “wrongly” ordered families, i.e. a wealthy family is dominated by a less wealthy one.

    +

    +

    In total, we find \(41\) such pairs (\(39\)% of all pairs). This implies that we are (potentially) quite far from being able to explain wealth perfectly with geodesic distances. In the following we will explore how far away.

    +

    We start by calculating the rank intervals to illustrate the difference to neighborhood-inclusion.

    +
    plot_rank_intervals(D,names=V(florentine_m)$name)
    +

    All intervals shrunk significantly and even correspond to a single point for two families (Pazzi and Medici). This implies that no matter which distance based index we use, the Pazzi family will always be ranked last and the Medici always on top.

    +

    For a more exact assessment we again use the function exact_rank_prob().

    +
    res <- exact_rank_prob(D,names = V(florentine_m)$name)
    +

    In total, there are 654 distance based rankings possible. This is a huge reduction from the general case where almost \(4\) billion are possible.

    +

    To determine the best possible correlation between wealth and any distance based ranking, we first need to determine all 654 rankings. For this purpose, we rerun the previous analysis with only.results=FALSE to obtain the necessary data structure.

    +
    res <- exact_rank_prob(D,names = V(florentine_m)$name,only.results = FALSE)
    +

    Now, we can use the function get_rankings() which returns all rankings as a matrix.

    +
    all_ranks <- get_rankings(res)
+dim(all_ranks)
    +
    ## [1]  15 654
    +

    No we can simply loop over all rankings and calculate the correlation between the ranking and the wealth attribute.

    +
    dist_cor <- apply(all_ranks,2,
+              function(x)cor(V(florentine_m)$wealth,x,method="kendall"))
+c(max_cor = max(dist_cor),mean_cor = mean(dist_cor))
    +
    ##    max_cor   mean_cor 
+## 0.15459118 0.04600506
    +

    The highest achievable correlation is 0.1546.

    +

    The figure below shows all correlations as a boxplot.

    +

    We can conclude, that there can not be any distance based centrality index that can reasonably explain the wealth attribute.

    +

    We can additionally consider the correlation between degree and wealth, calculated below.

    +
    cor(degree(florentine_m),V(florentine_m)$wealth,method="kendall")
    +
    ## [1] 0.1958605
    +

    The correlation is higher than any distance based index can have. Thus, we can additionally conclude that marriage ties are more indicative for wealth than proximity in the marriage network.

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    +

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    +
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100644 index 0000000..1b9dfc3 --- /dev/null +++ b/docs/authors.html @@ -0,0 +1,181 @@ + + + + + + + + +Citation and Authors • netrankr + + + + + + + + + + + + + + + + + + + + + + + + + + + +

    +
    + + + +
    + +
    +
    + +
    +

    Citation

    +
    + +

    Schoch D (2017). +netrankr: An R package to analyze partial rankings in networks. +https://schochastics.github.io/netrankr. +

    + 
    @Manual{,
+  title = {netrankr: An R package to analyze partial rankings in networks},
+  author = {David Schoch},
+  year = {2017},
+  url = {https://schochastics.github.io/netrankr},
+}
    +
    +

    Authors

    +
    + +
      +
    • +

      David Schoch. Author, maintainer. +

      +
      • +
    • +

      Julian Müller. Contributor. +

      +
      • +
    + +
    + +
    + + +
    +
    +

    Developed by David Schoch.

    +
    + +
    +

    Site built with pkgdown.

    +
    + +
    +
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    +
    + + + +
    + +
    +
    + + + + +
    +
    +

    +Overview

    +

    The literature is flooded with centrality indices and new ones are introduced on a regular basis. Although there exist several theoretical and empirical guidelines on when to use certain indices, there still exists plenty of ambiguity in the concept of network centrality. To date, network centrality is nothing more than applying indices to a network:

    +
    +

    The only degree of freedom is the choice of index.

    +

    The netrankr package is based on the idea that centrality is more than a conglomeration of indices. Decomposing them in a series of microsteps offers the posibility to gradually add ideas about centrality, without succumbing to trial-and-error approaches. Further, it allows for alternative assessment methods which can be more general than the index-driven approach:

    +
    +

    The new approach is centered around the concept of positions, which are defined as the relations and potential attributes of a node in a network. The aggregation of the relations leads to the definition of indices. However, positions can also be compared via positional dominance, leading to partial centrality rankings and the option to calculate probabilistic centrality rankings.

    +

    For a more detailed theoretical background, consult the Literature at the end of this page.

    +
    +
    +

    +Installation

    +

    To install from CRAN: [not released yet]

    +

    To install the developer version from github:

    +
    require(devtools)
+install_github("schochastics/netrankr")
    +
    +
    +
    +

    +Simple Example

    +

    This example briefly explains some of the functionality of the package and the difference to an index driven approach. For a more realistic application see the use case example.

    +

    We work with the following small graph.

    +
    library(igraph)
+library(netrankr)
+
+g <- graph.empty(n = 11,directed = FALSE)
+g <- add_edges(g,c(1,11,2,4,3,5,3,11,4,8,5,9,5,11,6,7,6,8,
+                    6,10,6,11,7,9,7,10,7,11,8,9,8,10,9,10))
    +

    +

    Say we are interested in the most central node of the graph and simply compute some standard centrality scores with the igraph package. Defining centrality indices in the netrankr package is explained here.

    +
    cent_scores <- data.frame(
+   degree = degree(g),
+   betweenness = round(betweenness(g),4),
+   closeness = round(closeness(g),4),
+   eigenvector = round(eigen_centrality(g)$vector,4),
+   subgraph = round(subgraph_centrality(g),4))
+
+# What are the most central nodes for each index?
+apply(cent_scores,2,which.max)
    +
    #>      degree betweenness   closeness eigenvector    subgraph 
+#>          11           8           6           7          10
    +

    +

    As you can see, each index assigns the highest value to a different vertex.

    +

    A more general assessment starts by calculating the neighborhood inclusion preorder.

    +
    P <- neighborhood_inclusion(g)
+P
    +
    #>       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11]
+#>  [1,]    0    0    1    0    1    1    1    0    0     0     1
+#>  [2,]    0    0    0    1    0    0    0    1    0     0     0
+#>  [3,]    0    0    0    0    1    0    0    0    0     0     1
+#>  [4,]    0    0    0    0    0    0    0    0    0     0     0
+#>  [5,]    0    0    0    0    0    0    0    0    0     0     0
+#>  [6,]    0    0    0    0    0    0    0    0    0     0     0
+#>  [7,]    0    0    0    0    0    0    0    0    0     0     0
+#>  [8,]    0    0    0    0    0    0    0    0    0     0     0
+#>  [9,]    0    0    0    0    0    0    0    0    0     0     0
+#> [10,]    0    0    0    0    0    0    0    0    0     0     0
+#> [11,]    0    0    0    0    0    0    0    0    0     0     0
    +

    If P[u,v]=1, then \(N(u) \subseteq N[v]\) which implies that \(c(u) \leq c(v)\) for all centrality indices \(c\)!

    +

    Neighborhood-inclusion defines a partial ranking on the set of nodes. Each ranking that is in accordance with this partial ranking yields a proper centrality ranking. Each of these ranking can thus potentially be the outcome of a centrality index.

    +

    Using rank intervals, we can examine the minimal and maximal possible rank of each node. The bigger the intervals are, the more freedom exists for indices to rank nodes differently.

    +
    plot_rank_intervals(P,names = 1:11,cent.df = cent_scores,ties.method="average")
    +

    +

    The potential ranks of nodes are not uniformly distributed in the intervals. To get the exact probabilities, the function exact_rank_prob() can be used.

    +
    res <- exact_rank_prob(P)
+str(res)
    +
    #> List of 7
+#>  $ lin.ext      : num 739200
+#>  $ names        : chr [1:11] "1" "2" "3" "4" ...
+#>  $ mse          : int [1:11] 1 2 3 4 5 6 7 8 9 10 ...
+#>  $ rank.prob    : num [1:11, 1:11] 0.545 0.273 0 0 0 ...
+#>  $ relative.rank: num [1:11, 1:11] 0 0.3333 0 0.0476 0 ...
+#>  $ expected.rank: num [1:11] 1.71 3 4.29 7.5 8.14 ...
+#>  $ rank.spread  : num [1:11] 0.958 1.897 1.725 2.54 2.16 ...
    +

    lin.ext is the number of possible rankings. For the graph g we could therefore come up with 739,200 indices that would rank the nodes differently.

    +

    rank.prob contains the probabilities for each node to occupy a certain rank. For instance, the probability for each node to be the most central one is as follows.

    +
    round(res$rank.prob[ ,11],2)
    +
    #>  [1] 0.00 0.00 0.00 0.14 0.16 0.11 0.11 0.14 0.09 0.09 0.16
    +

    relative.rank contains the relative rank probabilities. An entry relative.rank[u,v] indicates how likely it is that v is more central than u.

    +
    # How likely is it, that 6 is more central than 3?
+round(res$relative.rank[3,6],2)
    +
    #> [1] 0.75
    +

    expected.ranks contains the expected centrality ranks for all nodes. They are derived on the basis of rank.prob.

    +
    round(res$expected.rank,2)
    +
    #>  [1] 1.71 3.00 4.29 7.50 8.14 6.86 6.86 7.50 6.00 6.00 8.14
    +

    The higher the value, the more central a node is expected to be.

    +

    Note: The set of rankings grows exponentially in the number of nodes and the exact calculation becomes infeasible quite quickly and approximations need to be used.
    +Check the benchmark results for guidelines.

    +
    +
    +
    +

    +Theoretical Background

    +

    netrankr is based on a series of papers that appeared in recent years. If you want to learn more about the theoretical background of the package, consult the following literature:

    +
    +

    Brandes, Ulrik. (2016). Network Positions. Methodological Innovations, 9, 2059799116630650. (link)

    +
    +
    +

    Schoch, David & Brandes, Ulrik. (2016). Re-conceptualizing centrality in social networks. European Journal of Appplied Mathematics, 27(6), 971–985. (link)

    +
    +
    +

    Schoch, David & Valente, Thomas W., & Brandes, Ulrik. (2017). Correlations among centrality indices and a class of uniquely ranked graphs. Social Networks, 50, 46-54.(link)

    +
    + + +
    +
    +
    +
    + + + +
    + + +
    +

    Developed by David Schoch.

    +
    + +
    +

    Site built with pkgdown.

    +
    + +
    +
    + + + diff --git a/docs/index_files/DiagrammeR-binding-0.9.2/DiagrammeR.js b/docs/index_files/DiagrammeR-binding-0.9.2/DiagrammeR.js new file mode 100644 index 0000000..eb3abc5 --- /dev/null +++ b/docs/index_files/DiagrammeR-binding-0.9.2/DiagrammeR.js @@ -0,0 +1,190 @@ +HTMLWidgets.widget({ + + name: 'DiagrammeR', + + type: 'output', + + initialize: function(el, width, height) { + + /* wait to initialize until renderValue + since x not provided until then + and mermaid will try to build the diagram + as soon as class of the div is set to "mermaid" + */ + + /* to prevent auto init() by mermaid + not documented but + see lines https://github.com/knsv/mermaid/blob/master/src/main.js#L100-L109 + mermaid_config in global with mermaid_config.startOnLoad = false + appears to turn off the auto init behavior + allowing us to callback after manually init and then callback + after complete + */ + window.mermaid.startOnLoad = false; + + // set config options for Gantt + // undocumented but these can be provided + // so from R + // m1 <- mermaid(spec) + // m1$x$config = list(ganttConfig = list( barHeight = 100 ) ) + mermaid.ganttConfig = { + titleTopMargin:25, + barHeight:20, + barGap:4, + topPadding:50, + sidePadding:100, + gridLineStartPadding:35, + fontSize:11, + numberSectionStyles:4, + axisFormatter: [ + // Within a day + ["%I:%M", function (d) { + return d.getHours(); + }], + // Monday a week + ["w. %U", function (d) { + return d.getDay() == 1; + }], + // Day within a week (not monday) + ["%a %d", function (d) { + return d.getDay() && d.getDate() != 1; + }], + // within a month + ["%b %d", function (d) { + return d.getDate() != 1; + }], + // Month + ["%m-%y", function (d) { + return d.getMonth(); + }] + ] + }; + + return { + // TODO: add instance fields as required + } + + }, + + renderValue: function(el, x, instance) { + + // if no diagram provided then assume + // that the diagrams are provided through htmltools tags + // and DiagrammeR was just used for dependencies + if ( x.diagram != "" ) { + el.innerHTML = x.diagram; + //if dynamic such as shiny remove data-processed + // so mermaid will reprocess and redraw + el.removeAttribute("data-processed"); + el.classList.add('mermaid'); + //make sure if shiny that we turn display back on + el.style.display = ""; + //again if dynamic such as shiny + // explicitly run mermaid.init() + } else { + // set display to none + // should we remove instead?? + el.style.display = "none"; + } + + // check for undocumented ganttConfig + // to override the defaults manually entered + // in initialize above + // note this is really sloppy and will not + // work well if multiple gantt charts + // with custom configs here + if( typeof x.config !== "undefined" && + typeof x.config.ganttConfig !== "undefined" ){ + Object.keys(x.config.ganttConfig).map(function(k){ + window.mermaid.ganttConfig[k] = x.config.ganttConfig[k]; + }) + } + + + // use this to sort of make our diagram responsive + // or at a minimum fit within the bounds set by htmlwidgets + // for the parent container + function makeResponsive(el){ + var svg = el.getElementsByTagName("svg")[0]; + if(svg){ + if(svg.width) {svg.removeAttribute("width")}; + if(svg.height) {svg.removeAttribute("height")}; + svg.style.width = "100%"; + svg.style.height = "100%"; + } + }; + + + // get all DiagrammeR mermaids widgets + dg = document.getElementsByClassName("DiagrammeR"); + // run mermaid.init + // but use try catch block + // to send error to the htmlwidget for display + try{ + mermaid.init( el ); + + // sort of make our diagram responsive + // should we make this an option? + // if so, then could easily add to list of post process tasks + makeResponsive( el ); + + /* + // change the id of our SVG assigned by mermaid to prevent conflict + // mermaid.init has a counter that will reset to 0 + // and cause duplication of SVG id if multiple + d3.select(el).select("svg") + .attr("id", "mermaidChart-" + el.id); + // now we have to change the styling assigned by mermaid + // to point to our new id that we have assigned + // will add if since sequence diagrams do not have stylesheet + if(d3.select(el).select("svg").select("style")[0][0]){ + d3.select(el).select("svg").select("style")[0][0].innerHTML = d3.select(el).select("svg") + .select("style")[0][0].innerHTML + */ + /// sep comment for / in regex .replace(/mermaidChart[0-9]*/gi, "mermaidChart-" + el.id); + /*} + */ + + // set up a container for tasks to perform after completion + // one example would be add callbacks for event handling + // styling + if (!(typeof x.tasks === "undefined") ){ + if ( (typeof x.tasks.length === "undefined") || + (typeof x.tasks === "function" ) ) { + // handle a function not enclosed in array + // should be able to remove once using jsonlite + x.tasks = [x.tasks]; + } + x.tasks.map(function(t){ + // for each tasks add it to the mermaid.tasks with el + t.call(el); + }) + } + + } catch(e) { + // if error look for last processed DiagrammeR + // and send error to the container div + // with pre containing the errors + var processedDg = d3.selectAll(".DiagrammeR[data-processed=true]"); + // select the last + processedDg = d3.select(processedDg[0][processedDg[0].length - 1]) + // remove the svg + processedDg.select("svg").remove(); + + //if dynamic such as shiny remove data-processed + // so mermaid will reprocess and redraw + if (HTMLWidgets.shinyMode) { + el.removeAttribute("data-processed") + } + + processedDg.append("pre").html( ["parse error with " + x.diagram, e.message].join("\n") ) + } + + }, + + resize: function(el, width, height, instance) { + + } + + +}); diff --git a/docs/index_files/DiagrammeR-styles-0.2/styles.css b/docs/index_files/DiagrammeR-styles-0.2/styles.css new file mode 100644 index 0000000..d6446ab --- /dev/null +++ b/docs/index_files/DiagrammeR-styles-0.2/styles.css @@ -0,0 +1,14 @@ +.DiagrammeR,.grViz pre { + white-space: pre-wrap; /* CSS 3 */ + white-space: -moz-pre-wrap; /* Mozilla, since 1999 */ + white-space: -pre-wrap; /* Opera 4-6 */ + white-space: -o-pre-wrap; /* Opera 7 */ + word-wrap: break-word; /* Internet Explorer 5.5+ */ +} + +.DiagrammeR g .label { + font-family: Helvetica; + font-size: 14px; + color: #333333; +} + diff --git a/docs/index_files/chromatography-0.1/LICENSE b/docs/index_files/chromatography-0.1/LICENSE new file mode 100644 index 0000000..ea86fbd --- /dev/null +++ b/docs/index_files/chromatography-0.1/LICENSE @@ -0,0 +1,22 @@ +The MIT License (MIT) + +Copyright (c) 2015 We Are Visualizers + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. + diff --git a/docs/index_files/chromatography-0.1/chromatography.js b/docs/index_files/chromatography-0.1/chromatography.js new file mode 100644 index 0000000..bd25546 --- /dev/null +++ b/docs/index_files/chromatography-0.1/chromatography.js @@ -0,0 +1,1105 @@ +(function () { + + var Categories, Color, ColorScale, chromato, CSSColors, Ramp, root, type, _ref, _ref2, _ref3; + var __hasProp = Object.prototype.hasOwnProperty, __extends = function(child, parent) { for (var key in parent) { if (__hasProp.call(parent, key)) child[key] = parent[key]; } function ctor() { this.constructor = child; } ctor.prototype = parent.prototype; child.prototype = new ctor; child.__super__ = parent.prototype; return child; }; + + root = typeof exports !== 'undefined' && exports !== null ? exports : this; + + chromato = (_ref = root.chromato) != null ? _ref : root.chromato = {}; + + if (typeof module !== 'undefined' && module !== null) module.exports = chromato; + + Color = (function() { + function Color(x, y, z, m) { + var me, _ref2; + me = this; + if (!(x != null) && !(y != null) && !(z != null) && !(m != null)) { + x = [255, 0, 255]; + } + if (type(x) === 'array' && x.length === 3) { + if (m == null) m = y; + _ref2 = x, x = _ref2[0], y = _ref2[1], z = _ref2[2]; + } + if (type(x) === 'string') { + m = 'hex'; + } else { + if (m == null) m = 'rgb'; + } + if (m === 'rgb') { + me.rgb = [x, y, z]; + } else if (m === 'hsl') { + me.rgb = Color.hsl2rgb(x, y, z); + } else if (m === 'hsv') { + me.rgb = Color.hsv2rgb(x, y, z); + } else if (m === 'hex') { + me.rgb = Color.hex2rgb(x); + } else if (m === 'lab') { + me.rgb = Color.lab2rgb(x, y, z); + } else if (m === 'hcl') { + me.rgb = Color.hcl2rgb(x, y, z); + } else if (m === 'hsi') { + me.rgb = Color.hsi2rgb(x, y, z); + } + } + + Color.prototype.hex = function() { + return Color.rgb2hex(this.rgb); + }; + + Color.prototype.toString = function() { + return this.hex(); + }; + + Color.prototype.hsl = function() { + return Color.rgb2hsl(this.rgb); + }; + + Color.prototype.hsv = function() { + return Color.rgb2hsv(this.rgb); + }; + + Color.prototype.lab = function() { + return Color.rgb2lab(this.rgb); + }; + + Color.prototype.hcl = function() { + return Color.rgb2hcl(this.rgb); + }; + + Color.prototype.hsi = function() { + return Color.rgb2hsi(this.rgb); + }; + + Color.prototype.interpolate = function(f, col, m) { + var dh, hue, hue0, hue1, lbv, lbv0, lbv1, me, sat, sat0, sat1, xyz0, xyz1; + me = this; + if (m == null) m = 'rgb'; + if (type(col) === 'string') col = new Color(col); + if (m === 'hsl' || m === 'hsv' || m === 'hcl' || m === 'hsi') { + if (m === 'hsl') { + xyz0 = me.hsl(); + xyz1 = col.hsl(); + } else if (m === 'hsv') { + xyz0 = me.hsv(); + xyz1 = col.hsv(); + } else if (m === 'hcl') { + xyz0 = me.hcl(); + xyz1 = col.hcl(); + } else if (m === 'hsi') { + xyz0 = me.hsi(); + xyz1 = col.hsi(); + } + hue0 = xyz0[0], sat0 = xyz0[1], lbv0 = xyz0[2]; + hue1 = xyz1[0], sat1 = xyz1[1], lbv1 = xyz1[2]; + if (!isNaN(hue0) && !isNaN(hue1)) { + if (hue1 > hue0 && hue1 - hue0 > 180) { + dh = hue1 - (hue0 + 360); + } else if (hue1 < hue0 && hue0 - hue1 > 180) { + dh = hue1 + 360 - hue0; + } else { + dh = hue1 - hue0; + } + hue = hue0 + f * dh; + } else if (!isNaN(hue0)) { + hue = hue0; + if (lbv1 === 1 || lbv1 === 0) sat = sat0; + } else if (!isNaN(hue1)) { + hue = hue1; + if (lbv0 === 1 || lbv0 === 0) sat = sat1; + } else { + hue = void 0; + } + if (sat == null) sat = sat0 + f * (sat1 - sat0); + lbv = lbv0 + f * (lbv1 - lbv0); + return new Color(hue, sat, lbv, m); + } else if (m === 'rgb') { + xyz0 = me.rgb; + xyz1 = col.rgb; + return new Color(xyz0[0] + f * (xyz1[0] - xyz0[0]), xyz0[1] + f * (xyz1[1] - xyz0[1]), xyz0[2] + f * (xyz1[2] - xyz0[2]), m); + } else if (m === 'lab') { + xyz0 = me.lab(); + xyz1 = col.lab(); + return new Color(xyz0[0] + f * (xyz1[0] - xyz0[0]), xyz0[1] + f * (xyz1[1] - xyz0[1]), xyz0[2] + f * (xyz1[2] - xyz0[2]), m); + } else { + throw m + ' is not supported as a color mode'; + } + }; + return Color; + })(); + + Color.hex2rgb = function(hex) { + var b, g, r, u; + if (!hex.match(/^#?([A-Fa-f0-9]{6}|[A-Fa-f0-9]{3})$/)) { + if ((chromato.colors != null) && chromato.colors[hex]) { + hex = chromato.colors[hex]; + } else { + throw 'This color format is unknown: ' + hex; + } + } + if (hex.length === 4 || hex.length === 7) hex = hex.substr(1); + if (hex.length === 3) { + hex = hex[0] + hex[0] + hex[1] + hex[1] + hex[2] + hex[2]; + } + u = parseInt(hex, 16); + r = u >> 16; + g = u >> 8 & 0xFF; + b = u & 0xFF; + return [r, g, b]; + }; + + Color.rgb2hex = function(r, g, b) { + var str, u, _ref2; + if (r !== void 0 && r.length === 3) { + _ref2 = r, r = _ref2[0], g = _ref2[1], b = _ref2[2]; + } + u = r << 16 | g << 8 | b; + str = '000000' + u.toString(16).toUpperCase(); + return '#' + str.substr(str.length - 6); + }; + + Color.hsv2rgb = function(h, s, v) { + var b, f, g, i, l, p, q, r, t, _ref2, _ref3, _ref4, _ref5, _ref6, _ref7, _ref8; + if (type(h) === 'array' && h.length === 3) { + _ref2 = h, h = _ref2[0], s = _ref2[1], l = _ref2[2]; + } + v *= 255; + if (s === 0 && isNaN(h)) { + r = g = b = v; + } else { + if (h === 360) h = 0; + if (h > 360) h -= 360; + if (h < 0) h += 360; + h /= 60; + i = Math.floor(h); + f = h - i; + p = v * (1 - s); + q = v * (1 - s * f); + t = v * (1 - s * (1 - f)); + switch (i) { + case 0: + _ref3 = [v, t, p], r = _ref3[0], g = _ref3[1], b = _ref3[2]; + break; + case 1: + _ref4 = [q, v, p], r = _ref4[0], g = _ref4[1], b = _ref4[2]; + break; + case 2: + _ref5 = [p, v, t], r = _ref5[0], g = _ref5[1], b = _ref5[2]; + break; + case 3: + _ref6 = [p, q, v], r = _ref6[0], g = _ref6[1], b = _ref6[2]; + break; + case 4: + _ref7 = [t, p, v], r = _ref7[0], g = _ref7[1], b = _ref7[2]; + break; + case 5: + _ref8 = [v, p, q], r = _ref8[0], g = _ref8[1], b = _ref8[2]; + } + } + r = Math.round(r); + g = Math.round(g); + b = Math.round(b); + return [r, g, b]; + }; + + Color.rgb2hsv = function(r, g, b) { + var delta, h, max, min, s, v, _ref2; + if (r !== void 0 && r.length === 3) { + _ref2 = r, r = _ref2[0], g = _ref2[1], b = _ref2[2]; + } + min = Math.min(r, g, b); + max = Math.max(r, g, b); + delta = max - min; + v = max / 255.0; + s = delta / max; + if (s === 0) { + h = void 0; + s = 0; + } else { + if (r === max) h = (g - b) / delta; + if (g === max) h = 2 + (b - r) / delta; + if (b === max) h = 4 + (r - g) / delta; + h *= 60; + if (h < 0) h += 360; + } + return [h, s, v]; + }; + + Color.hsl2rgb = function(h, s, l) { + var b, c, g, i, r, t1, t2, t3, _ref2, _ref3; + if (h !== void 0 && h.length === 3) { + _ref2 = h, h = _ref2[0], s = _ref2[1], l = _ref2[2]; + } + if (s === 0) { + r = g = b = l * 255; + } else { + t3 = [0, 0, 0]; + c = [0, 0, 0]; + t2 = l < 0.5 ? l * (1 + s) : l + s - l * s; + t1 = 2 * l - t2; + h /= 360; + t3[0] = h + 1 / 3; + t3[1] = h; + t3[2] = h - 1 / 3; + for (i = 0; i <= 2; i++) { + if (t3[i] < 0) t3[i] += 1; + if (t3[i] > 1) t3[i] -= 1; + if (6 * t3[i] < 1) { + c[i] = t1 + (t2 - t1) * 6 * t3[i]; + } else if (2 * t3[i] < 1) { + c[i] = t2; + } else if (3 * t3[i] < 2) { + c[i] = t1 + (t2 - t1) * ((2 / 3) - t3[i]) * 6; + } else { + c[i] = t1; + } + } + _ref3 = [Math.round(c[0] * 255), Math.round(c[1] * 255), Math.round(c[2] * 255)], r = _ref3[0], g = _ref3[1], b = _ref3[2]; + } + return [r, g, b]; + }; + + Color.rgb2hsl = function(r, g, b) { + var h, l, max, min, s, _ref2; + if (r !== void 0 && r.length === 3) { + _ref2 = r, r = _ref2[0], g = _ref2[1], b = _ref2[2]; + } + r /= 255; + g /= 255; + b /= 255; + min = Math.min(r, g, b); + max = Math.max(r, g, b); + l = (max + min) / 2; + if (max === min) { + s = 0; + h = void 0; + } else { + s = l < 0.5 ? (max - min) / (max + min) : (max - min) / (2 - max - min); + } + if (r === max) { + h = (g - b) / (max - min); + } else if (g === max) { + h = 2 + (b - r) / (max - min); + } else if (b === max) { + h = 4 + (r - g) / (max - min); + } + h *= 60; + if (h < 0) h += 360; + return [h, s, l]; + }; + + Color.lab2xyz = function(l, a, b) { + var finv, ill, sl, x, y, z, _ref2; + if (type(l) === 'array' && l.length === 3) { + _ref2 = l, l = _ref2[0], a = _ref2[1], b = _ref2[2]; + } + finv = function(t) { + if (t > (6.0 / 29.0)) { + return t * t * t; + } else { + return 3 * (6.0 / 29.0) * (6.0 / 29.0) * (t - 4.0 / 29.0); + } + }; + sl = (l + 0.16) / 1.16; + ill = [0.96421, 1.00000, 0.82519]; + y = ill[1] * finv(sl); + x = ill[0] * finv(sl + (a / 5.0)); + z = ill[2] * finv(sl - (b / 2.0)); + return [x, y, z]; + }; + + Color.xyz2rgb = function(x, y, z) { + var b, bl, clip, correct, g, gl, r, rl, _ref2, _ref3; + if (type(x) === 'array' && x.length === 3) { + _ref2 = x, x = _ref2[0], y = _ref2[1], z = _ref2[2]; + } + rl = 3.2406 * x - 1.5372 * y - 0.4986 * z; + gl = -0.9689 * x + 1.8758 * y + 0.0415 * z; + bl = 0.0557 * x - 0.2040 * y + 1.0570 * z; + clip = Math.min(rl, gl, bl) < -0.001 || Math.max(rl, gl, bl) > 1.001; + if (clip) { + rl = rl < 0.0 ? 0.0 : rl > 1.0 ? 1.0 : rl; + gl = gl < 0.0 ? 0.0 : gl > 1.0 ? 1.0 : gl; + bl = bl < 0.0 ? 0.0 : bl > 1.0 ? 1.0 : bl; + } + if (clip) { + _ref3 = [void 0, void 0, void 0], rl = _ref3[0], gl = _ref3[1], bl = _ref3[2]; + } + correct = function(cl) { + var a; + a = 0.055; + if (cl <= 0.0031308) { + return 12.92 * cl; + } else { + return (1 + a) * Math.pow(cl, 1 / 2.4) - a; + } + }; + r = Math.round(255.0 * correct(rl)); + g = Math.round(255.0 * correct(gl)); + b = Math.round(255.0 * correct(bl)); + return [r, g, b]; + }; + + Color.lab2rgb = function(l, a, b) { + var x, y, z, _ref2, _ref3, _ref4; + if (l !== void 0 && l.length === 3) { + _ref2 = l, l = _ref2[0], a = _ref2[1], b = _ref2[2]; + } + if (l !== void 0 && l.length === 3) { + _ref3 = l, l = _ref3[0], a = _ref3[1], b = _ref3[2]; + } + _ref4 = Color.lab2xyz(l, a, b), x = _ref4[0], y = _ref4[1], z = _ref4[2]; + return Color.xyz2rgb(x, y, z); + }; + + Color.hcl2lab = function(c, s, l) { + var L, tau_const, a, angle, b, r, _ref2; + if (type(c) === 'array' && c.length === 3) { + _ref2 = c, c = _ref2[0], s = _ref2[1], l = _ref2[2]; + } + c /= 360.0; + tau_const = 6.283185307179586476925287; + L = l * 0.61 + 0.09; + angle = tau_const / 6.0 - c * tau_const; + r = (l * 0.311 + 0.125) * s; + a = Math.sin(angle) * r; + b = Math.cos(angle) * r; + return [L, a, b]; + }; + + Color.hcl2rgb = function(c, s, l) { + var L, a, b, _ref2; + _ref2 = Color.hcl2lab(c, s, l), L = _ref2[0], a = _ref2[1], b = _ref2[2]; + return Color.lab2rgb(L, a, b); + }; + + Color.rgb2xyz = function(r, g, b) { + var bl, correct, gl, rl, x, y, z, _ref2; + if (r !== void 0 && r.length === 3) { + _ref2 = r, r = _ref2[0], g = _ref2[1], b = _ref2[2]; + } + correct = function(c) { + var a; + a = 0.055; + if (c <= 0.04045) { + return c / 12.92; + } else { + return Math.pow((c + a) / (1 + a), 2.4); + } + }; + rl = correct(r / 255.0); + gl = correct(g / 255.0); + bl = correct(b / 255.0); + x = 0.4124 * rl + 0.3576 * gl + 0.1805 * bl; + y = 0.2126 * rl + 0.7152 * gl + 0.0722 * bl; + z = 0.0193 * rl + 0.1192 * gl + 0.9505 * bl; + return [x, y, z]; + }; + + Color.xyz2lab = function(x, y, z) { + var a, b, f, ill, l, _ref2; + if (x !== void 0 && x.length === 3) { + _ref2 = x, x = _ref2[0], y = _ref2[1], z = _ref2[2]; + } + ill = [0.96421, 1.00000, 0.82519]; + f = function(t) { + if (t > Math.pow(6.0 / 29.0, 3)) { + return Math.pow(t, 1 / 3); + } else { + return (1 / 3) * (29 / 6) * (29 / 6) * t + 4.0 / 29.0; + } + }; + l = 1.16 * f(y / ill[1]) - 0.16; + a = 5 * (f(x / ill[0]) - f(y / ill[1])); + b = 2 * (f(y / ill[1]) - f(z / ill[2])); + return [l, a, b]; + }; + + Color.rgb2lab = function(r, g, b) { + var x, y, z, _ref2, _ref3; + if (r !== void 0 && r.length === 3) { + _ref2 = r, r = _ref2[0], g = _ref2[1], b = _ref2[2]; + } + _ref3 = Color.rgb2xyz(r, g, b), x = _ref3[0], y = _ref3[1], z = _ref3[2]; + return Color.xyz2lab(x, y, z); + }; + + Color.lab2hcl = function(l, a, b) { + var L, tau_const, angle, c, r, s, _ref2; + if (type(l) === 'array' && l.length === 3) { + _ref2 = l, l = _ref2[0], a = _ref2[1], b = _ref2[2]; + } + L = l; + l = (l - 0.09) / 0.61; + r = Math.sqrt(a * a + b * b); + s = r / (l * 0.311 + 0.125); + tau_const = 6.283185307179586476925287; + angle = Math.atan2(a, b); + c = (tau_const / 6 - angle) / tau_const; + c *= 360; + if (c < 0) c += 360; + return [c, s, l]; + }; + + Color.rgb2hcl = function(r, g, b) { + var a, l, _ref2, _ref3; + if (type(r) === 'array' && r.length === 3) { + _ref2 = r, r = _ref2[0], g = _ref2[1], b = _ref2[2]; + } + _ref3 = Color.rgb2lab(r, g, b), l = _ref3[0], a = _ref3[1], b = _ref3[2]; + return Color.lab2hcl(l, a, b); + }; + + Color.rgb2hsi = function(r, g, b) { + var pi_const_x2, h, i, min, s, _ref2; + if (type(r) === 'array' && r.length === 3) { + _ref2 = r, r = _ref2[0], g = _ref2[1], b = _ref2[2]; + } + pi_const_x2 = Math.PI * 2; + r /= 255; + g /= 255; + b /= 255; + min = Math.min(r, g, b); + i = (r + g + b) / 3; + s = 1 - min / i; + if (s === 0) { + h = 0; + } else { + h = ((r - g) + (r - b)) / 2; + h /= Math.sqrt((r - g) * (r - g) + (r - b) * (g - b)); + h = Math.acos(h); + if (b > g) h = pi_const_x2 - h; + h /= pi_const_x2; + } + return [h * 360, s, i]; + }; + + Color.hsi2rgb = function(h, s, i) { + var pi_const_div3, pi_const_x2, b, cos, g, r, _ref2; + if (type(h) === 'array' && h.length === 3) { + _ref2 = h, h = _ref2[0], s = _ref2[1], i = _ref2[2]; + } + pi_const_x2 = Math.PI * 2; + pi_const_div3 = Math.PI / 3; + cos = Math.cos; + if (h < 0) h += 360; + if (h > 360) h -= 360; + h /= 360; + if (h < 1 / 3) { + b = (1 - s) / 3; + r = (1 + s * cos(pi_const_x2 * h) / cos(pi_const_div3 - pi_const_x2 * h)) / 3; + g = 1 - (b + r); + } else if (h < 2 / 3) { + h -= 1 / 3; + r = (1 - s) / 3; + g = (1 + s * cos(pi_const_x2 * h) / cos(pi_const_div3 - pi_const_x2 * h)) / 3; + b = 1 - (r + g); + } else { + h -= 2 / 3; + g = (1 - s) / 3; + b = (1 + s * cos(pi_const_x2 * h) / cos(pi_const_div3 - pi_const_x2 * h)) / 3; + r = 1 - (g + b); + } + r = i * r * 3; + g = i * g * 3; + b = i * b * 3; + return [r * 255, g * 255, b * 255]; + }; + + chromato.Color = Color; + + chromato.hsl = function(h, s, l) { + return new Color(h, s, l, 'hsl'); + }; + + chromato.hsv = function(h, s, v) { + return new Color(h, s, v, 'hsv'); + }; + + chromato.rgb = function(r, g, b) { + return new Color(r, g, b, 'rgb'); + }; + + chromato.hex = function(x) { + return new Color(x); + }; + + chromato.lab = function(l, a, b) { + return new Color(l, a, b, 'lab'); + }; + + chromato.hcl = function(c, s, l) { + return new Color(c, s, l, 'hcl'); + }; + + chromato.hsi = function(h, s, i) { + return new Color(h, s, i, 'hsi'); + }; + + chromato.interpolate = function(a, b, f, m) { + if (type(a) === 'string') a = new Color(a); + if (type(b) === 'string') b = new Color(b); + return a.interpolate(f, b, m); + }; + + ColorScale = (function() { + + function ColorScale(opts) { + var c, col, cols, me, _ref2, _ref3, _ref4, _ref5, _ref6, _ref7; + me = this; + me.colors = cols = (_ref2 = opts.colors) != null ? _ref2 : ['#ddd', '#222']; + for (c = 0, _ref3 = cols.length - 1; 0 <= _ref3 ? c <= _ref3 : c >= _ref3; 0 <= _ref3 ? c++ : c--) { + col = cols[c]; + if (type(col) === 'string') cols[c] = new Color(col); + } + if (opts.positions != null) { + me.pos = opts.positions; + } else { + me.pos = []; + for (c = 0, _ref4 = cols.length - 1; 0 <= _ref4 ? c <= _ref4 : c >= _ref4; 0 <= _ref4 ? c++ : c--) { + me.pos.push(c / (cols.length - 1)); + } + } + me.mode = (_ref5 = opts.mode) != null ? _ref5 : 'hsv'; + me.nacol = (_ref6 = opts.nacol) != null ? _ref6 : '#ccc'; + me.setClasses((_ref7 = opts.limits) != null ? _ref7 : [0, 1]); + me; + } + + ColorScale.prototype.getColor = function(value) { + var c, f, f0, me; + me = this; + if (isNaN(value)) return me.nacol; + if (me.classLimits.length > 2) { + c = me.getClass(value); + f = c / (me.numClasses - 1); + } else { + f = f0 = (value - me.min) / (me.max - me.min); + f = Math.min(1, Math.max(0, f)); + } + return me.fColor(f); + }; + + ColorScale.prototype.fColor = function(f) { + var col, cols, i, me, p, _ref2; + me = this; + cols = me.colors; + for (i = 0, _ref2 = me.pos.length - 1; 0 <= _ref2 ? i <= _ref2 : i >= _ref2; 0 <= _ref2 ? i++ : i--) { + p = me.pos[i]; + if (f <= p) { + col = cols[i]; + break; + } + if (f >= p && i === me.pos.length - 1) { + col = cols[i]; + break; + } + if (f > p && f < me.pos[i + 1]) { + f = (f - p) / (me.pos[i + 1] - p); + col = chromato.interpolate(cols[i], cols[i + 1], f, me.mode); + break; + } + } + return col; + }; + + ColorScale.prototype.classifyValue = function(value) { + var i, limits, maxc, minc, n, self; + self = this; + limits = self.classLimits; + if (limits.length > 2) { + n = limits.length - 1; + i = self.getClass(value); + value = limits[i] + (limits[i + 1] - limits[i]) * 0.5; + minc = limits[0]; + maxc = limits[n - 1]; + value = self.min + ((value - minc) / (maxc - minc)) * (self.max - self.min); + } + return value; + }; + + ColorScale.prototype.setClasses = function(limits) { + var me; + if (limits == null) limits = []; + me = this; + me.classLimits = limits; + me.min = limits[0]; + me.max = limits[limits.length - 1]; + if (limits.length === 2) { + return me.numClasses = 0; + } else { + return me.numClasses = limits.length - 1; + } + }; + + ColorScale.prototype.getClass = function(value) { + var i, limits, n, self; + self = this; + limits = self.classLimits; + if (limits != null) { + n = limits.length - 1; + i = 0; + while (i < n && value >= limits[i]) { + i++; + } + return i - 1; + } + }; + + ColorScale.prototype.validValue = function(value) { + return !isNaN(value); + }; + return ColorScale; + })(); + + chromato.ColorScale = ColorScale; + + Ramp = (function() { + __extends(Ramp, ColorScale); + + function Ramp(col0, col1, mode) { + if (col0 == null) col0 = '#fe0000'; + if (col1 == null) col1 = '#feeeee'; + if (mode == null) mode = 'hsl'; + Ramp.__super__.constructor.call(this, [col0, col1], [0, 1], mode); + } + return Ramp; + })(); + + chromato.Ramp = Ramp; + + Categories = (function() { + __extends(Categories, ColorScale); + + function Categories(colors) { + var me; + me = this; + me.colors = colors; + } + + Categories.prototype.parseData = function(data, data_col) {}; + + Categories.prototype.getColor = function(value) { + var me; + me = this; + if (me.colors.hasOwnProperty(value)) { + return me.colors[value]; + } else { + return '#cccccc'; + } + }; + + Categories.prototype.validValue = function(value) { + return this.colors.hasOwnProperty(value); + }; + return Categories; + })(); + + chromato.Categories = Categories; + + CSSColors = (function() { + __extends(CSSColors, ColorScale); + + function CSSColors(name) { + var me; + me = this; + me.name = name; + me.setClasses(7); + me; + } + + CSSColors.prototype.getColor = function(value) { + var c, me; + me = this; + c = me.getClass(value); + return me.name + ' l' + me.numClasses + ' c' + c; + }; + + return CSSColors; + })(); + + chromato.CSSColors = CSSColors; + + if ((_ref2 = chromato.scales) == null) chromato.scales = {}; + + chromato.limits = function(data, mode, num, prop) { + var assignments, best, centroids, cluster, clusterSizes, dist, i, j, k, kClusters, limits, max, min, mindist, n, nb_iters, newCentroids, p, pb, pr, repeat, row, sum, tmpKMeansBreaks, val, value, values, _i, _j, _k, _len, _len2, _len3, _ref10, _ref11, _ref12, _ref13, _ref14, _ref15, _ref16, _ref3, _ref4, _ref5, _ref6, _ref7, _ref8, _ref9; + if (mode == null) mode = 'equal'; + if (num == null) num = 7; + if (prop == null) prop = null; + min = Number.MAX_VALUE; + max = Number.MAX_VALUE * -1; + sum = 0; + values = []; + if (type(data) === 'array') { + if (type(data[0]) !== 'object' && type(data[0]) !== 'array') { + for (_i = 0, _len = data.length; _i < _len; _i++) { + val = data[_i]; + if (!isNaN(val)) values.push(Number(val)); + } + } else { + for (_j = 0, _len2 = data.length; _j < _len2; _j++) { + row = data[_j]; + values.push(Number(row[prop])); + } + } + } else if (type(data) === 'object') { + for (k in data) { + val = data[k]; + if (type(val) === 'object' && type(prop) === 'string') { + if (!isNaN(val[prop])) values.push(Number(val[prop])); + } else if (type(val) === 'array' && type(prop) === 'number') { + if (!isNaN(val[prop])) values.push(Number(val[prop])); + } else if (type(val) === 'number') { + if (!isNaN(val)) values.push(Number(val)); + } + } + } + for (_k = 0, _len3 = values.length; _k < _len3; _k++) { + val = values[_k]; + if (!!isNaN(val)) continue; + if (val < min) min = val; + if (val > max) max = val; + sum += val; + } + values = values.sort(function(a, b) { + return a - b; + }); + limits = []; + if (mode.substr(0, 1) === 'c') { + limits.push(min); + limits.push(max); + } + if (mode.substr(0, 1) === 'e') { + limits.push(min); + for (i = 1, _ref3 = num - 1; 1 <= _ref3 ? i <= _ref3 : i >= _ref3; 1 <= _ref3 ? i++ : i--) { + limits.push(min + (i / num) * (max - min)); + } + limits.push(max); + } else if (mode.substr(0, 1) === 'q') { + limits.push(min); + for (i = 1, _ref4 = num - 1; 1 <= _ref4 ? i <= _ref4 : i >= _ref4; 1 <= _ref4 ? i++ : i--) { + p = values.length * i / num; + pb = Math.floor(p); + if (pb === p) { + limits.push(values[pb]); + } else { + pr = p - pb; + limits.push(values[pb] * pr + values[pb + 1] * (1 - pr)); + } + } + limits.push(max); + } else if (mode.substr(0, 1) === 'k') { + n = values.length; + assignments = new Array(n); + clusterSizes = new Array(num); + repeat = true; + nb_iters = 0; + centroids = null; + centroids = []; + centroids.push(min); + for (i = 1, _ref5 = num - 1; 1 <= _ref5 ? i <= _ref5 : i >= _ref5; 1 <= _ref5 ? i++ : i--) { + centroids.push(min + (i / num) * (max - min)); + } + centroids.push(max); + while (repeat) { + for (j = 0, _ref6 = num - 1; 0 <= _ref6 ? j <= _ref6 : j >= _ref6; 0 <= _ref6 ? j++ : j--) { + clusterSizes[j] = 0; + } + for (i = 0, _ref7 = n - 1; 0 <= _ref7 ? i <= _ref7 : i >= _ref7; 0 <= _ref7 ? i++ : i--) { + value = values[i]; + mindist = Number.MAX_VALUE; + for (j = 0, _ref8 = num - 1; 0 <= _ref8 ? j <= _ref8 : j >= _ref8; 0 <= _ref8 ? j++ : j--) { + dist = Math.abs(centroids[j] - value); + if (dist < mindist) { + mindist = dist; + best = j; + } + } + clusterSizes[best]++; + assignments[i] = best; + } + newCentroids = new Array(num); + for (j = 0, _ref9 = num - 1; 0 <= _ref9 ? j <= _ref9 : j >= _ref9; 0 <= _ref9 ? j++ : j--) { + newCentroids[j] = null; + } + for (i = 0, _ref10 = n - 1; 0 <= _ref10 ? i <= _ref10 : i >= _ref10; 0 <= _ref10 ? i++ : i--) { + cluster = assignments[i]; + if (newCentroids[cluster] === null) { + newCentroids[cluster] = values[i]; + } else { + newCentroids[cluster] += values[i]; + } + } + for (j = 0, _ref11 = num - 1; 0 <= _ref11 ? j <= _ref11 : j >= _ref11; 0 <= _ref11 ? j++ : j--) { + newCentroids[j] *= 1 / clusterSizes[j]; + } + repeat = false; + for (j = 0, _ref12 = num - 1; 0 <= _ref12 ? j <= _ref12 : j >= _ref12; 0 <= _ref12 ? j++ : j--) { + if (newCentroids[j] !== centroids[i]) { + repeat = true; + break; + } + } + centroids = newCentroids; + nb_iters++; + if (nb_iters > 200) repeat = false; + } + kClusters = {}; + for (j = 0, _ref13 = num - 1; 0 <= _ref13 ? j <= _ref13 : j >= _ref13; 0 <= _ref13 ? j++ : j--) { + kClusters[j] = []; + } + for (i = 0, _ref14 = n - 1; 0 <= _ref14 ? i <= _ref14 : i >= _ref14; 0 <= _ref14 ? i++ : i--) { + cluster = assignments[i]; + kClusters[cluster].push(values[i]); + } + tmpKMeansBreaks = []; + for (j = 0, _ref15 = num - 1; 0 <= _ref15 ? j <= _ref15 : j >= _ref15; 0 <= _ref15 ? j++ : j--) { + tmpKMeansBreaks.push(kClusters[j][0]); + tmpKMeansBreaks.push(kClusters[j][kClusters[j].length - 1]); + } + tmpKMeansBreaks = tmpKMeansBreaks.sort(function(a, b) { + return a - b; + }); + limits.push(tmpKMeansBreaks[0]); + for (i = 1, _ref16 = tmpKMeansBreaks.length - 1; i <= _ref16; i += 2) { + if (!isNaN(tmpKMeansBreaks[i])) limits.push(tmpKMeansBreaks[i]); + } + } + return limits; + }; + + root = typeof exports !== 'undefined' && exports !== null ? exports : this; + + type = (function() { + var classToType, name, _i, _len, _ref3; + classToType = {}; + _ref3 = 'Boolean Number String Function Array Date RegExp Undefined Null'.split(' '); + for (_i = 0, _len = _ref3.length; _i < _len; _i++) { + name = _ref3[_i]; + classToType['[object ' + name + ']'] = name.toLowerCase(); + } + return function(obj) { + var strType; + strType = Object.prototype.toString.call(obj); + return classToType[strType] || 'object'; + }; + })(); + + if ((_ref3 = root.type) == null) root.type = type; + + Array.max = function(array) { + return Math.max.apply(Math, array); + }; + + Array.min = function(array) { + return Math.min.apply(Math, array); + }; + +}).call(this); + +var createPalette = { + generate: function(colorsCount, checkColor, forceMode, quality, ultra_precision){ + if(colorsCount === undefined) + colorsCount = 8; + if(checkColor === undefined) + checkColor = function(x){return true;}; + if(forceMode === undefined) + forceMode = false; + if(quality === undefined) + quality = 50; + ultra_precision = ultra_precision || false + + if(forceMode){ + var colors = []; + function checkLab(lab){ + var color = chromato.lab(lab[0], lab[1], lab[2]); + return !isNaN(color.rgb[0]) && color.rgb[0] >= 0 && color.rgb[1] >= 0 && color.rgb[2] >= 0 && color.rgb[0] < 256 && color.rgb[1] < 256 && color.rgb[2] < 256 && checkColor(color); + } + + var vectors = {}; + for(i = 0; i < colorsCount; i++){ + var color = [Math.random(), 2 * Math.random() - 1, 2 * Math.random() - 1]; + while(!checkLab(color)){ + color = [Math.random(), 2 * Math.random() - 1, 2 * Math.random() - 1]; + } + colors.push(color); + } + + var repulsion = 0.3; + var speed = 0.05; + var steps = quality * 20; + while(steps-- > 0){ + for(i = 0; i < colors.length; i++){ + vectors[i] = {dl:0, da:0, db:0}; + } + for(i = 0; i < colors.length; i++){ + var color_a = colors[i]; + for(j = 0; j < i; j++){ + var color_b = colors[j]; + var dl = color_a[0] - color_b[0]; + var da = color_a[1] - color_b[1]; + var db = color_a[2] - color_b[2]; + var d = Math.sqrt(Math.pow(dl, 2) + Math.pow(da, 2) + Math.pow(db, 2)); + if(d > 0){ + var force = repulsion / Math.pow(d, 2); + vectors[i].dl += dl * force / d; + vectors[i].da += da * force / d; + vectors[i].db += db * force / d; + vectors[j].dl -= dl * force / d; + vectors[j].da -= da * force / d; + vectors[j].db -= db * force / d; + } else { + vectors[j].dl += 0.02 - 0.04 * Math.random(); + vectors[j].da += 0.02 - 0.04 * Math.random(); + vectors[j].db += 0.02 - 0.04 * Math.random(); + } + } + } + for(i = 0; i < colors.length; i++){ + var color = colors[i]; + var displacement = speed * Math.sqrt(Math.pow(vectors[i].dl, 2) + Math.pow(vectors[i].da, 2) + Math.pow(vectors[i].db, 2)); + if(displacement>0){ + var ratio = speed * Math.min(0.1, displacement)/displacement; + candidateLab = [color[0] + vectors[i].dl * ratio, color[1] + vectors[i].da * ratio, color[2] + vectors[i].db * ratio]; + if(checkLab(candidateLab)){ + colors[i] = candidateLab; + } + } + } + } + return colors.map(function(lab){return chromato.lab(lab[0], lab[1], lab[2]);}); + } else { + function checkColor2(color){ + var lab = color.lab(); + var hcl = color.hcl(); + return !isNaN(color.rgb[0]) && color.rgb[0] >= 0 && color.rgb[1] >= 0 && color.rgb[2] >= 0 && color.rgb[0]<256 && color.rgb[1]<256 && color.rgb[2]<256 && checkColor(color); + } + var kMeans = []; + for(i = 0; i < colorsCount; i++){ + var lab = [Math.random(), 2 * Math.random() - 1, 2 * Math.random() - 1]; + while(!checkColor2(chromato.lab(lab))){ + lab = [Math.random(), 2 * Math.random() - 1, 2 * Math.random() - 1]; + } + kMeans.push(lab); + } + var colorSamples = []; + var samplesClosest = []; + if(ultra_precision){ + for(l = 0; l <= 1; l += 0.01){ + for(a =- 1; a <= 1; a += 0.05){ + for(b =- 1; b <= 1; b += 0.05){ + if(checkColor2(chromato.lab(l, a, b))){ + colorSamples.push([l, a, b]); + samplesClosest.push(null); + } + } + } + } + } else { + for(l = 0; l <= 1; l += 0.05){ + for(a =- 1; a <= 1; a += 0.1){ + for(b =- 1; b <= 1; b += 0.1){ + if(checkColor2(chromato.lab(l, a, b))){ + colorSamples.push([l, a, b]); + samplesClosest.push(null); + } + } + } + } + } + var steps = quality; + while(steps-- > 0){ + for(i = 0; i < colorSamples.length; i++){ + var lab = colorSamples[i]; + var min_dist = 1000000; + for(j = 0; j < kMeans.length; j++){ + var kMean = kMeans[j]; + var distance = Math.sqrt(Math.pow(lab[0] - kMean[0], 2) + Math.pow(lab[1]-kMean[1], 2) + Math.pow(lab[2] - kMean[2], 2)); + if(distance < min_dist){ + min_dist = distance; + samplesClosest[i] = j; + } + } + } + var freeColorSamples = colorSamples.slice(0); + for(j = 0; j < kMeans.length; j++){ + var count = 0; + var candidateKMean = [0, 0, 0]; + for(i = 0; i < colorSamples.length; i++){ + if(samplesClosest[i] == j){ + count++; + candidateKMean[0] += colorSamples[i][0]; + candidateKMean[1] += colorSamples[i][1]; + candidateKMean[2] += colorSamples[i][2]; + } + } + if(count != 0){ + candidateKMean[0] /= count; + candidateKMean[1] /= count; + candidateKMean[2] /= count; + } + if(count != 0 && checkColor2(chromato.lab(candidateKMean[0], candidateKMean[1], candidateKMean[2])) && candidateKMean){ + kMeans[j] = candidateKMean; + } else { + if(freeColorSamples.length>0){ + var min_dist = 10000000000; + var closest = -1; + for(i = 0; i 0){ + var index = -1; + var maxDistance = -1; + for(candidate_index = 0; candidate_index < colorsToSort.length; candidate_index++){ + var d = 1000000000; + for(i = 0; i < diffColors.length; i++){ + var color_a = colorsToSort[candidate_index].lab(); + var color_b = diffColors[i].lab(); + var dl = color_a[0] - color_b[0]; + var da = color_a[1] - color_b[1]; + var db = color_a[2] - color_b[2]; + d = Math.min(d, Math.sqrt(Math.pow(dl, 2)+Math.pow(da, 2)+Math.pow(db, 2))); + } + if(d > maxDistance){ + maxDistance = d; + index = candidate_index; + } + } + var color = colorsToSort[index]; + diffColors.push(color); + colorsToSort = colorsToSort.filter(function(c,i){return i != index;}); + } + return diffColors; + } +} diff --git a/docs/index_files/d3-3.3.8/LICENSE b/docs/index_files/d3-3.3.8/LICENSE new file mode 100644 index 0000000..8301346 --- /dev/null +++ b/docs/index_files/d3-3.3.8/LICENSE @@ -0,0 +1,26 @@ +Copyright (c) 2010-2014, Michael Bostock +All rights reserved. + +Redistribution and use in source and binary forms, with or without +modification, are permitted provided that the following conditions are met: + +* Redistributions of source code must retain the above copyright notice, this + list of conditions and the following disclaimer. + +* Redistributions in binary form must reproduce the above copyright notice, + this list of conditions and the following disclaimer in the documentation + and/or other materials provided with the distribution. + +* The name Michael Bostock may not be used to endorse or promote products + derived from this software without specific prior written permission. + +THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" +AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE +DISCLAIMED. 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+++ b/docs/index_files/dagre-0.4.0/LICENSE @@ -0,0 +1,19 @@ +Copyright (c) 2013 Chris Pettitt + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. diff --git a/docs/index_files/dagre-0.4.0/dagre-d3.min.js b/docs/index_files/dagre-0.4.0/dagre-d3.min.js new file mode 100644 index 0000000..7b8a890 --- /dev/null +++ b/docs/index_files/dagre-0.4.0/dagre-d3.min.js @@ -0,0 +1,27 @@ +!function(e){if("object"==typeof exports&&"undefined"!=typeof module)module.exports=e();else if("function"==typeof define&&define.amd)define([],e);else{var f;"undefined"!=typeof window?f=window:"undefined"!=typeof global?f=global:"undefined"!=typeof self&&(f=self),f.dagreD3=e()}}(function(){var define,module,exports;return function e(t,n,r){function s(o,u){if(!n[o]){if(!t[o]){var a=typeof require=="function"&&require;if(!u&&a)return a(o,!0);if(i)return i(o,!0);var f=new Error("Cannot find module '"+o+"'");throw f.code="MODULE_NOT_FOUND",f}var l=n[o]={exports:{}};t[o][0].call(l.exports,function(e){var n=t[o][1][e];return s(n?n:e)},l,l.exports,e,t,n,r)}return n[o].exports}var i=typeof require=="function"&&require;for(var o=0;o0}},{}],14:[function(require,module,exports){module.exports=intersectNode;function intersectNode(node,point){return node.intersect(point)}},{}],15:[function(require,module,exports){var intersectLine=require("./intersect-line");module.exports=intersectPolygon;function intersectPolygon(node,polyPoints,point){var x1=node.x;var y1=node.y;var intersections=[];var minX=Number.POSITIVE_INFINITY,minY=Number.POSITIVE_INFINITY;polyPoints.forEach(function(entry){minX=Math.min(minX,entry.x);minY=Math.min(minY,entry.y)});var left=x1-node.width/2-minX;var top=y1-node.height/2-minY;for(var i=0;i1){intersections.sort(function(p,q){var pdx=p.x-point.x,pdy=p.y-point.y,distp=Math.sqrt(pdx*pdx+pdy*pdy),qdx=q.x-point.x,qdy=q.y-point.y,distq=Math.sqrt(qdx*qdx+qdy*qdy);return distpMath.abs(dx)*h){if(dy<0){h=-h}sx=dy===0?0:h*dx/dy;sy=h}else{if(dx<0){w=-w}sx=w;sy=dx===0?0:w*dy/dx}return{x:x+sx,y:y+sy}}},{}],17:[function(require,module,exports){var util=require("../util");module.exports=addHtmlLabel;function addHtmlLabel(root,node){var fo=root.append("foreignObject").attr("width","100000");var div=fo.append("xhtml:div");var label=node.label;switch(typeof label){case"function":div.insert(label);break;case"object":div.insert(function(){return label});break;default:div.html(label)}util.applyStyle(div,node.labelStyle);div.style("display","inline-block");div.style("white-space","nowrap");var w,h;div.each(function(){w=this.clientWidth;h=this.clientHeight});fo.attr("width",w).attr("height",h);return fo}},{"../util":25}],18:[function(require,module,exports){var addTextLabel=require("./add-text-label"),addHtmlLabel=require("./add-html-label");module.exports=addLabel;function addLabel(root,node){var label=node.label;var labelSvg=root.append("g");if(typeof label!=="string"||node.labelType==="html"){addHtmlLabel(labelSvg,node)}else{addTextLabel(labelSvg,node)}var labelBBox=labelSvg.node().getBBox();labelSvg.attr("transform","translate("+-labelBBox.width/2+","+-labelBBox.height/2+")");return labelSvg}},{"./add-html-label":17,"./add-text-label":19}],19:[function(require,module,exports){var util=require("../util");module.exports=addTextLabel;function addTextLabel(root,node){var domNode=root.append("text");var lines=processEscapeSequences(node.label).split("\n");for(var i=0;i0;--i){entry=buckets[i].dequeue();if(entry){results=results.concat(removeNode(g,buckets,zeroIdx,entry,true));break}}}}return results}function removeNode(g,buckets,zeroIdx,entry,collectPredecessors){var results=collectPredecessors?[]:undefined;_.each(g.inEdges(entry.v),function(edge){var weight=g.edge(edge),uEntry=g.node(edge.v);if(collectPredecessors){results.push({v:edge.v,w:edge.w})}uEntry.out-=weight;assignBucket(buckets,zeroIdx,uEntry)});_.each(g.outEdges(entry.v),function(edge){var weight=g.edge(edge),w=edge.w,wEntry=g.node(w);wEntry["in"]-=weight;assignBucket(buckets,zeroIdx,wEntry)});g.removeNode(entry.v);return results}function buildState(g,weightFn){var fasGraph=new Graph,maxIn=0,maxOut=0;_.each(g.nodes(),function(v){fasGraph.setNode(v,{v:v,"in":0,out:0})});_.each(g.edges(),function(e){var prevWeight=fasGraph.edge(e.v,e.w)||0,weight=weightFn(e),edgeWeight=prevWeight+weight;fasGraph.setEdge(e.v,e.w,edgeWeight);maxOut=Math.max(maxOut,fasGraph.node(e.v).out+=weight);maxIn=Math.max(maxIn,fasGraph.node(e.w)["in"]+=weight)});var buckets=_.range(maxOut+maxIn+3).map(function(){return new List});var zeroIdx=maxIn+1;_.each(fasGraph.nodes(),function(v){assignBucket(buckets,zeroIdx,fasGraph.node(v))});return{graph:fasGraph,buckets:buckets,zeroIdx:zeroIdx}}function assignBucket(buckets,zeroIdx,entry){if(!entry.out){buckets[0].enqueue(entry)}else if(!entry["in"]){buckets[buckets.length-1].enqueue(entry)}else{buckets[entry.out-entry["in"]+zeroIdx].enqueue(entry)}}},{"./data/list":31,"./graphlib":33,"./lodash":36}],35:[function(require,module,exports){"use strict";var _=require("./lodash"),acyclic=require("./acyclic"),normalize=require("./normalize"),rank=require("./rank"),normalizeRanks=require("./util").normalizeRanks,parentDummyChains=require("./parent-dummy-chains"),removeEmptyRanks=require("./util").removeEmptyRanks,nestingGraph=require("./nesting-graph"),addBorderSegments=require("./add-border-segments"),coordinateSystem=require("./coordinate-system"),order=require("./order"),position=require("./position"),util=require("./util"),Graph=require("./graphlib").Graph;module.exports=layout;function layout(g,opts){var time=opts&&opts.debugTiming?util.time:util.notime;time("layout",function(){var layoutGraph=time(" buildLayoutGraph",function(){return buildLayoutGraph(g)});time(" runLayout",function(){runLayout(layoutGraph,time)});time(" updateInputGraph",function(){updateInputGraph(g,layoutGraph)})})}function runLayout(g,time){time(" makeSpaceForEdgeLabels",function(){makeSpaceForEdgeLabels(g)});time(" removeSelfEdges",function(){removeSelfEdges(g)});time(" acyclic",function(){acyclic.run(g)});time(" nestingGraph.run",function(){nestingGraph.run(g)});time(" rank",function(){rank(util.asNonCompoundGraph(g))});time(" injectEdgeLabelProxies",function(){injectEdgeLabelProxies(g)});time(" removeEmptyRanks",function(){removeEmptyRanks(g)});time(" nestingGraph.cleanup",function(){nestingGraph.cleanup(g)});time(" normalizeRanks",function(){normalizeRanks(g)});time(" assignRankMinMax",function(){assignRankMinMax(g)});time(" removeEdgeLabelProxies",function(){removeEdgeLabelProxies(g)});time(" normalize.run",function(){normalize.run(g)});time(" parentDummyChains",function(){parentDummyChains(g)});time(" addBorderSegments",function(){addBorderSegments(g)});time(" order",function(){order(g)});time(" insertSelfEdges",function(){insertSelfEdges(g)});time(" adjustCoordinateSystem",function(){coordinateSystem.adjust(g)});time(" position",function(){position(g)});time(" positionSelfEdges",function(){positionSelfEdges(g)});time(" removeBorderNodes",function(){removeBorderNodes(g)});time(" normalize.undo",function(){normalize.undo(g)});time(" fixupEdgeLabelCoords",function(){fixupEdgeLabelCoords(g)});time(" undoCoordinateSystem",function(){coordinateSystem.undo(g)});time(" translateGraph",function(){translateGraph(g)});time(" assignNodeIntersects",function(){assignNodeIntersects(g)});time(" reversePoints",function(){reversePointsForReversedEdges(g)});time(" acyclic.undo",function(){acyclic.undo(g)})}function updateInputGraph(inputGraph,layoutGraph){_.each(inputGraph.nodes(),function(v){var inputLabel=inputGraph.node(v),layoutLabel=layoutGraph.node(v);if(inputLabel){inputLabel.x=layoutLabel.x;inputLabel.y=layoutLabel.y;if(layoutGraph.children(v).length){inputLabel.width=layoutLabel.width;inputLabel.height=layoutLabel.height}}});_.each(inputGraph.edges(),function(e){var inputLabel=inputGraph.edge(e),layoutLabel=layoutGraph.edge(e);inputLabel.points=layoutLabel.points;if(_.has(layoutLabel,"x")){inputLabel.x=layoutLabel.x;inputLabel.y=layoutLabel.y}});inputGraph.graph().width=layoutGraph.graph().width;inputGraph.graph().height=layoutGraph.graph().height}var graphNumAttrs=["nodesep","edgesep","ranksep","marginx","marginy"],graphDefaults={ranksep:50,edgesep:20,nodesep:50,rankdir:"tb"},graphAttrs=["acyclicer","ranker","rankdir","align"],nodeNumAttrs=["width","height"],nodeDefaults={width:0,height:0},edgeNumAttrs=["minlen","weight","width","height","labeloffset"],edgeDefaults={minlen:1,weight:1,width:0,height:0,labeloffset:10,labelpos:"r"},edgeAttrs=["labelpos"];function buildLayoutGraph(inputGraph){var g=new Graph({multigraph:true,compound:true}),graph=canonicalize(inputGraph.graph());g.setGraph(_.merge({},graphDefaults,selectNumberAttrs(graph,graphNumAttrs),_.pick(graph,graphAttrs)));_.each(inputGraph.nodes(),function(v){var node=canonicalize(inputGraph.node(v));g.setNode(v,_.defaults(selectNumberAttrs(node,nodeNumAttrs),nodeDefaults));g.setParent(v,inputGraph.parent(v))});_.each(inputGraph.edges(),function(e){var edge=canonicalize(inputGraph.edge(e));g.setEdge(e,_.merge({},edgeDefaults,selectNumberAttrs(edge,edgeNumAttrs),_.pick(edge,edgeAttrs)))});return g}function makeSpaceForEdgeLabels(g){var graph=g.graph();graph.ranksep/=2;_.each(g.edges(),function(e){var edge=g.edge(e);edge.minlen*=2;if(edge.labelpos.toLowerCase()!=="c"){if(graph.rankdir==="TB"||graph.rankdir==="BT"){edge.width+=edge.labeloffset}else{edge.height+=edge.labeloffset}}})}function injectEdgeLabelProxies(g){_.each(g.edges(),function(e){var edge=g.edge(e);if(edge.width&&edge.height){var v=g.node(e.v),w=g.node(e.w),label={rank:(w.rank-v.rank)/2+v.rank,e:e};util.addDummyNode(g,"edge-proxy",label,"_ep")}})}function assignRankMinMax(g){var maxRank=0;_.each(g.nodes(),function(v){var node=g.node(v);if(node.borderTop){node.minRank=g.node(node.borderTop).rank;node.maxRank=g.node(node.borderBottom).rank;maxRank=_.max(maxRank,node.maxRank)}});g.graph().maxRank=maxRank}function removeEdgeLabelProxies(g){_.each(g.nodes(),function(v){var node=g.node(v);if(node.dummy==="edge-proxy"){g.edge(node.e).labelRank=node.rank;g.removeNode(v)}})}function translateGraph(g){var minX=Number.POSITIVE_INFINITY,maxX=0,minY=Number.POSITIVE_INFINITY,maxY=0,graphLabel=g.graph(),marginX=graphLabel.marginx||0,marginY=graphLabel.marginy||0;function getExtremes(attrs){var x=attrs.x,y=attrs.y,w=attrs.width,h=attrs.height; +minX=Math.min(minX,x-w/2);maxX=Math.max(maxX,x+w/2);minY=Math.min(minY,y-h/2);maxY=Math.max(maxY,y+h/2)}_.each(g.nodes(),function(v){getExtremes(g.node(v))});_.each(g.edges(),function(e){var edge=g.edge(e);if(_.has(edge,"x")){getExtremes(edge)}});minX-=marginX;minY-=marginY;_.each(g.nodes(),function(v){var node=g.node(v);node.x-=minX;node.y-=minY});_.each(g.edges(),function(e){var edge=g.edge(e);_.each(edge.points,function(p){p.x-=minX;p.y-=minY});if(_.has(edge,"x")){edge.x-=minX}if(_.has(edge,"y")){edge.y-=minY}});graphLabel.width=maxX-minX+marginX;graphLabel.height=maxY-minY+marginY}function assignNodeIntersects(g){_.each(g.edges(),function(e){var edge=g.edge(e),nodeV=g.node(e.v),nodeW=g.node(e.w),p1,p2;if(!edge.points){edge.points=[];p1=nodeW;p2=nodeV}else{p1=edge.points[0];p2=edge.points[edge.points.length-1]}edge.points.unshift(util.intersectRect(nodeV,p1));edge.points.push(util.intersectRect(nodeW,p2))})}function fixupEdgeLabelCoords(g){_.each(g.edges(),function(e){var edge=g.edge(e);if(_.has(edge,"x")){if(edge.labelpos==="l"||edge.labelpos==="r"){edge.width-=edge.labeloffset}switch(edge.labelpos){case"l":edge.x-=edge.width/2+edge.labeloffset;break;case"r":edge.x+=edge.width/2+edge.labeloffset;break}}})}function reversePointsForReversedEdges(g){_.each(g.edges(),function(e){var edge=g.edge(e);if(edge.reversed){edge.points.reverse()}})}function removeBorderNodes(g){_.each(g.nodes(),function(v){if(g.children(v).length){var node=g.node(v),t=g.node(node.borderTop),b=g.node(node.borderBottom),l=g.node(_.last(node.borderLeft)),r=g.node(_.last(node.borderRight));node.width=Math.abs(r.x-l.x);node.height=Math.abs(b.y-t.y);node.x=l.x+node.width/2;node.y=t.y+node.height/2}});_.each(g.nodes(),function(v){if(g.node(v).dummy==="border"){g.removeNode(v)}})}function removeSelfEdges(g){_.each(g.edges(),function(e){if(e.v===e.w){var node=g.node(e.v);if(!node.selfEdges){node.selfEdges=[]}node.selfEdges.push({e:e,label:g.edge(e)});g.removeEdge(e)}})}function insertSelfEdges(g){var layers=util.buildLayerMatrix(g);_.each(layers,function(layer){var orderShift=0;_.each(layer,function(v,i){var node=g.node(v);node.order=i+orderShift;_.each(node.selfEdges,function(selfEdge){util.addDummyNode(g,"selfedge",{width:selfEdge.label.width,height:selfEdge.label.height,rank:node.rank,order:i+ ++orderShift,e:selfEdge.e,label:selfEdge.label},"_se")});delete node.selfEdges})})}function positionSelfEdges(g){_.each(g.nodes(),function(v){var node=g.node(v);if(node.dummy==="selfedge"){var selfNode=g.node(node.e.v),x=selfNode.x+selfNode.width/2,y=selfNode.y,dx=node.x-x,dy=selfNode.height/2;g.setEdge(node.e,node.label);g.removeNode(v);node.label.points=[{x:x+2*dx/3,y:y-dy},{x:x+5*dx/6,y:y-dy},{x:x+dx,y:y},{x:x+5*dx/6,y:y+dy},{x:x+2*dx/3,y:y+dy}];node.label.x=node.x;node.label.y=node.y}})}function selectNumberAttrs(obj,attrs){return _.mapValues(_.pick(obj,attrs),Number)}function canonicalize(attrs){var newAttrs={};_.each(attrs,function(v,k){newAttrs[k.toLowerCase()]=v});return newAttrs}},{"./acyclic":28,"./add-border-segments":29,"./coordinate-system":30,"./graphlib":33,"./lodash":36,"./nesting-graph":37,"./normalize":38,"./order":43,"./parent-dummy-chains":48,"./position":50,"./rank":52,"./util":55}],36:[function(require,module,exports){module.exports=require(20)},{"/Users/cpettitt/projects/dagre-d3/lib/lodash.js":20,lodash:77}],37:[function(require,module,exports){var _=require("./lodash"),util=require("./util");module.exports={run:run,cleanup:cleanup};function run(g){var root=util.addDummyNode(g,"root",{},"_root"),depths=treeDepths(g),height=_.max(depths)-1,nodeSep=2*height+1;g.graph().nestingRoot=root;_.each(g.edges(),function(e){g.edge(e).minlen*=nodeSep});var weight=sumWeights(g)+1;_.each(g.children(),function(child){dfs(g,root,nodeSep,weight,height,depths,child)});g.graph().nodeRankFactor=nodeSep}function dfs(g,root,nodeSep,weight,height,depths,v){var children=g.children(v);if(!children.length){if(v!==root){g.setEdge(root,v,{weight:0,minlen:nodeSep})}return}var top=util.addBorderNode(g,"_bt"),bottom=util.addBorderNode(g,"_bb"),label=g.node(v);g.setParent(top,v);label.borderTop=top;g.setParent(bottom,v);label.borderBottom=bottom;_.each(children,function(child){dfs(g,root,nodeSep,weight,height,depths,child);var childNode=g.node(child),childTop=childNode.borderTop?childNode.borderTop:child,childBottom=childNode.borderBottom?childNode.borderBottom:child,thisWeight=childNode.borderTop?weight:2*weight,minlen=childTop!==childBottom?1:height-depths[v]+1;g.setEdge(top,childTop,{weight:thisWeight,minlen:minlen,nestingEdge:true});g.setEdge(childBottom,bottom,{weight:thisWeight,minlen:minlen,nestingEdge:true})});if(!g.parent(v)){g.setEdge(root,top,{weight:0,minlen:height+depths[v]})}}function treeDepths(g){var depths={};function dfs(v,depth){var children=g.children(v);if(children&&children.length){_.each(children,function(child){dfs(child,depth+1)})}depths[v]=depth}_.each(g.children(),function(v){dfs(v,1)});return depths}function sumWeights(g){return _.reduce(g.edges(),function(acc,e){return acc+g.edge(e).weight},0)}function cleanup(g){var graphLabel=g.graph();g.removeNode(graphLabel.nestingRoot);delete graphLabel.nestingRoot;_.each(g.edges(),function(e){var edge=g.edge(e);if(edge.nestingEdge){g.removeEdge(e)}})}},{"./lodash":36,"./util":55}],38:[function(require,module,exports){"use strict";var _=require("./lodash"),util=require("./util");module.exports={run:run,undo:undo};function run(g){g.graph().dummyChains=[];_.each(g.edges(),function(edge){normalizeEdge(g,edge)})}function normalizeEdge(g,e){var v=e.v,vRank=g.node(v).rank,w=e.w,wRank=g.node(w).rank,name=e.name,edgeLabel=g.edge(e),labelRank=edgeLabel.labelRank;if(wRank===vRank+1)return;g.removeEdge(e);var dummy,attrs,i;for(i=0,++vRank;vRank0){if(index%2){weightSum+=tree[index+1]}index=index-1>>1;tree[index]+=entry.weight}cc+=entry.weight*weightSum}));return cc}},{"../lodash":36}],43:[function(require,module,exports){"use strict";var _=require("../lodash"),initOrder=require("./init-order"),crossCount=require("./cross-count"),sortSubgraph=require("./sort-subgraph"),buildLayerGraph=require("./build-layer-graph"),addSubgraphConstraints=require("./add-subgraph-constraints"),Graph=require("../graphlib").Graph,util=require("../util");module.exports=order;function order(g){var maxRank=util.maxRank(g),downLayerGraphs=buildLayerGraphs(g,_.range(1,maxRank+1),"inEdges"),upLayerGraphs=buildLayerGraphs(g,_.range(maxRank-1,-1,-1),"outEdges");var layering=initOrder(g);assignOrder(g,layering);var bestCC=Number.POSITIVE_INFINITY,best;for(var i=0,lastBest=0;lastBest<4;++i,++lastBest){sweepLayerGraphs(i%2?downLayerGraphs:upLayerGraphs,i%4>=2);layering=util.buildLayerMatrix(g);var cc=crossCount(g,layering);if(cc=vEntry.barycenter){mergeEntries(vEntry,uEntry)}}}function handleOut(vEntry){return function(wEntry){wEntry["in"].push(vEntry);if(--wEntry.indegree===0){sourceSet.push(wEntry)}}}while(sourceSet.length){var entry=sourceSet.pop();entries.push(entry);_.each(entry["in"].reverse(),handleIn(entry));_.each(entry.out,handleOut(entry))}return _.chain(entries).filter(function(entry){return!entry.merged}).map(function(entry){return _.pick(entry,["vs","i","barycenter","weight"])}).value()}function mergeEntries(target,source){var sum=0,weight=0;if(target.weight){sum+=target.barycenter*target.weight;weight+=target.weight}if(source.weight){sum+=source.barycenter*source.weight;weight+=source.weight}target.vs=source.vs.concat(target.vs);target.barycenter=sum/weight;target.weight=weight;target.i=Math.min(source.i,target.i);source.merged=true}},{"../lodash":36}],46:[function(require,module,exports){var _=require("../lodash"),barycenter=require("./barycenter"),resolveConflicts=require("./resolve-conflicts"),sort=require("./sort");module.exports=sortSubgraph;function sortSubgraph(g,v,cg,biasRight){var movable=g.children(v),node=g.node(v),bl=node?node.borderLeft:undefined,br=node?node.borderRight:undefined,subgraphs={};if(bl){movable=_.filter(movable,function(w){return w!==bl&&w!==br})}var barycenters=barycenter(g,movable);_.each(barycenters,function(entry){if(g.children(entry.v).length){var subgraphResult=sortSubgraph(g,entry.v,cg,biasRight);subgraphs[entry.v]=subgraphResult;if(_.has(subgraphResult,"barycenter")){mergeBarycenters(entry,subgraphResult)}}});var entries=resolveConflicts(barycenters,cg);expandSubgraphs(entries,subgraphs);var result=sort(entries,biasRight);if(bl){result.vs=_.flatten([bl,result.vs,br],true);if(g.predecessors(bl).length){var blPred=g.node(g.predecessors(bl)[0]),brPred=g.node(g.predecessors(br)[0]);if(!_.has(result,"barycenter")){result.barycenter=0;result.weight=0}result.barycenter=(result.barycenter*result.weight+blPred.order+brPred.order)/(result.weight+2);result.weight+=2}}return result}function expandSubgraphs(entries,subgraphs){_.each(entries,function(entry){entry.vs=_.flatten(entry.vs.map(function(v){if(subgraphs[v]){return subgraphs[v].vs}return v}),true)})}function mergeBarycenters(target,other){if(!_.isUndefined(target.barycenter)){target.barycenter=(target.barycenter*target.weight+other.barycenter*other.weight)/(target.weight+other.weight);target.weight+=other.weight}else{target.barycenter=other.barycenter;target.weight=other.weight}}},{"../lodash":36,"./barycenter":40,"./resolve-conflicts":45,"./sort":47}],47:[function(require,module,exports){var _=require("../lodash"),util=require("../util");module.exports=sort;function sort(entries,biasRight){var parts=util.partition(entries,function(entry){return _.has(entry,"barycenter")});var sortable=parts.lhs,unsortable=_.sortBy(parts.rhs,function(entry){return-entry.i}),vs=[],sum=0,weight=0,vsIndex=0;sortable.sort(compareWithBias(!!biasRight));vsIndex=consumeUnsortable(vs,unsortable,vsIndex);_.each(sortable,function(entry){vsIndex+=entry.vs.length;vs.push(entry.vs);sum+=entry.barycenter*entry.weight;weight+=entry.weight;vsIndex=consumeUnsortable(vs,unsortable,vsIndex)});var result={vs:_.flatten(vs,true)};if(weight){result.barycenter=sum/weight;result.weight=weight}return result}function consumeUnsortable(vs,unsortable,index){var last;while(unsortable.length&&(last=_.last(unsortable)).i<=index){unsortable.pop();vs.push(last.vs);index++}return index}function compareWithBias(bias){return function(entryV,entryW){if(entryV.barycenterentryW.barycenter){return 1}return!bias?entryV.i-entryW.i:entryW.i-entryV.i}}},{"../lodash":36,"../util":55}],48:[function(require,module,exports){var _=require("./lodash");module.exports=parentDummyChains;function parentDummyChains(g){var postorderNums=postorder(g);_.each(g.graph().dummyChains,function(v){var node=g.node(v),edgeObj=node.edgeObj,pathData=findPath(g,postorderNums,edgeObj.v,edgeObj.w),path=pathData.path,lca=pathData.lca,pathIdx=0,pathV=path[pathIdx],ascending=true;while(v!==edgeObj.w){node=g.node(v);if(ascending){while((pathV=path[pathIdx])!==lca&&g.node(pathV).maxRanklow||lim>postorderNums[parent].lim));lca=parent;parent=w;while((parent=g.parent(parent))!==lca){wPath.push(parent)}return{path:vPath.concat(wPath.reverse()),lca:lca}}function postorder(g){var result={},lim=0;function dfs(v){var low=lim;_.each(g.children(v),dfs);result[v]={low:low,lim:lim++}}_.each(g.children(),dfs);return result}},{"./lodash":36}],49:[function(require,module,exports){"use strict";var _=require("../lodash"),Graph=require("../graphlib").Graph,util=require("../util");module.exports={positionX:positionX,findType1Conflicts:findType1Conflicts,findType2Conflicts:findType2Conflicts,addConflict:addConflict,hasConflict:hasConflict,verticalAlignment:verticalAlignment,horizontalCompaction:horizontalCompaction,alignCoordinates:alignCoordinates,findSmallestWidthAlignment:findSmallestWidthAlignment,balance:balance};function findType1Conflicts(g,layering){var conflicts={};function visitLayer(prevLayer,layer){var k0=0,scanPos=0,prevLayerLength=prevLayer.length,lastNode=_.last(layer);_.each(layer,function(v,i){var w=findOtherInnerSegmentNode(g,v),k1=w?g.node(w).order:prevLayerLength;if(w||v===lastNode){_.each(layer.slice(scanPos,i+1),function(scanNode){_.each(g.predecessors(scanNode),function(u){var uLabel=g.node(u),uPos=uLabel.order;if((uPosnextNorthBorder)){addConflict(conflicts,u,v)}})}})}function visitLayer(north,south){var prevNorthPos=-1,nextNorthPos,southPos=0;_.each(south,function(v,southLookahead){if(g.node(v).dummy==="border"){var predecessors=g.predecessors(v);if(predecessors.length){nextNorthPos=g.node(predecessors[0]).order;scan(south,southPos,southLookahead,prevNorthPos,nextNorthPos);southPos=southLookahead;prevNorthPos=nextNorthPos}}scan(south,southPos,south.length,nextNorthPos,north.length)});return south}_.reduce(layering,visitLayer);return conflicts}function findOtherInnerSegmentNode(g,v){if(g.node(v).dummy){return _.find(g.predecessors(v),function(u){return g.node(u).dummy})}}function addConflict(conflicts,v,w){if(v>w){var tmp=v;v=w;w=tmp}var conflictsV=conflicts[v];if(!conflictsV){conflicts[v]=conflictsV={}}conflictsV[w]=true}function hasConflict(conflicts,v,w){if(v>w){var tmp=v;v=w;w=tmp}return _.has(conflicts[v],w)}function verticalAlignment(g,layering,conflicts,neighborFn){var root={},align={},pos={};_.each(layering,function(layer){_.each(layer,function(v,order){root[v]=v;align[v]=v;pos[v]=order})});_.each(layering,function(layer){var prevIdx=-1;_.each(layer,function(v){var ws=neighborFn(v);if(ws.length){ws=_.sortBy(ws,function(w){return pos[w]});var mp=(ws.length-1)/2;for(var i=Math.floor(mp),il=Math.ceil(mp);i<=il;++i){var w=ws[i];if(align[v]===v&&prevIdxwLabel.lim){tailLabel=wLabel;flip=true}var candidates=_.filter(g.edges(),function(edge){return flip===isDescendant(t,t.node(edge.v),tailLabel)&&flip!==isDescendant(t,t.node(edge.w),tailLabel)});return _.min(candidates,function(edge){return slack(g,edge)})}function exchangeEdges(t,g,e,f){var v=e.v,w=e.w;t.removeEdge(v,w);t.setEdge(f.v,f.w,{});initLowLimValues(t);initCutValues(t,g);updateRanks(t,g)}function updateRanks(t,g){var root=_.find(t.nodes(),function(v){return!g.node(v).parent}),vs=preorder(t,root);vs=vs.slice(1);_.each(vs,function(v){var parent=t.node(v).parent,edge=g.edge(v,parent),flipped=false;if(!edge){edge=g.edge(parent,v);flipped=true}g.node(v).rank=g.node(parent).rank+(flipped?edge.minlen:-edge.minlen)})}function isTreeEdge(tree,u,v){return tree.hasEdge(u,v)}function isDescendant(tree,vLabel,rootLabel){return rootLabel.low<=vLabel.lim&&vLabel.lim<=rootLabel.lim}},{"../graphlib":33,"../lodash":36,"../util":55,"./feasible-tree":51,"./util":54}],54:[function(require,module,exports){"use strict";var _=require("../lodash");module.exports={longestPath:longestPath,slack:slack};function longestPath(g){var visited={};function dfs(v){var label=g.node(v);if(_.has(visited,v)){return label.rank}visited[v]=true;var rank=_.min(_.map(g.outEdges(v),function(e){return dfs(e.w)-g.edge(e).minlen}));if(rank===Number.POSITIVE_INFINITY){rank=0}return label.rank=rank}_.each(g.sources(),dfs)}function slack(g,e){return g.node(e.w).rank-g.node(e.v).rank-g.edge(e).minlen}},{"../lodash":36}],55:[function(require,module,exports){"use strict";var _=require("./lodash"),Graph=require("./graphlib").Graph;module.exports={addDummyNode:addDummyNode,simplify:simplify,asNonCompoundGraph:asNonCompoundGraph,successorWeights:successorWeights,predecessorWeights:predecessorWeights,intersectRect:intersectRect,buildLayerMatrix:buildLayerMatrix,normalizeRanks:normalizeRanks,removeEmptyRanks:removeEmptyRanks,addBorderNode:addBorderNode,maxRank:maxRank,partition:partition,time:time,notime:notime};function addDummyNode(g,type,attrs,name){var v;do{v=_.uniqueId(name)}while(g.hasNode(v));attrs.dummy=type;g.setNode(v,attrs);return v}function simplify(g){var simplified=(new Graph).setGraph(g.graph());_.each(g.nodes(),function(v){simplified.setNode(v,g.node(v))});_.each(g.edges(),function(e){var simpleLabel=simplified.edge(e.v,e.w)||{weight:0,minlen:1},label=g.edge(e);simplified.setEdge(e.v,e.w,{weight:simpleLabel.weight+label.weight,minlen:Math.max(simpleLabel.minlen,label.minlen)})});return simplified}function asNonCompoundGraph(g){var simplified=new Graph({multigraph:g.isMultigraph()}).setGraph(g.graph());_.each(g.nodes(),function(v){if(!g.children(v).length){simplified.setNode(v,g.node(v))}});_.each(g.edges(),function(e){simplified.setEdge(e,g.edge(e))});return simplified}function successorWeights(g){var weightMap=_.map(g.nodes(),function(v){var sucs={};_.each(g.outEdges(v),function(e){sucs[e.w]=(sucs[e.w]||0)+g.edge(e).weight});return sucs});return _.zipObject(g.nodes(),weightMap)}function predecessorWeights(g){var weightMap=_.map(g.nodes(),function(v){var preds={};_.each(g.inEdges(v),function(e){preds[e.v]=(preds[e.v]||0)+g.edge(e).weight});return preds});return _.zipObject(g.nodes(),weightMap)}function intersectRect(rect,point){var x=rect.x;var y=rect.y;var dx=point.x-x;var dy=point.y-y;var w=rect.width/2;var h=rect.height/2;if(!dx&&!dy){throw new Error("Not possible to find intersection inside of the rectangle")}var sx,sy;if(Math.abs(dy)*w>Math.abs(dx)*h){if(dy<0){h=-h}sx=h*dx/dy;sy=h}else{if(dx<0){w=-w}sx=w;sy=w*dy/dx}return{x:x+sx,y:y+sy}}function buildLayerMatrix(g){var layering=_.map(_.range(maxRank(g)+1),function(){return[] +});_.each(g.nodes(),function(v){var node=g.node(v),rank=node.rank;if(!_.isUndefined(rank)){layering[rank][node.order]=v}});return layering}function normalizeRanks(g){var min=_.min(_.map(g.nodes(),function(v){return g.node(v).rank}));_.each(g.nodes(),function(v){var node=g.node(v);if(_.has(node,"rank")){node.rank-=min}})}function removeEmptyRanks(g){var offset=_.min(_.map(g.nodes(),function(v){return g.node(v).rank}));var layers=[];_.each(g.nodes(),function(v){var rank=g.node(v).rank-offset;if(!_.has(layers,rank)){layers[rank]=[]}layers[rank].push(v)});var delta=0,nodeRankFactor=g.graph().nodeRankFactor;_.each(layers,function(vs,i){if(_.isUndefined(vs)&&i%nodeRankFactor!==0){--delta}else if(delta){_.each(vs,function(v){g.node(v).rank+=delta})}})}function addBorderNode(g,prefix,rank,order){var node={width:0,height:0};if(arguments.length>=4){node.rank=rank;node.order=order}return addDummyNode(g,"border",node,prefix)}function maxRank(g){return _.max(_.map(g.nodes(),function(v){var rank=g.node(v).rank;if(!_.isUndefined(rank)){return rank}}))}function partition(collection,fn){var result={lhs:[],rhs:[]};_.each(collection,function(value){if(fn(value)){result.lhs.push(value)}else{result.rhs.push(value)}});return result}function time(name,fn){var start=_.now();try{return fn()}finally{console.log(name+" time: "+(_.now()-start)+"ms")}}function notime(name,fn){return fn()}},{"./graphlib":33,"./lodash":36}],56:[function(require,module,exports){module.exports="0.7.1"},{}],57:[function(require,module,exports){var lib=require("./lib");module.exports={Graph:lib.Graph,json:require("./lib/json"),alg:require("./lib/alg"),version:lib.version}},{"./lib":73,"./lib/alg":64,"./lib/json":74}],58:[function(require,module,exports){var _=require("../lodash");module.exports=components;function components(g){var visited={},cmpts=[],cmpt;function dfs(v){if(_.has(visited,v))return;visited[v]=true;cmpt.push(v);_.each(g.successors(v),dfs);_.each(g.predecessors(v),dfs)}_.each(g.nodes(),function(v){cmpt=[];dfs(v);if(cmpt.length){cmpts.push(cmpt)}});return cmpts}},{"../lodash":75}],59:[function(require,module,exports){var _=require("../lodash");module.exports=dfs;function dfs(g,vs,order){if(!_.isArray(vs)){vs=[vs]}var acc=[],visited={};_.each(vs,function(v){if(!g.hasNode(v)){throw new Error("Graph does not have node: "+v)}doDfs(g,v,order==="post",visited,acc)});return acc}function doDfs(g,v,postorder,visited,acc){if(!_.has(visited,v)){visited[v]=true;if(!postorder){acc.push(v)}_.each(g.neighbors(v),function(w){doDfs(g,w,postorder,visited,acc)});if(postorder){acc.push(v)}}}},{"../lodash":75}],60:[function(require,module,exports){var dijkstra=require("./dijkstra"),_=require("../lodash");module.exports=dijkstraAll;function dijkstraAll(g,weightFunc,edgeFunc){return _.transform(g.nodes(),function(acc,v){acc[v]=dijkstra(g,v,weightFunc,edgeFunc)},{})}},{"../lodash":75,"./dijkstra":61}],61:[function(require,module,exports){var _=require("../lodash"),PriorityQueue=require("../data/priority-queue");module.exports=dijkstra;var DEFAULT_WEIGHT_FUNC=_.constant(1);function dijkstra(g,source,weightFn,edgeFn){return runDijkstra(g,String(source),weightFn||DEFAULT_WEIGHT_FUNC,edgeFn||function(v){return g.outEdges(v)})}function runDijkstra(g,source,weightFn,edgeFn){var results={},pq=new PriorityQueue,v,vEntry;var updateNeighbors=function(edge){var w=edge.v!==v?edge.v:edge.w,wEntry=results[w],weight=weightFn(edge),distance=vEntry.distance+weight;if(weight<0){throw new Error("dijkstra does not allow negative edge weights. 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    ").addClass(errClass).css("position", "absolute") + .css("top", el.offsetTop) + .css("left", el.offsetLeft) + // setting width can push out the page size, forcing otherwise + // unnecessary scrollbars to appear and making it impossible for + // the element to shrink; so use max-width instead + .css("maxWidth", el.offsetWidth) + .css("height", el.offsetHeight); + errorDiv.text(err.message); + $el.after(errorDiv); + + // Really dumb way to keep the size/position of the error in sync with + // the parent element as the window is resized or whatever. + var intId = setInterval(function() { + if (!errorDiv[0].parentElement) { + clearInterval(intId); + return; + } + errorDiv + .css("top", el.offsetTop) + .css("left", el.offsetLeft) + .css("maxWidth", el.offsetWidth) + .css("height", el.offsetHeight); + }, 500); + } + } + }, + clearError: function(el) { + var $el = $(el); + var display = $el.data("restore-display-mode"); + $el.data("restore-display-mode", null); + + if (display === "inline" || display === "inline-block") { + if (display) + $el.css("display", display); + $(el.nextSibling).filter(".htmlwidgets-error").remove(); + } else if (display === "block"){ + $el.css("visibility", "inherit"); + $(el.nextSibling).filter(".htmlwidgets-error").remove(); + } + }, + sizing: {} + }; + + // Called by widget bindings to register a new type of widget. The definition + // object can contain the following properties: + // - name (required) - A string indicating the binding name, which will be + // used by default as the CSS classname to look for. + // - initialize (optional) - A function(el) that will be called once per + // widget element; if a value is returned, it will be passed as the third + // value to renderValue. + // - renderValue (required) - A function(el, data, initValue) that will be + // called with data. Static contexts will cause this to be called once per + // element; Shiny apps will cause this to be called multiple times per + // element, as the data changes. + window.HTMLWidgets.widget = function(definition) { + if (!definition.name) { + throw new Error("Widget must have a name"); + } + if (!definition.type) { + throw new Error("Widget must have a type"); + } + // Currently we only support output widgets + if (definition.type !== "output") { + throw new Error("Unrecognized widget type '" + definition.type + "'"); + } + // TODO: Verify that .name is a valid CSS classname + + // Support new-style instance-bound definitions. Old-style class-bound + // definitions have one widget "object" per widget per type/class of + // widget; the renderValue and resize methods on such widget objects + // take el and instance arguments, because the widget object can't + // store them. New-style instance-bound definitions have one widget + // object per widget instance; the definition that's passed in doesn't + // provide renderValue or resize methods at all, just the single method + // factory(el, width, height) + // which returns an object that has renderValue(x) and resize(w, h). + // This enables a far more natural programming style for the widget + // author, who can store per-instance state using either OO-style + // instance fields or functional-style closure variables (I guess this + // is in contrast to what can only be called C-style pseudo-OO which is + // what we required before). + if (definition.factory) { + definition = createLegacyDefinitionAdapter(definition); + } + + if (!definition.renderValue) { + throw new Error("Widget must have a renderValue function"); + } + + // For static rendering (non-Shiny), use a simple widget registration + // scheme. We also use this scheme for Shiny apps/documents that also + // contain static widgets. + window.HTMLWidgets.widgets = window.HTMLWidgets.widgets || []; + // Merge defaults into the definition; don't mutate the original definition. + var staticBinding = extend({}, defaults, definition); + overrideMethod(staticBinding, "find", function(superfunc) { + return function(scope) { + var results = superfunc(scope); + // Filter out Shiny outputs, we only want the static kind + return filterByClass(results, "html-widget-output", false); + }; + }); + window.HTMLWidgets.widgets.push(staticBinding); + + if (shinyMode) { + // Shiny is running. Register the definition with an output binding. + // The definition itself will not be the output binding, instead + // we will make an output binding object that delegates to the + // definition. This is because we foolishly used the same method + // name (renderValue) for htmlwidgets definition and Shiny bindings + // but they actually have quite different semantics (the Shiny + // bindings receive data that includes lots of metadata that it + // strips off before calling htmlwidgets renderValue). We can't + // just ignore the difference because in some widgets it's helpful + // to call this.renderValue() from inside of resize(), and if + // we're not delegating, then that call will go to the Shiny + // version instead of the htmlwidgets version. + + // Merge defaults with definition, without mutating either. + var bindingDef = extend({}, defaults, definition); + + // This object will be our actual Shiny binding. + var shinyBinding = new Shiny.OutputBinding(); + + // With a few exceptions, we'll want to simply use the bindingDef's + // version of methods if they are available, otherwise fall back to + // Shiny's defaults. NOTE: If Shiny's output bindings gain additional + // methods in the future, and we want them to be overrideable by + // HTMLWidget binding definitions, then we'll need to add them to this + // list. + delegateMethod(shinyBinding, bindingDef, "getId"); + delegateMethod(shinyBinding, bindingDef, "onValueChange"); + delegateMethod(shinyBinding, bindingDef, "onValueError"); + delegateMethod(shinyBinding, bindingDef, "renderError"); + delegateMethod(shinyBinding, bindingDef, "clearError"); + delegateMethod(shinyBinding, bindingDef, "showProgress"); + + // The find, renderValue, and resize are handled differently, because we + // want to actually decorate the behavior of the bindingDef methods. + + shinyBinding.find = function(scope) { + var results = bindingDef.find(scope); + + // Only return elements that are Shiny outputs, not static ones + var dynamicResults = results.filter(".html-widget-output"); + + // It's possible that whatever caused Shiny to think there might be + // new dynamic outputs, also caused there to be new static outputs. + // Since there might be lots of different htmlwidgets bindings, we + // schedule execution for later--no need to staticRender multiple + // times. + if (results.length !== dynamicResults.length) + scheduleStaticRender(); + + return dynamicResults; + }; + + // Wrap renderValue to handle initialization, which unfortunately isn't + // supported natively by Shiny at the time of this writing. + + shinyBinding.renderValue = function(el, data) { + Shiny.renderDependencies(data.deps); + // Resolve strings marked as javascript literals to objects + if (!(data.evals instanceof Array)) data.evals = [data.evals]; + for (var i = 0; data.evals && i < data.evals.length; i++) { + window.HTMLWidgets.evaluateStringMember(data.x, data.evals[i]); + } + if (!bindingDef.renderOnNullValue) { + if (data.x === null) { + el.style.visibility = "hidden"; + return; + } else { + el.style.visibility = "inherit"; + } + } + if (!elementData(el, "initialized")) { + initSizing(el); + + elementData(el, "initialized", true); + if (bindingDef.initialize) { + var result = bindingDef.initialize(el, el.offsetWidth, + el.offsetHeight); + elementData(el, "init_result", result); + } + } + bindingDef.renderValue(el, data.x, elementData(el, "init_result")); + evalAndRun(data.jsHooks.render, elementData(el, "init_result"), [el, data.x]); + }; + + // Only override resize if bindingDef implements it + if (bindingDef.resize) { + shinyBinding.resize = function(el, width, height) { + // Shiny can call resize before initialize/renderValue have been + // called, which doesn't make sense for widgets. + if (elementData(el, "initialized")) { + bindingDef.resize(el, width, height, elementData(el, "init_result")); + } + }; + } + + Shiny.outputBindings.register(shinyBinding, bindingDef.name); + } + }; + + var scheduleStaticRenderTimerId = null; + function scheduleStaticRender() { + if (!scheduleStaticRenderTimerId) { + scheduleStaticRenderTimerId = setTimeout(function() { + scheduleStaticRenderTimerId = null; + window.HTMLWidgets.staticRender(); + }, 1); + } + } + + // Render static widgets after the document finishes loading + // Statically render all elements that are of this widget's class + window.HTMLWidgets.staticRender = function() { + var bindings = window.HTMLWidgets.widgets || []; + forEach(bindings, function(binding) { + var matches = binding.find(document.documentElement); + forEach(matches, function(el) { + var sizeObj = initSizing(el, binding); + + if (hasClass(el, "html-widget-static-bound")) + return; + el.className = el.className + " html-widget-static-bound"; + + var initResult; + if (binding.initialize) { + initResult = binding.initialize(el, + sizeObj ? sizeObj.getWidth() : el.offsetWidth, + sizeObj ? sizeObj.getHeight() : el.offsetHeight + ); + elementData(el, "init_result", initResult); + } + + if (binding.resize) { + var lastSize = {}; + var resizeHandler = function(e) { + var size = { + w: sizeObj ? sizeObj.getWidth() : el.offsetWidth, + h: sizeObj ? sizeObj.getHeight() : el.offsetHeight + }; + if (size.w === 0 && size.h === 0) + return; + if (size.w === lastSize.w && size.h === lastSize.h) + return; + lastSize = size; + binding.resize(el, size.w, size.h, initResult); + }; + + on(window, "resize", resizeHandler); + + // This is needed for cases where we're running in a Shiny + // app, but the widget itself is not a Shiny output, but + // rather a simple static widget. One example of this is + // an rmarkdown document that has runtime:shiny and widget + // that isn't in a render function. Shiny only knows to + // call resize handlers for Shiny outputs, not for static + // widgets, so we do it ourselves. + if (window.jQuery) { + window.jQuery(document).on( + "shown.htmlwidgets shown.bs.tab.htmlwidgets shown.bs.collapse.htmlwidgets", + resizeHandler + ); + window.jQuery(document).on( + "hidden.htmlwidgets hidden.bs.tab.htmlwidgets hidden.bs.collapse.htmlwidgets", + resizeHandler + ); + } + + // This is needed for the specific case of ioslides, which + // flips slides between display:none and display:block. + // Ideally we would not have to have ioslide-specific code + // here, but rather have ioslides raise a generic event, + // but the rmarkdown package just went to CRAN so the + // window to getting that fixed may be long. + if (window.addEventListener) { + // It's OK to limit this to window.addEventListener + // browsers because ioslides itself only supports + // such browsers. + on(document, "slideenter", resizeHandler); + on(document, "slideleave", resizeHandler); + } + } + + var scriptData = document.querySelector("script[data-for='" + el.id + "'][type='application/json']"); + if (scriptData) { + var data = JSON.parse(scriptData.textContent || scriptData.text); + // Resolve strings marked as javascript literals to objects + if (!(data.evals instanceof Array)) data.evals = [data.evals]; + for (var k = 0; data.evals && k < data.evals.length; k++) { + window.HTMLWidgets.evaluateStringMember(data.x, data.evals[k]); + } + binding.renderValue(el, data.x, initResult); + evalAndRun(data.jsHooks.render, initResult, [el, data.x]); + } + }); + }); + + invokePostRenderHandlers(); + } + + // Wait until after the document has loaded to render the widgets. + if (document.addEventListener) { + document.addEventListener("DOMContentLoaded", function() { + document.removeEventListener("DOMContentLoaded", arguments.callee, false); + window.HTMLWidgets.staticRender(); + }, false); + } else if (document.attachEvent) { + document.attachEvent("onreadystatechange", function() { + if (document.readyState === "complete") { + document.detachEvent("onreadystatechange", arguments.callee); + window.HTMLWidgets.staticRender(); + } + }); + } + + + window.HTMLWidgets.getAttachmentUrl = function(depname, key) { + // If no key, default to the first item + if (typeof(key) === "undefined") + key = 1; + + var link = document.getElementById(depname + "-" + key + "-attachment"); + if (!link) { + throw new Error("Attachment " + depname + "/" + key + " not found in document"); + } + return link.getAttribute("href"); + }; + + window.HTMLWidgets.dataframeToD3 = function(df) { + var names = []; + var length; + for (var name in df) { + if (df.hasOwnProperty(name)) + names.push(name); + if (typeof(df[name]) !== "object" || typeof(df[name].length) === "undefined") { + throw new Error("All fields must be arrays"); + } else if (typeof(length) !== "undefined" && length !== df[name].length) { + throw new Error("All fields must be arrays of the same length"); + } + length = df[name].length; + } + var results = []; + var item; + for (var row = 0; row < length; row++) { + item = {}; + for (var col = 0; col < names.length; col++) { + item[names[col]] = df[names[col]][row]; + } + results.push(item); + } + return results; + }; + + window.HTMLWidgets.transposeArray2D = function(array) { + if (array.length === 0) return array; + var newArray = array[0].map(function(col, i) { + return array.map(function(row) { + return row[i] + }) + }); + return newArray; + }; + // Split value at splitChar, but allow splitChar to be escaped + // using escapeChar. Any other characters escaped by escapeChar + // will be included as usual (including escapeChar itself). + function splitWithEscape(value, splitChar, escapeChar) { + var results = []; + var escapeMode = false; + var currentResult = ""; + for (var pos = 0; pos < value.length; pos++) { + if (!escapeMode) { + if (value[pos] === splitChar) { + results.push(currentResult); + currentResult = ""; + } else if (value[pos] === escapeChar) { + escapeMode = true; + } else { + currentResult += value[pos]; + } + } else { + currentResult += value[pos]; + escapeMode = false; + } + } + if (currentResult !== "") { + results.push(currentResult); + } + return results; + } + // Function authored by Yihui/JJ Allaire + window.HTMLWidgets.evaluateStringMember = function(o, member) { + var parts = splitWithEscape(member, '.', '\\'); + for (var i = 0, l = parts.length; i < l; i++) { + var part = parts[i]; + // part may be a character or 'numeric' member name + if (o !== null && typeof o === "object" && part in o) { + if (i == (l - 1)) { // if we are at the end of the line then evalulate + if (typeof o[part] === "string") + o[part] = eval("(" + o[part] + ")"); + } else { // otherwise continue to next embedded object + o = o[part]; + } + } + } + }; + + // Retrieve the HTMLWidget instance (i.e. the return value of an + // HTMLWidget binding's initialize() or factory() function) + // associated with an element, or null if none. + window.HTMLWidgets.getInstance = function(el) { + return elementData(el, "init_result"); + }; + + // Finds the first element in the scope that matches the selector, + // and returns the HTMLWidget instance (i.e. the return value of + // an HTMLWidget binding's initialize() or factory() function) + // associated with that element, if any. If no element matches the + // selector, or the first matching element has no HTMLWidget + // instance associated with it, then null is returned. + // + // The scope argument is optional, and defaults to window.document. + window.HTMLWidgets.find = function(scope, selector) { + if (arguments.length == 1) { + selector = scope; + scope = document; + } + + var el = scope.querySelector(selector); + if (el === null) { + return null; + } else { + return window.HTMLWidgets.getInstance(el); + } + }; + + // Finds all elements in the scope that match the selector, and + // returns the HTMLWidget instances (i.e. the return values of + // an HTMLWidget binding's initialize() or factory() function) + // associated with the elements, in an array. If elements that + // match the selector don't have an associated HTMLWidget + // instance, the returned array will contain nulls. + // + // The scope argument is optional, and defaults to window.document. + window.HTMLWidgets.findAll = function(scope, selector) { + if (arguments.length == 1) { + selector = scope; + scope = document; + } + + var nodes = scope.querySelectorAll(selector); + var results = []; + for (var i = 0; i < nodes.length; i++) { + results.push(window.HTMLWidgets.getInstance(nodes[i])); + } + return results; + }; + + var postRenderHandlers = []; + function invokePostRenderHandlers() { + while (postRenderHandlers.length) { + var handler = postRenderHandlers.shift(); + if (handler) { + handler(); + } + } + } + + // Register the given callback function to be invoked after the + // next time static widgets are rendered. + window.HTMLWidgets.addPostRenderHandler = function(callback) { + postRenderHandlers.push(callback); + }; + + // Takes a new-style instance-bound definition, and returns an + // old-style class-bound definition. This saves us from having + // to rewrite all the logic in this file to accomodate both + // types of definitions. + function createLegacyDefinitionAdapter(defn) { + var result = { + name: defn.name, + type: defn.type, + initialize: function(el, width, height) { + return defn.factory(el, width, height); + }, + renderValue: function(el, x, instance) { + return instance.renderValue(x); + }, + resize: function(el, width, height, instance) { + return instance.resize(width, height); + } + }; + + if (defn.find) + result.find = defn.find; + if (defn.renderError) + result.renderError = defn.renderError; + if (defn.clearError) + result.clearError = defn.clearError; + + return result; + } +})(); + diff --git a/docs/index_files/mermaid-0.3.0/LICENSE b/docs/index_files/mermaid-0.3.0/LICENSE new file mode 100644 index 0000000..faae921 --- /dev/null +++ b/docs/index_files/mermaid-0.3.0/LICENSE @@ -0,0 +1,22 @@ +The MIT License (MIT) + +Copyright (c) 2014 Knut Sveidqvist + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. + diff --git a/docs/index_files/mermaid-0.3.0/dist/mermaid.css b/docs/index_files/mermaid-0.3.0/dist/mermaid.css new file mode 100755 index 0000000..d169f84 --- /dev/null +++ b/docs/index_files/mermaid-0.3.0/dist/mermaid.css @@ -0,0 +1,275 @@ +/* Flowchart variables */ +/* Sequence Diagram variables */ +/* Gantt chart variables */ +.mermaid .label { + color: #333333; + font-weight: 400; +} + +.mermaid .node rect, +.node circle, +.mermaid .node ellipse, +.mermaid .node polygon { + fill: #ECECFF; + stroke: #CCCCFF; + stroke-width: 1px; +} +.mermaid .edgePath .path { + stroke: #333333; +} + +.mermaid g .edgeLabel { + background-color: white; +} + +.mermaid .cluster rect { + fill: #ffffde !important; + rx: 4 !important; + stroke: #aaaa33 !important; + stroke-width: 1px !important; +} +.mermaid .cluster text { + fill: #333333; +} +.mermaid .actor { + stroke: #CCCCFF; + fill: #ECECFF; +} +.mermaid text.actor { + fill: black; + stroke: none; +} +.mermaid .actor-line { + stroke: grey; +} +.mermaid .messageLine0 { + stroke-width: 1.5; + stroke-dasharray: "2 2"; + stroke: #333333; +} +.mermaid .messageLine1 { + stroke-width: 1.5; + stroke-dasharray: "2 2"; + stroke: #333333; +} +.mermaid #arrowhead { + fill: #333333; +} +.mermaid #crosshead path { + fill: #333333 !important; + stroke: #333333 !important; +} +.mermaid .messageText { + fill: #333333; + stroke: none; +} +.mermaid .labelBox { + stroke: #CCCCFF; + fill: #ECECFF; +} +.mermaid .labelText { + fill: black; + stroke: none; +} +.mermaid .loopText { + fill: black; + stroke: none; +} +.mermaid .loopLine { + stroke-width: 2; + stroke-dasharray: "2 2"; + stroke: #CCCCFF; +} +.mermaid .note { + stroke: #aaaa33; + fill: #fff5ad; +} +.mermaid .noteText { + fill: black; + stroke: none; + font-family: 'trebuchet ms', verdana, arial; + font-size: 14px; +} +/** Section styling */ +.mermaid .section { + stroke: none; + opacity: 0.2; +} +.mermaid .section0 { + fill: rgba(102, 102, 255, 0.49); +} +.mermaid .section2 { + fill: #fff400; +} +.mermaid .section1, +.mermaid .section3 { + fill: white; + opacity: 0.2; +} +.mermaid .sectionTitle0 { + fill: #333333; +} +.mermaid .sectionTitle1 { + fill: #333333; +} +.mermaid .sectionTitle2 { + fill: #333333; +} +.mermaid .sectionTitle3 { + fill: #333333; +} +.mermaid .sectionTitle { + text-anchor: start; + font-size: 11px; + text-height: 14px; +} +/* Grid and axis */ +.mermaid .grid .tick { + stroke: lightgrey; + opacity: 0.3; + shape-rendering: crispEdges; +} +.mermaid .grid path { + stroke-width: 0; +} +/* Today line */ +.mermaid .today { + fill: none; + stroke: red; + stroke-width: 2px; +} +/* Task styling */ +/* Default task */ +.mermaid .task { + stroke-width: 2; +} +.mermaid .taskText { + text-anchor: middle; + font-size: 11px; +} +.mermaid .taskTextOutsideRight { + fill: black; + text-anchor: start; + font-size: 11px; +} +.mermaid .taskTextOutsideLeft { + fill: black; + text-anchor: end; + font-size: 11px; +} +/* Specific task settings for the sections*/ +.mermaid .taskText0, +.mermaid .taskText1, +.mermaid .taskText2, +.mermaid .taskText3 { + fill: white; +} +.mermaid .task0, +.mermaid .task1, +.mermaid .task2, +.mermaid .task3 { + fill: #8a90dd; + stroke: #534fbc; +} +.mermaid .taskTextOutside0, +.mermaid .taskTextOutside2 { + fill: black; +} +.mermaid .taskTextOutside1, +.mermaid .taskTextOutside3 { + fill: black; +} +/* Active task */ +.mermaid .active0, +.mermaid .active1, +.mermaid .active2, +.mermaid .active3 { + fill: #bfc7ff; + stroke: #534fbc; +} +.mermaid .activeText0, +.mermaid .activeText1, +.mermaid .activeText2, +.mermaid .activeText3 { + fill: black !important; +} +/* Completed task */ +.mermaid .done0, +.mermaid .done1, +.mermaid .done2, +.mermaid .done3 { + stroke: grey; + fill: lightgrey; + stroke-width: 2; +} +.mermaid .doneText0, +.mermaid .doneText1, +.mermaid .doneText2, +.mermaid .doneText3 { + fill: black !important; +} +/* Tasks on the critical line */ +.mermaid .crit0, +.mermaid .crit1, +.mermaid .crit2, +.mermaid .crit3 { + stroke: #ff8888; + fill: red; + stroke-width: 2; +} +.mermaid .activeCrit0, +.mermaid .activeCrit1, +.mermaid .activeCrit2, +.mermaid .activeCrit3 { + stroke: #ff8888; + fill: #bfc7ff; + stroke-width: 2; +} +.mermaid .doneCrit0, +.mermaid .doneCrit1, +.mermaid .doneCrit2, +.mermaid .doneCrit3 { + stroke: #ff8888; + fill: lightgrey; + stroke-width: 2; + cursor: pointer; + shape-rendering: crispEdges; +} +.mermaid .doneCritText0, +.mermaid .doneCritText1, +.mermaid .doneCritText2, +.mermaid .doneCritText3 { + fill: black !important; +} +.mermaid .activeCritText0, +.mermaid .activeCritText1, +.mermaid .activeCritText2, +.mermaid .activeCritText3 { + fill: black !important; +} +.mermaid .titleText { + text-anchor: middle; + font-size: 18px; + fill: black; +} +/* + + +*/ +.node text { + font-family: 'trebuchet ms', verdana, arial; + font-size: 14px; +} +div.mermaidTooltip { + position: absolute; + text-align: center; + max-width: 200px; + padding: 2px; + font-family: 'trebuchet ms', verdana, arial; + font-size: 12px; + background: #ffffde; + border: 1px solid #aaaa33; + border-radius: 2px; + pointer-events: none; + z-index: 100; +} diff --git a/docs/index_files/mermaid-0.3.0/dist/mermaid.slim.min.js b/docs/index_files/mermaid-0.3.0/dist/mermaid.slim.min.js new file mode 100644 index 0000000..7657103 --- /dev/null +++ b/docs/index_files/mermaid-0.3.0/dist/mermaid.slim.min.js @@ -0,0 +1,12 @@ +!function(t){if("object"==typeof exports&&"undefined"!=typeof module)module.exports=t();else if("function"==typeof define&&define.amd)define([],t);else{var e;"undefined"!=typeof window?e=window:"undefined"!=typeof global?e=global:"undefined"!=typeof self&&(e=self),e.mermaid=t()}}(function(){var 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╔",boxh:"─",boxH:"═",boxhd:"┬",boxHd:"╤",boxhD:"╥",boxHD:"╦",boxhu:"┴",boxHu:"╧",boxhU:"╨",boxHU:"╩",boxminus:"⊟",boxplus:"⊞",boxtimes:"⊠",boxul:"┘",boxuL:"╛",boxUl:"╜",boxUL:"╝",boxur:"└",boxuR:"╘",boxUr:"╙",boxUR:"╚",boxv:"│",boxV:"║",boxvh:"┼",boxvH:"╪",boxVh:"╫",boxVH:"╬",boxvl:"┤",boxvL:"╡",boxVl:"╢",boxVL:"╣",boxvr:"├",boxvR:"╞",boxVr:"╟",boxVR:"╠",bprime:"‵",breve:"˘",Breve:"˘",brvbar:"¦",bscr:"𝒷",Bscr:"ℬ",bsemi:"⁏",bsim:"∽",bsime:"⋍",bsolb:"⧅",bsol:"\\",bsolhsub:"⟈",bull:"•",bullet:"•",bump:"≎",bumpE:"⪮",bumpe:"≏",Bumpeq:"≎",bumpeq:"≏",Cacute:"Ć",cacute:"ć",capand:"⩄",capbrcup:"⩉",capcap:"⩋",cap:"∩",Cap:"⋒",capcup:"⩇",capdot:"⩀",CapitalDifferentialD:"ⅅ",caps:"∩︀",caret:"⁁",caron:"ˇ",Cayleys:"ℭ",ccaps:"⩍",Ccaron:"Č",ccaron:"č",Ccedil:"Ç",ccedil:"ç",Ccirc:"Ĉ",ccirc:"ĉ",Cconint:"∰",ccups:"⩌",ccupssm:"⩐",Cdot:"Ċ",cdot:"ċ",cedil:"¸",Cedilla:"¸",cemptyv:"⦲",cent:"¢",centerdot:"·",CenterDot:"·",cfr:"𝔠",Cfr:"ℭ",CHcy:"Ч",chcy:"ч",check:"✓",checkmark:"✓",Chi:"Χ",chi:"χ",circ:"ˆ",circeq:"≗",circlearrowleft:"↺",circlearrowright:"↻",circledast:"⊛",circledcirc:"⊚",circleddash:"⊝",CircleDot:"⊙",circledR:"®",circledS:"Ⓢ",CircleMinus:"⊖",CirclePlus:"⊕",CircleTimes:"⊗",cir:"○",cirE:"⧃",cire:"≗",cirfnint:"⨐",cirmid:"⫯",cirscir:"⧂",ClockwiseContourIntegral:"∲",CloseCurlyDoubleQuote:"”",CloseCurlyQuote:"’",clubs:"♣",clubsuit:"♣",colon:":",Colon:"∷",Colone:"⩴",colone:"≔",coloneq:"≔",comma:",",commat:"@",comp:"∁",compfn:"∘",complement:"∁",complexes:"ℂ",cong:"≅",congdot:"⩭",Congruent:"≡",conint:"∮",Conint:"∯",ContourIntegral:"∮",copf:"𝕔",Copf:"ℂ",coprod:"∐",Coproduct:"∐",copy:"©",COPY:"©",copysr:"℗",CounterClockwiseContourIntegral:"∳",crarr:"↵",cross:"✗",Cross:"⨯",Cscr:"𝒞",cscr:"𝒸",csub:"⫏",csube:"⫑",csup:"⫐",csupe:"⫒",ctdot:"⋯",cudarrl:"⤸",cudarrr:"⤵",cuepr:"⋞",cuesc:"⋟",cularr:"↶",cularrp:"⤽",cupbrcap:"⩈",cupcap:"⩆",CupCap:"≍",cup:"∪",Cup:"⋓",cupcup:"⩊",cupdot:"⊍",cupor:"⩅",cups:"∪︀",curarr:"↷",curarrm:"⤼",curlyeqprec:"⋞",curlyeqsucc:"⋟",curlyvee:"⋎",curlywedge:"⋏",curren:"¤",curvearrowleft:"↶",curvearrowright:"↷",cuvee:"⋎",cuwed:"⋏",cwconint:"∲",cwint:"∱",cylcty:"⌭",dagger:"†",Dagger:"‡",daleth:"ℸ",darr:"↓",Darr:"↡",dArr:"⇓",dash:"‐",Dashv:"⫤",dashv:"⊣",dbkarow:"⤏",dblac:"˝",Dcaron:"Ď",dcaron:"ď",Dcy:"Д",dcy:"д",ddagger:"‡",ddarr:"⇊",DD:"ⅅ",dd:"ⅆ",DDotrahd:"⤑",ddotseq:"⩷",deg:"°",Del:"∇",Delta:"Δ",delta:"δ",demptyv:"⦱",dfisht:"⥿",Dfr:"𝔇",dfr:"𝔡",dHar:"⥥",dharl:"⇃",dharr:"⇂",DiacriticalAcute:"´",DiacriticalDot:"˙",DiacriticalDoubleAcute:"˝",DiacriticalGrave:"`",DiacriticalTilde:"˜",diam:"⋄",diamond:"⋄",Diamond:"⋄",diamondsuit:"♦",diams:"♦",die:"¨",DifferentialD:"ⅆ",digamma:"ϝ",disin:"⋲",div:"÷",divide:"÷",divideontimes:"⋇",divonx:"⋇",DJcy:"Ђ",djcy:"ђ",dlcorn:"⌞",dlcrop:"⌍",dollar:"$",Dopf:"𝔻",dopf:"𝕕",Dot:"¨",dot:"˙",DotDot:"⃜",doteq:"≐",doteqdot:"≑",DotEqual:"≐",dotminus:"∸",dotplus:"∔",dotsquare:"⊡",doublebarwedge:"⌆",DoubleContourIntegral:"∯",DoubleDot:"¨",DoubleDownArrow:"⇓",DoubleLeftArrow:"⇐",DoubleLeftRightArrow:"⇔",DoubleLeftTee:"⫤",DoubleLongLeftArrow:"⟸",DoubleLongLeftRightArrow:"⟺",DoubleLongRightArrow:"⟹",DoubleRightArrow:"⇒",DoubleRightTee:"⊨",DoubleUpArrow:"⇑",DoubleUpDownArrow:"⇕",DoubleVerticalBar:"∥",DownArrowBar:"⤓",downarrow:"↓",DownArrow:"↓",Downarrow:"⇓",DownArrowUpArrow:"⇵",DownBreve:"̑",downdownarrows:"⇊",downharpoonleft:"⇃",downharpoonright:"⇂",DownLeftRightVector:"⥐",DownLeftTeeVector:"⥞",DownLeftVectorBar:"⥖",DownLeftVector:"↽",DownRightTeeVector:"⥟",DownRightVectorBar:"⥗",DownRightVector:"⇁",DownTeeArrow:"↧",DownTee:"⊤",drbkarow:"⤐",drcorn:"⌟",drcrop:"⌌",Dscr:"𝒟",dscr:"𝒹",DScy:"Ѕ",dscy:"ѕ",dsol:"⧶",Dstrok:"Đ",dstrok:"đ",dtdot:"⋱",dtri:"▿",dtrif:"▾",duarr:"⇵",duhar:"⥯",dwangle:"⦦",DZcy:"Џ",dzcy:"џ",dzigrarr:"⟿",Eacute:"É",eacute:"é",easter:"⩮",Ecaron:"Ě",ecaron:"ě",Ecirc:"Ê",ecirc:"ê",ecir:"≖",ecolon:"≕",Ecy:"Э",ecy:"э",eDDot:"⩷",Edot:"Ė",edot:"ė",eDot:"≑",ee:"ⅇ",efDot:"≒",Efr:"𝔈",efr:"𝔢",eg:"⪚",Egrave:"È",egrave:"è",egs:"⪖",egsdot:"⪘",el:"⪙",Element:"∈",elinters:"⏧",ell:"ℓ",els:"⪕",elsdot:"⪗",Emacr:"Ē",emacr:"ē",empty:"∅",emptyset:"∅",EmptySmallSquare:"◻",emptyv:"∅",EmptyVerySmallSquare:"▫",emsp13:" ",emsp14:" ",emsp:" ",ENG:"Ŋ",eng:"ŋ",ensp:" ",Eogon:"Ę",eogon:"ę",Eopf:"𝔼",eopf:"𝕖",epar:"⋕",eparsl:"⧣",eplus:"⩱",epsi:"ε",Epsilon:"Ε",epsilon:"ε",epsiv:"ϵ",eqcirc:"≖",eqcolon:"≕",eqsim:"≂",eqslantgtr:"⪖",eqslantless:"⪕",Equal:"⩵",equals:"=",EqualTilde:"≂",equest:"≟",Equilibrium:"⇌",equiv:"≡",equivDD:"⩸",eqvparsl:"⧥",erarr:"⥱",erDot:"≓",escr:"ℯ",Escr:"ℰ",esdot:"≐",Esim:"⩳",esim:"≂",Eta:"Η",eta:"η",ETH:"Ð",eth:"ð",Euml:"Ë",euml:"ë",euro:"€",excl:"!",exist:"∃",Exists:"∃",expectation:"ℰ",exponentiale:"ⅇ",ExponentialE:"ⅇ",fallingdotseq:"≒",Fcy:"Ф",fcy:"ф",female:"♀",ffilig:"ffi",fflig:"ff",ffllig:"ffl",Ffr:"𝔉",ffr:"𝔣",filig:"fi",FilledSmallSquare:"◼",FilledVerySmallSquare:"▪",fjlig:"fj",flat:"♭",fllig:"fl",fltns:"▱",fnof:"ƒ",Fopf:"𝔽",fopf:"𝕗",forall:"∀",ForAll:"∀",fork:"⋔",forkv:"⫙",Fouriertrf:"ℱ",fpartint:"⨍",frac12:"½",frac13:"⅓",frac14:"¼",frac15:"⅕",frac16:"⅙",frac18:"⅛",frac23:"⅔",frac25:"⅖",frac34:"¾",frac35:"⅗",frac38:"⅜",frac45:"⅘",frac56:"⅚",frac58:"⅝",frac78:"⅞",frasl:"⁄",frown:"⌢",fscr:"𝒻",Fscr:"ℱ",gacute:"ǵ",Gamma:"Γ",gamma:"γ",Gammad:"Ϝ",gammad:"ϝ",gap:"⪆",Gbreve:"Ğ",gbreve:"ğ",Gcedil:"Ģ",Gcirc:"Ĝ",gcirc:"ĝ",Gcy:"Г",gcy:"г",Gdot:"Ġ",gdot:"ġ",ge:"≥",gE:"≧",gEl:"⪌",gel:"⋛",geq:"≥",geqq:"≧",geqslant:"⩾",gescc:"⪩",ges:"⩾",gesdot:"⪀",gesdoto:"⪂",gesdotol:"⪄",gesl:"⋛︀",gesles:"⪔",Gfr:"𝔊",gfr:"𝔤",gg:"≫",Gg:"⋙",ggg:"⋙",gimel:"ℷ",GJcy:"Ѓ",gjcy:"ѓ",gla:"⪥",gl:"≷",glE:"⪒",glj:"⪤",gnap:"⪊",gnapprox:"⪊",gne:"⪈",gnE:"≩",gneq:"⪈",gneqq:"≩",gnsim:"⋧",Gopf:"𝔾",gopf:"𝕘",grave:"`",GreaterEqual:"≥",GreaterEqualLess:"⋛",GreaterFullEqual:"≧",GreaterGreater:"⪢",GreaterLess:"≷",GreaterSlantEqual:"⩾",GreaterTilde:"≳",Gscr:"𝒢",gscr:"ℊ",gsim:"≳",gsime:"⪎",gsiml:"⪐",gtcc:"⪧",gtcir:"⩺",gt:">",GT:">",Gt:"≫",gtdot:"⋗",gtlPar:"⦕",gtquest:"⩼",gtrapprox:"⪆",gtrarr:"⥸",gtrdot:"⋗",gtreqless:"⋛",gtreqqless:"⪌",gtrless:"≷",gtrsim:"≳",gvertneqq:"≩︀",gvnE:"≩︀",Hacek:"ˇ",hairsp:" ",half:"½",hamilt:"ℋ",HARDcy:"Ъ",hardcy:"ъ",harrcir:"⥈",harr:"↔",hArr:"⇔",harrw:"↭",Hat:"^",hbar:"ℏ",Hcirc:"Ĥ",hcirc:"ĥ",hearts:"♥",heartsuit:"♥",hellip:"…",hercon:"⊹",hfr:"𝔥",Hfr:"ℌ",HilbertSpace:"ℋ",hksearow:"⤥",hkswarow:"⤦",hoarr:"⇿",homtht:"∻",hookleftarrow:"↩",hookrightarrow:"↪",hopf:"𝕙",Hopf:"ℍ",horbar:"―",HorizontalLine:"─",hscr:"𝒽",Hscr:"ℋ",hslash:"ℏ",Hstrok:"Ħ",hstrok:"ħ",HumpDownHump:"≎",HumpEqual:"≏",hybull:"⁃",hyphen:"‐",Iacute:"Í",iacute:"í",ic:"⁣",Icirc:"Î",icirc:"î",Icy:"И",icy:"и",Idot:"İ",IEcy:"Е",iecy:"е",iexcl:"¡",iff:"⇔",ifr:"𝔦",Ifr:"ℑ",Igrave:"Ì",igrave:"ì",ii:"ⅈ",iiiint:"⨌",iiint:"∭",iinfin:"⧜",iiota:"℩",IJlig:"IJ",ijlig:"ij",Imacr:"Ī",imacr:"ī",image:"ℑ",ImaginaryI:"ⅈ",imagline:"ℐ",imagpart:"ℑ",imath:"ı",Im:"ℑ",imof:"⊷",imped:"Ƶ",Implies:"⇒",incare:"℅","in":"∈",infin:"∞",infintie:"⧝",inodot:"ı",intcal:"⊺","int":"∫",Int:"∬",integers:"ℤ",Integral:"∫",intercal:"⊺",Intersection:"⋂",intlarhk:"⨗",intprod:"⨼",InvisibleComma:"⁣",InvisibleTimes:"⁢",IOcy:"Ё",iocy:"ё",Iogon:"Į",iogon:"į",Iopf:"𝕀",iopf:"𝕚",Iota:"Ι",iota:"ι",iprod:"⨼",iquest:"¿",iscr:"𝒾",Iscr:"ℐ",isin:"∈",isindot:"⋵",isinE:"⋹",isins:"⋴",isinsv:"⋳",isinv:"∈",it:"⁢",Itilde:"Ĩ",itilde:"ĩ",Iukcy:"І",iukcy:"і",Iuml:"Ï",iuml:"ï",Jcirc:"Ĵ",jcirc:"ĵ",Jcy:"Й",jcy:"й",Jfr:"𝔍",jfr:"𝔧",jmath:"ȷ",Jopf:"𝕁",jopf:"𝕛",Jscr:"𝒥",jscr:"𝒿",Jsercy:"Ј",jsercy:"ј",Jukcy:"Є",jukcy:"є",Kappa:"Κ",kappa:"κ",kappav:"ϰ",Kcedil:"Ķ",kcedil:"ķ",Kcy:"К",kcy:"к",Kfr:"𝔎",kfr:"𝔨",kgreen:"ĸ",KHcy:"Х",khcy:"х",KJcy:"Ќ",kjcy:"ќ",Kopf:"𝕂",kopf:"𝕜",Kscr:"𝒦",kscr:"𝓀",lAarr:"⇚",Lacute:"Ĺ",lacute:"ĺ",laemptyv:"⦴",lagran:"ℒ",Lambda:"Λ",lambda:"λ",lang:"⟨",Lang:"⟪",langd:"⦑",langle:"⟨",lap:"⪅",Laplacetrf:"ℒ",laquo:"«",larrb:"⇤",larrbfs:"⤟",larr:"←",Larr:"↞",lArr:"⇐",larrfs:"⤝",larrhk:"↩",larrlp:"↫",larrpl:"⤹",larrsim:"⥳",larrtl:"↢",latail:"⤙",lAtail:"⤛",lat:"⪫",late:"⪭",lates:"⪭︀",lbarr:"⤌",lBarr:"⤎",lbbrk:"❲",lbrace:"{",lbrack:"[",lbrke:"⦋",lbrksld:"⦏",lbrkslu:"⦍",Lcaron:"Ľ",lcaron:"ľ",Lcedil:"Ļ",lcedil:"ļ",lceil:"⌈",lcub:"{",Lcy:"Л",lcy:"л",ldca:"⤶",ldquo:"“",ldquor:"„",ldrdhar:"⥧",ldrushar:"⥋",ldsh:"↲",le:"≤",lE:"≦",LeftAngleBracket:"⟨",LeftArrowBar:"⇤",leftarrow:"←",LeftArrow:"←",Leftarrow:"⇐",LeftArrowRightArrow:"⇆",leftarrowtail:"↢",LeftCeiling:"⌈",LeftDoubleBracket:"⟦",LeftDownTeeVector:"⥡",LeftDownVectorBar:"⥙",LeftDownVector:"⇃",LeftFloor:"⌊",leftharpoondown:"↽",leftharpoonup:"↼",leftleftarrows:"⇇",leftrightarrow:"↔",LeftRightArrow:"↔",Leftrightarrow:"⇔",leftrightarrows:"⇆",leftrightharpoons:"⇋",leftrightsquigarrow:"↭",LeftRightVector:"⥎",LeftTeeArrow:"↤",LeftTee:"⊣",LeftTeeVector:"⥚",leftthreetimes:"⋋",LeftTriangleBar:"⧏",LeftTriangle:"⊲",LeftTriangleEqual:"⊴",LeftUpDownVector:"⥑",LeftUpTeeVector:"⥠",LeftUpVectorBar:"⥘",LeftUpVector:"↿",LeftVectorBar:"⥒",LeftVector:"↼",lEg:"⪋",leg:"⋚",leq:"≤",leqq:"≦",leqslant:"⩽",lescc:"⪨",les:"⩽",lesdot:"⩿",lesdoto:"⪁",lesdotor:"⪃",lesg:"⋚︀",lesges:"⪓",lessapprox:"⪅",lessdot:"⋖",lesseqgtr:"⋚",lesseqqgtr:"⪋",LessEqualGreater:"⋚",LessFullEqual:"≦",LessGreater:"≶",lessgtr:"≶",LessLess:"⪡",lesssim:"≲",LessSlantEqual:"⩽",LessTilde:"≲",lfisht:"⥼",lfloor:"⌊",Lfr:"𝔏",lfr:"𝔩",lg:"≶",lgE:"⪑",lHar:"⥢",lhard:"↽",lharu:"↼",lharul:"⥪",lhblk:"▄",LJcy:"Љ",ljcy:"љ",llarr:"⇇",ll:"≪",Ll:"⋘",llcorner:"⌞",Lleftarrow:"⇚",llhard:"⥫",lltri:"◺",Lmidot:"Ŀ",lmidot:"ŀ",lmoustache:"⎰",lmoust:"⎰",lnap:"⪉",lnapprox:"⪉",lne:"⪇",lnE:"≨",lneq:"⪇",lneqq:"≨",lnsim:"⋦",loang:"⟬",loarr:"⇽",lobrk:"⟦",longleftarrow:"⟵",LongLeftArrow:"⟵",Longleftarrow:"⟸",longleftrightarrow:"⟷",LongLeftRightArrow:"⟷",Longleftrightarrow:"⟺",longmapsto:"⟼",longrightarrow:"⟶",LongRightArrow:"⟶",Longrightarrow:"⟹",looparrowleft:"↫",looparrowright:"↬",lopar:"⦅",Lopf:"𝕃",lopf:"𝕝",loplus:"⨭",lotimes:"⨴",lowast:"∗",lowbar:"_",LowerLeftArrow:"↙",LowerRightArrow:"↘",loz:"◊",lozenge:"◊",lozf:"⧫",lpar:"(",lparlt:"⦓",lrarr:"⇆",lrcorner:"⌟",lrhar:"⇋",lrhard:"⥭",lrm:"‎",lrtri:"⊿",lsaquo:"‹",lscr:"𝓁",Lscr:"ℒ",lsh:"↰",Lsh:"↰",lsim:"≲",lsime:"⪍",lsimg:"⪏",lsqb:"[",lsquo:"‘",lsquor:"‚",Lstrok:"Ł",lstrok:"ł",ltcc:"⪦",ltcir:"⩹",lt:"<",LT:"<",Lt:"≪",ltdot:"⋖",lthree:"⋋",ltimes:"⋉",ltlarr:"⥶",ltquest:"⩻",ltri:"◃",ltrie:"⊴",ltrif:"◂",ltrPar:"⦖",lurdshar:"⥊",luruhar:"⥦",lvertneqq:"≨︀",lvnE:"≨︀",macr:"¯",male:"♂",malt:"✠",maltese:"✠",Map:"⤅",map:"↦",mapsto:"↦",mapstodown:"↧",mapstoleft:"↤",mapstoup:"↥",marker:"▮",mcomma:"⨩",Mcy:"М",mcy:"м",mdash:"—",mDDot:"∺",measuredangle:"∡",MediumSpace:" ",Mellintrf:"ℳ",Mfr:"𝔐",mfr:"𝔪",mho:"℧",micro:"µ",midast:"*",midcir:"⫰",mid:"∣",middot:"·",minusb:"⊟",minus:"−",minusd:"∸",minusdu:"⨪",MinusPlus:"∓",mlcp:"⫛",mldr:"…",mnplus:"∓",models:"⊧",Mopf:"𝕄",mopf:"𝕞",mp:"∓",mscr:"𝓂",Mscr:"ℳ",mstpos:"∾",Mu:"Μ",mu:"μ",multimap:"⊸",mumap:"⊸",nabla:"∇",Nacute:"Ń",nacute:"ń",nang:"∠⃒",nap:"≉",napE:"⩰̸",napid:"≋̸",napos:"ʼn",napprox:"≉",natural:"♮",naturals:"ℕ",natur:"♮",nbsp:" ",nbump:"≎̸",nbumpe:"≏̸",ncap:"⩃",Ncaron:"Ň",ncaron:"ň",Ncedil:"Ņ",ncedil:"ņ",ncong:"≇",ncongdot:"⩭̸",ncup:"⩂",Ncy:"Н",ncy:"н",ndash:"–",nearhk:"⤤",nearr:"↗",neArr:"⇗",nearrow:"↗",ne:"≠",nedot:"≐̸",NegativeMediumSpace:"​",NegativeThickSpace:"​",NegativeThinSpace:"​",NegativeVeryThinSpace:"​",nequiv:"≢",nesear:"⤨",nesim:"≂̸",NestedGreaterGreater:"≫",NestedLessLess:"≪",NewLine:"\n",nexist:"∄",nexists:"∄",Nfr:"𝔑",nfr:"𝔫",ngE:"≧̸",nge:"≱",ngeq:"≱",ngeqq:"≧̸",ngeqslant:"⩾̸",nges:"⩾̸",nGg:"⋙̸",ngsim:"≵",nGt:"≫⃒",ngt:"≯",ngtr:"≯",nGtv:"≫̸",nharr:"↮",nhArr:"⇎",nhpar:"⫲",ni:"∋",nis:"⋼",nisd:"⋺",niv:"∋",NJcy:"Њ",njcy:"њ",nlarr:"↚",nlArr:"⇍",nldr:"‥",nlE:"≦̸",nle:"≰",nleftarrow:"↚",nLeftarrow:"⇍",nleftrightarrow:"↮",nLeftrightarrow:"⇎",nleq:"≰",nleqq:"≦̸",nleqslant:"⩽̸",nles:"⩽̸",nless:"≮",nLl:"⋘̸",nlsim:"≴",nLt:"≪⃒",nlt:"≮",nltri:"⋪",nltrie:"⋬",nLtv:"≪̸",nmid:"∤",NoBreak:"⁠",NonBreakingSpace:" ",nopf:"𝕟",Nopf:"ℕ",Not:"⫬",not:"¬",NotCongruent:"≢",NotCupCap:"≭",NotDoubleVerticalBar:"∦",NotElement:"∉",NotEqual:"≠",NotEqualTilde:"≂̸",NotExists:"∄",NotGreater:"≯",NotGreaterEqual:"≱",NotGreaterFullEqual:"≧̸",NotGreaterGreater:"≫̸",NotGreaterLess:"≹",NotGreaterSlantEqual:"⩾̸",NotGreaterTilde:"≵",NotHumpDownHump:"≎̸",NotHumpEqual:"≏̸",notin:"∉",notindot:"⋵̸",notinE:"⋹̸",notinva:"∉",notinvb:"⋷",notinvc:"⋶",NotLeftTriangleBar:"⧏̸",NotLeftTriangle:"⋪",NotLeftTriangleEqual:"⋬",NotLess:"≮",NotLessEqual:"≰",NotLessGreater:"≸",NotLessLess:"≪̸",NotLessSlantEqual:"⩽̸",NotLessTilde:"≴",NotNestedGreaterGreater:"⪢̸",NotNestedLessLess:"⪡̸",notni:"∌",notniva:"∌",notnivb:"⋾",notnivc:"⋽",NotPrecedes:"⊀",NotPrecedesEqual:"⪯̸",NotPrecedesSlantEqual:"⋠",NotReverseElement:"∌",NotRightTriangleBar:"⧐̸",NotRightTriangle:"⋫",NotRightTriangleEqual:"⋭",NotSquareSubset:"⊏̸",NotSquareSubsetEqual:"⋢",NotSquareSuperset:"⊐̸",NotSquareSupersetEqual:"⋣",NotSubset:"⊂⃒",NotSubsetEqual:"⊈",NotSucceeds:"⊁",NotSucceedsEqual:"⪰̸",NotSucceedsSlantEqual:"⋡",NotSucceedsTilde:"≿̸",NotSuperset:"⊃⃒",NotSupersetEqual:"⊉",NotTilde:"≁",NotTildeEqual:"≄",NotTildeFullEqual:"≇",NotTildeTilde:"≉",NotVerticalBar:"∤",nparallel:"∦",npar:"∦",nparsl:"⫽⃥",npart:"∂̸",npolint:"⨔",npr:"⊀",nprcue:"⋠",nprec:"⊀",npreceq:"⪯̸",npre:"⪯̸",nrarrc:"⤳̸",nrarr:"↛",nrArr:"⇏",nrarrw:"↝̸",nrightarrow:"↛",nRightarrow:"⇏",nrtri:"⋫",nrtrie:"⋭",nsc:"⊁",nsccue:"⋡",nsce:"⪰̸",Nscr:"𝒩",nscr:"𝓃",nshortmid:"∤",nshortparallel:"∦",nsim:"≁",nsime:"≄",nsimeq:"≄",nsmid:"∤",nspar:"∦",nsqsube:"⋢",nsqsupe:"⋣",nsub:"⊄",nsubE:"⫅̸",nsube:"⊈",nsubset:"⊂⃒",nsubseteq:"⊈",nsubseteqq:"⫅̸",nsucc:"⊁",nsucceq:"⪰̸",nsup:"⊅",nsupE:"⫆̸",nsupe:"⊉",nsupset:"⊃⃒",nsupseteq:"⊉",nsupseteqq:"⫆̸",ntgl:"≹",Ntilde:"Ñ",ntilde:"ñ",ntlg:"≸",ntriangleleft:"⋪",ntrianglelefteq:"⋬",ntriangleright:"⋫",ntrianglerighteq:"⋭",Nu:"Ν",nu:"ν",num:"#",numero:"№",numsp:" ",nvap:"≍⃒",nvdash:"⊬",nvDash:"⊭",nVdash:"⊮",nVDash:"⊯",nvge:"≥⃒",nvgt:">⃒",nvHarr:"⤄",nvinfin:"⧞",nvlArr:"⤂",nvle:"≤⃒",nvlt:"<⃒",nvltrie:"⊴⃒",nvrArr:"⤃",nvrtrie:"⊵⃒",nvsim:"∼⃒",nwarhk:"⤣",nwarr:"↖",nwArr:"⇖",nwarrow:"↖",nwnear:"⤧",Oacute:"Ó",oacute:"ó",oast:"⊛",Ocirc:"Ô",ocirc:"ô",ocir:"⊚",Ocy:"О",ocy:"о",odash:"⊝",Odblac:"Ő",odblac:"ő",odiv:"⨸",odot:"⊙",odsold:"⦼",OElig:"Œ",oelig:"œ",ofcir:"⦿",Ofr:"𝔒",ofr:"𝔬",ogon:"˛",Ograve:"Ò",ograve:"ò",ogt:"⧁",ohbar:"⦵",ohm:"Ω",oint:"∮",olarr:"↺",olcir:"⦾",olcross:"⦻",oline:"‾",olt:"⧀",Omacr:"Ō",omacr:"ō",Omega:"Ω",omega:"ω",Omicron:"Ο",omicron:"ο",omid:"⦶",ominus:"⊖",Oopf:"𝕆",oopf:"𝕠",opar:"⦷",OpenCurlyDoubleQuote:"“",OpenCurlyQuote:"‘",operp:"⦹",oplus:"⊕",orarr:"↻",Or:"⩔",or:"∨",ord:"⩝",order:"ℴ",orderof:"ℴ",ordf:"ª",ordm:"º",origof:"⊶",oror:"⩖",orslope:"⩗",orv:"⩛",oS:"Ⓢ",Oscr:"𝒪",oscr:"ℴ",Oslash:"Ø",oslash:"ø",osol:"⊘",Otilde:"Õ",otilde:"õ",otimesas:"⨶",Otimes:"⨷",otimes:"⊗",Ouml:"Ö",ouml:"ö",ovbar:"⌽",OverBar:"‾",OverBrace:"⏞",OverBracket:"⎴",OverParenthesis:"⏜",para:"¶",parallel:"∥",par:"∥",parsim:"⫳",parsl:"⫽",part:"∂",PartialD:"∂",Pcy:"П",pcy:"п",percnt:"%",period:".",permil:"‰",perp:"⊥",pertenk:"‱",Pfr:"𝔓",pfr:"𝔭",Phi:"Φ",phi:"φ",phiv:"ϕ",phmmat:"ℳ",phone:"☎",Pi:"Π",pi:"π",pitchfork:"⋔",piv:"ϖ",planck:"ℏ",planckh:"ℎ",plankv:"ℏ",plusacir:"⨣",plusb:"⊞",pluscir:"⨢",plus:"+",plusdo:"∔",plusdu:"⨥",pluse:"⩲",PlusMinus:"±",plusmn:"±",plussim:"⨦",plustwo:"⨧",pm:"±",Poincareplane:"ℌ",pointint:"⨕",popf:"𝕡",Popf:"ℙ",pound:"£",prap:"⪷",Pr:"⪻",pr:"≺",prcue:"≼",precapprox:"⪷",prec:"≺",preccurlyeq:"≼",Precedes:"≺",PrecedesEqual:"⪯",PrecedesSlantEqual:"≼",PrecedesTilde:"≾",preceq:"⪯",precnapprox:"⪹",precneqq:"⪵",precnsim:"⋨",pre:"⪯",prE:"⪳",precsim:"≾",prime:"′",Prime:"″",primes:"ℙ",prnap:"⪹",prnE:"⪵",prnsim:"⋨",prod:"∏",Product:"∏",profalar:"⌮",profline:"⌒",profsurf:"⌓",prop:"∝",Proportional:"∝",Proportion:"∷",propto:"∝",prsim:"≾",prurel:"⊰",Pscr:"𝒫",pscr:"𝓅",Psi:"Ψ",psi:"ψ",puncsp:" ",Qfr:"𝔔",qfr:"𝔮",qint:"⨌",qopf:"𝕢",Qopf:"ℚ",qprime:"⁗",Qscr:"𝒬",qscr:"𝓆",quaternions:"ℍ",quatint:"⨖",quest:"?",questeq:"≟",quot:'"',QUOT:'"',rAarr:"⇛",race:"∽̱",Racute:"Ŕ",racute:"ŕ",radic:"√",raemptyv:"⦳",rang:"⟩",Rang:"⟫",rangd:"⦒",range:"⦥",rangle:"⟩",raquo:"»",rarrap:"⥵",rarrb:"⇥",rarrbfs:"⤠",rarrc:"⤳",rarr:"→",Rarr:"↠",rArr:"⇒",rarrfs:"⤞",rarrhk:"↪",rarrlp:"↬",rarrpl:"⥅",rarrsim:"⥴",Rarrtl:"⤖",rarrtl:"↣",rarrw:"↝",ratail:"⤚",rAtail:"⤜",ratio:"∶",rationals:"ℚ",rbarr:"⤍",rBarr:"⤏",RBarr:"⤐",rbbrk:"❳",rbrace:"}",rbrack:"]",rbrke:"⦌",rbrksld:"⦎",rbrkslu:"⦐",Rcaron:"Ř",rcaron:"ř",Rcedil:"Ŗ",rcedil:"ŗ", +rceil:"⌉",rcub:"}",Rcy:"Р",rcy:"р",rdca:"⤷",rdldhar:"⥩",rdquo:"”",rdquor:"”",rdsh:"↳",real:"ℜ",realine:"ℛ",realpart:"ℜ",reals:"ℝ",Re:"ℜ",rect:"▭",reg:"®",REG:"®",ReverseElement:"∋",ReverseEquilibrium:"⇋",ReverseUpEquilibrium:"⥯",rfisht:"⥽",rfloor:"⌋",rfr:"𝔯",Rfr:"ℜ",rHar:"⥤",rhard:"⇁",rharu:"⇀",rharul:"⥬",Rho:"Ρ",rho:"ρ",rhov:"ϱ",RightAngleBracket:"⟩",RightArrowBar:"⇥",rightarrow:"→",RightArrow:"→",Rightarrow:"⇒",RightArrowLeftArrow:"⇄",rightarrowtail:"↣",RightCeiling:"⌉",RightDoubleBracket:"⟧",RightDownTeeVector:"⥝",RightDownVectorBar:"⥕",RightDownVector:"⇂",RightFloor:"⌋",rightharpoondown:"⇁",rightharpoonup:"⇀",rightleftarrows:"⇄",rightleftharpoons:"⇌",rightrightarrows:"⇉",rightsquigarrow:"↝",RightTeeArrow:"↦",RightTee:"⊢",RightTeeVector:"⥛",rightthreetimes:"⋌",RightTriangleBar:"⧐",RightTriangle:"⊳",RightTriangleEqual:"⊵",RightUpDownVector:"⥏",RightUpTeeVector:"⥜",RightUpVectorBar:"⥔",RightUpVector:"↾",RightVectorBar:"⥓",RightVector:"⇀",ring:"˚",risingdotseq:"≓",rlarr:"⇄",rlhar:"⇌",rlm:"‏",rmoustache:"⎱",rmoust:"⎱",rnmid:"⫮",roang:"⟭",roarr:"⇾",robrk:"⟧",ropar:"⦆",ropf:"𝕣",Ropf:"ℝ",roplus:"⨮",rotimes:"⨵",RoundImplies:"⥰",rpar:")",rpargt:"⦔",rppolint:"⨒",rrarr:"⇉",Rrightarrow:"⇛",rsaquo:"›",rscr:"𝓇",Rscr:"ℛ",rsh:"↱",Rsh:"↱",rsqb:"]",rsquo:"’",rsquor:"’",rthree:"⋌",rtimes:"⋊",rtri:"▹",rtrie:"⊵",rtrif:"▸",rtriltri:"⧎",RuleDelayed:"⧴",ruluhar:"⥨",rx:"℞",Sacute:"Ś",sacute:"ś",sbquo:"‚",scap:"⪸",Scaron:"Š",scaron:"š",Sc:"⪼",sc:"≻",sccue:"≽",sce:"⪰",scE:"⪴",Scedil:"Ş",scedil:"ş",Scirc:"Ŝ",scirc:"ŝ",scnap:"⪺",scnE:"⪶",scnsim:"⋩",scpolint:"⨓",scsim:"≿",Scy:"С",scy:"с",sdotb:"⊡",sdot:"⋅",sdote:"⩦",searhk:"⤥",searr:"↘",seArr:"⇘",searrow:"↘",sect:"§",semi:";",seswar:"⤩",setminus:"∖",setmn:"∖",sext:"✶",Sfr:"𝔖",sfr:"𝔰",sfrown:"⌢",sharp:"♯",SHCHcy:"Щ",shchcy:"щ",SHcy:"Ш",shcy:"ш",ShortDownArrow:"↓",ShortLeftArrow:"←",shortmid:"∣",shortparallel:"∥",ShortRightArrow:"→",ShortUpArrow:"↑",shy:"­",Sigma:"Σ",sigma:"σ",sigmaf:"ς",sigmav:"ς",sim:"∼",simdot:"⩪",sime:"≃",simeq:"≃",simg:"⪞",simgE:"⪠",siml:"⪝",simlE:"⪟",simne:"≆",simplus:"⨤",simrarr:"⥲",slarr:"←",SmallCircle:"∘",smallsetminus:"∖",smashp:"⨳",smeparsl:"⧤",smid:"∣",smile:"⌣",smt:"⪪",smte:"⪬",smtes:"⪬︀",SOFTcy:"Ь",softcy:"ь",solbar:"⌿",solb:"⧄",sol:"/",Sopf:"𝕊",sopf:"𝕤",spades:"♠",spadesuit:"♠",spar:"∥",sqcap:"⊓",sqcaps:"⊓︀",sqcup:"⊔",sqcups:"⊔︀",Sqrt:"√",sqsub:"⊏",sqsube:"⊑",sqsubset:"⊏",sqsubseteq:"⊑",sqsup:"⊐",sqsupe:"⊒",sqsupset:"⊐",sqsupseteq:"⊒",square:"□",Square:"□",SquareIntersection:"⊓",SquareSubset:"⊏",SquareSubsetEqual:"⊑",SquareSuperset:"⊐",SquareSupersetEqual:"⊒",SquareUnion:"⊔",squarf:"▪",squ:"□",squf:"▪",srarr:"→",Sscr:"𝒮",sscr:"𝓈",ssetmn:"∖",ssmile:"⌣",sstarf:"⋆",Star:"⋆",star:"☆",starf:"★",straightepsilon:"ϵ",straightphi:"ϕ",strns:"¯",sub:"⊂",Sub:"⋐",subdot:"⪽",subE:"⫅",sube:"⊆",subedot:"⫃",submult:"⫁",subnE:"⫋",subne:"⊊",subplus:"⪿",subrarr:"⥹",subset:"⊂",Subset:"⋐",subseteq:"⊆",subseteqq:"⫅",SubsetEqual:"⊆",subsetneq:"⊊",subsetneqq:"⫋",subsim:"⫇",subsub:"⫕",subsup:"⫓",succapprox:"⪸",succ:"≻",succcurlyeq:"≽",Succeeds:"≻",SucceedsEqual:"⪰",SucceedsSlantEqual:"≽",SucceedsTilde:"≿",succeq:"⪰",succnapprox:"⪺",succneqq:"⪶",succnsim:"⋩",succsim:"≿",SuchThat:"∋",sum:"∑",Sum:"∑",sung:"♪",sup1:"¹",sup2:"²",sup3:"³",sup:"⊃",Sup:"⋑",supdot:"⪾",supdsub:"⫘",supE:"⫆",supe:"⊇",supedot:"⫄",Superset:"⊃",SupersetEqual:"⊇",suphsol:"⟉",suphsub:"⫗",suplarr:"⥻",supmult:"⫂",supnE:"⫌",supne:"⊋",supplus:"⫀",supset:"⊃",Supset:"⋑",supseteq:"⊇",supseteqq:"⫆",supsetneq:"⊋",supsetneqq:"⫌",supsim:"⫈",supsub:"⫔",supsup:"⫖",swarhk:"⤦",swarr:"↙",swArr:"⇙",swarrow:"↙",swnwar:"⤪",szlig:"ß",Tab:" 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32:this.$=n.lineType.DOTTED_LINE}},table:[{3:1,4:2,5:[1,3]},{1:[3]},{1:[2,1]},{6:[1,4]},{7:5,9:6,10:10,11:14,12:7,14:8,15:9,16:r,20:n,21:i,45:a,46:s,47:o},{8:[1,18]},{6:[1,19],8:[2,3]},e(u,[2,7],{13:[1,20]}),e(u,[2,9]),e(u,[2,10]),e(u,[2,15],{22:21,24:24,25:25,13:[1,23],23:[1,22],26:c,27:l,28:h,29:d,30:f,31:p}),{10:32,11:14,45:a,46:s,47:o},e(u,[2,17]),e(u,[2,18]),e(g,[2,6],{11:14,10:33,45:a,46:s,47:o}),e(m,[2,46]),e(m,[2,47]),e(m,[2,48]),{1:[2,2]},{7:34,9:6,10:10,11:14,12:7,14:8,15:9,16:r,20:n,21:i,45:a,46:s,47:o},e(u,[2,8]),{10:35,11:14,23:[1,36],45:a,46:s,47:o},{22:37,24:24,25:25,26:c,27:l,28:h,29:d,30:f,31:p},e(u,[2,16]),{25:38,30:f,31:p},e(y,[2,26],{24:39,26:c,27:l,28:h,29:d}),e(v,[2,27]),e(v,[2,28]),e(v,[2,29]),e(v,[2,30]),e(b,[2,31]),e(b,[2,32]),e(u,[2,11],{17:[1,40]}),e(g,[2,5]),{8:[2,4]},e(_,[2,19]),{10:41,11:14,45:a,46:s,47:o},{10:42,11:14,23:[1,43],45:a,46:s,47:o},e(y,[2,25],{24:44,26:c,27:l,28:h,29:d}),e(y,[2,24]),{18:45,20:A},e(_,[2,21]),e(_,[2,20]),{10:47,11:14,45:a,46:s,47:o},e(y,[2,23]),{19:[1,48]},{18:49,19:[2,13],20:A},e(_,[2,22]),e(u,[2,12]),{19:[2,14]}],defaultActions:{2:[2,1],18:[2,2],34:[2,4],49:[2,14]},parseError:function(t,e){if(!e.recoverable){var r=function(t,e){this.message=t,this.hash=e};throw r.prototype=new Error,new r(t,e)}this.trace(t)},parse:function(t){var e=this,r=[0],n=[null],i=[],a=this.table,s="",o=0,u=0,c=0,l=2,h=1,d=i.slice.call(arguments,1),f=Object.create(this.lexer),p={yy:{}};for(var g in this.yy)Object.prototype.hasOwnProperty.call(this.yy,g)&&(p.yy[g]=this.yy[g]);f.setInput(t,p.yy),p.yy.lexer=f,p.yy.parser=this,"undefined"==typeof f.yylloc&&(f.yylloc={});var m=f.yylloc;i.push(m);var y=f.options&&f.options.ranges;"function"==typeof p.yy.parseError?this.parseError=p.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;for(var v,b,_,A,w,x,E,k,D,C=function(){var t;return t=f.lex()||h,"number"!=typeof t&&(t=e.symbols_[t]||t),t},F={};;){if(_=r[r.length-1],this.defaultActions[_]?A=this.defaultActions[_]:((null===v||"undefined"==typeof v)&&(v=C()),A=a[_]&&a[_][v]),"undefined"==typeof A||!A.length||!A[0]){var T="";D=[];for(x in a[_])this.terminals_[x]&&x>l&&D.push("'"+this.terminals_[x]+"'");T=f.showPosition?"Parse error on line "+(o+1)+":\n"+f.showPosition()+"\nExpecting "+D.join(", ")+", got '"+(this.terminals_[v]||v)+"'":"Parse error on line "+(o+1)+": Unexpected "+(v==h?"end of input":"'"+(this.terminals_[v]||v)+"'"),this.parseError(T,{text:f.match,token:this.terminals_[v]||v,line:f.yylineno,loc:m,expected:D})}if(A[0]instanceof Array&&A.length>1)throw new Error("Parse Error: multiple actions possible at state: "+_+", token: "+v);switch(A[0]){case 1:r.push(v),n.push(f.yytext),i.push(f.yylloc),r.push(A[1]),v=null,b?(v=b,b=null):(u=f.yyleng,s=f.yytext,o=f.yylineno,m=f.yylloc,c>0&&c--);break;case 2:if(E=this.productions_[A[1]][1],F.$=n[n.length-E],F._$={first_line:i[i.length-(E||1)].first_line,last_line:i[i.length-1].last_line,first_column:i[i.length-(E||1)].first_column,last_column:i[i.length-1].last_column},y&&(F._$.range=[i[i.length-(E||1)].range[0],i[i.length-1].range[1]]),w=this.performAction.apply(F,[s,u,o,p.yy,A[1],n,i].concat(d)),"undefined"!=typeof w)return w;E&&(r=r.slice(0,-1*E*2),n=n.slice(0,-1*E),i=i.slice(0,-1*E)),r.push(this.productions_[A[1]][0]),n.push(F.$),i.push(F._$),k=a[r[r.length-2]][r[r.length-1]],r.push(k);break;case 3:return!0}}return!0}},x=function(){var t={EOF:1,parseError:function(t,e){if(!this.yy.parser)throw new Error(t);this.yy.parser.parseError(t,e)},setInput:function(t,e){return this.yy=e||this.yy||{},this._input=t,this._more=this._backtrack=this.done=!1,this.yylineno=this.yyleng=0,this.yytext=this.matched=this.match="",this.conditionStack=["INITIAL"],this.yylloc={first_line:1,first_column:0,last_line:1,last_column:0},this.options.ranges&&(this.yylloc.range=[0,0]),this.offset=0,this},input:function(){var t=this._input[0];this.yytext+=t,this.yyleng++,this.offset++,this.match+=t,this.matched+=t;var e=t.match(/(?:\r\n?|\n).*/g);return e?(this.yylineno++,this.yylloc.last_line++):this.yylloc.last_column++,this.options.ranges&&this.yylloc.range[1]++,this._input=this._input.slice(1),t},unput:function(t){var e=t.length,r=t.split(/(?:\r\n?|\n)/g);this._input=t+this._input,this.yytext=this.yytext.substr(0,this.yytext.length-e),this.offset-=e;var n=this.match.split(/(?:\r\n?|\n)/g);this.match=this.match.substr(0,this.match.length-1),this.matched=this.matched.substr(0,this.matched.length-1),r.length-1&&(this.yylineno-=r.length-1);var i=this.yylloc.range;return this.yylloc={first_line:this.yylloc.first_line,last_line:this.yylineno+1,first_column:this.yylloc.first_column,last_column:r?(r.length===n.length?this.yylloc.first_column:0)+n[n.length-r.length].length-r[0].length:this.yylloc.first_column-e},this.options.ranges&&(this.yylloc.range=[i[0],i[0]+this.yyleng-e]),this.yyleng=this.yytext.length,this},more:function(){return this._more=!0,this},reject:function(){return this.options.backtrack_lexer?(this._backtrack=!0,this):this.parseError("Lexical error on line "+(this.yylineno+1)+". You can only invoke reject() in the lexer when the lexer is of the backtracking persuasion (options.backtrack_lexer = true).\n"+this.showPosition(),{text:"",token:null,line:this.yylineno})},less:function(t){this.unput(this.match.slice(t))},pastInput:function(){var t=this.matched.substr(0,this.matched.length-this.match.length);return(t.length>20?"...":"")+t.substr(-20).replace(/\n/g,"")},upcomingInput:function(){var t=this.match;return t.length<20&&(t+=this._input.substr(0,20-t.length)),(t.substr(0,20)+(t.length>20?"...":"")).replace(/\n/g,"")},showPosition:function(){var t=this.pastInput(),e=new Array(t.length+1).join("-");return t+this.upcomingInput()+"\n"+e+"^"},test_match:function(t,e){var r,n,i;if(this.options.backtrack_lexer&&(i={yylineno:this.yylineno,yylloc:{first_line:this.yylloc.first_line,last_line:this.last_line,first_column:this.yylloc.first_column,last_column:this.yylloc.last_column},yytext:this.yytext,match:this.match,matches:this.matches,matched:this.matched,yyleng:this.yyleng,offset:this.offset,_more:this._more,_input:this._input,yy:this.yy,conditionStack:this.conditionStack.slice(0),done:this.done},this.options.ranges&&(i.yylloc.range=this.yylloc.range.slice(0))),n=t[0].match(/(?:\r\n?|\n).*/g),n&&(this.yylineno+=n.length),this.yylloc={first_line:this.yylloc.last_line,last_line:this.yylineno+1,first_column:this.yylloc.last_column,last_column:n?n[n.length-1].length-n[n.length-1].match(/\r?\n?/)[0].length:this.yylloc.last_column+t[0].length},this.yytext+=t[0],this.match+=t[0],this.matches=t,this.yyleng=this.yytext.length,this.options.ranges&&(this.yylloc.range=[this.offset,this.offset+=this.yyleng]),this._more=!1,this._backtrack=!1,this._input=this._input.slice(t[0].length),this.matched+=t[0],r=this.performAction.call(this,this.yy,this,e,this.conditionStack[this.conditionStack.length-1]),this.done&&this._input&&(this.done=!1),r)return r;if(this._backtrack){for(var a in i)this[a]=i[a];return!1}return!1},next:function(){if(this.done)return this.EOF;this._input||(this.done=!0);var t,e,r,n;this._more||(this.yytext="",this.match="");for(var i=this._currentRules(),a=0;ae[0].length)){if(e=r,n=a,this.options.backtrack_lexer){if(t=this.test_match(r,i[a]),t!==!1)return t;if(this._backtrack){e=!1;continue}return!1}if(!this.options.flex)break}return e?(t=this.test_match(e,i[n]),t!==!1?t:!1):""===this._input?this.EOF:this.parseError("Lexical error on line "+(this.yylineno+1)+". Unrecognized text.\n"+this.showPosition(),{text:"",token:null,line:this.yylineno})},lex:function(){var t=this.next();return t?t:this.lex()},begin:function(t){this.conditionStack.push(t)},popState:function(){var t=this.conditionStack.length-1;return t>0?this.conditionStack.pop():this.conditionStack[0]},_currentRules:function(){return this.conditionStack.length&&this.conditionStack[this.conditionStack.length-1]?this.conditions[this.conditionStack[this.conditionStack.length-1]].rules:this.conditions.INITIAL.rules},topState:function(t){return t=this.conditionStack.length-1-Math.abs(t||0),t>=0?this.conditionStack[t]:"INITIAL"},pushState:function(t){this.begin(t)},stateStackSize:function(){return this.conditionStack.length},options:{},performAction:function(t,e,r,n){switch(r){case 0:break;case 1:return 6;case 2:break;case 3:return 5;case 4:return this.begin("struct"),17;case 5:return this.popState(),19;case 6:break;case 7:return"MEMBER";case 8:return 16;case 9:this.begin("string");break;case 10:this.popState();break;case 11:return"STR";case 12:return 27;case 13:return 27;case 14:return 29;case 15:return 29;case 16:return 28;case 17:return 26;case 18:return 30;case 19:return 31;case 20:return 13;case 21:return 43;case 22:return"DOT";case 23:return"PLUS";case 24:return 40;case 25:return"EQUALS";case 26:return"EQUALS";case 27:return 47;case 28:return"PUNCTUATION";case 29:return 46;case 30:return 45;case 31:return 42;case 32:return 8}},rules:[/^(?:%%[^\n]*)/,/^(?:\n+)/,/^(?:\s+)/,/^(?:classDiagram\b)/,/^(?:[\{])/,/^(?:\})/,/^(?:[\n])/,/^(?:[^\{\}\n]*)/,/^(?:class\b)/,/^(?:["])/,/^(?:["])/,/^(?:[^"]*)/,/^(?:\s*<\|)/,/^(?:\s*\|>)/,/^(?:\s*>)/,/^(?:\s*<)/,/^(?:\s*\*)/,/^(?:\s*o\b)/,/^(?:--)/,/^(?:\.\.)/,/^(?::[^#\n;]+)/,/^(?:-)/,/^(?:\.)/,/^(?:\+)/,/^(?:%)/,/^(?:=)/,/^(?:=)/,/^(?:[A-Za-z]+)/,/^(?:[!"#$%&'*+,-.`?\\_\/])/,/^(?:[0-9]+)/,/^(?:[\u00AA\u00B5\u00BA\u00C0-\u00D6\u00D8-\u00F6]|[\u00F8-\u02C1\u02C6-\u02D1\u02E0-\u02E4\u02EC\u02EE\u0370-\u0374\u0376\u0377]|[\u037A-\u037D\u0386\u0388-\u038A\u038C\u038E-\u03A1\u03A3-\u03F5]|[\u03F7-\u0481\u048A-\u0527\u0531-\u0556\u0559\u0561-\u0587\u05D0-\u05EA]|[\u05F0-\u05F2\u0620-\u064A\u066E\u066F\u0671-\u06D3\u06D5\u06E5\u06E6\u06EE]|[\u06EF\u06FA-\u06FC\u06FF\u0710\u0712-\u072F\u074D-\u07A5\u07B1\u07CA-\u07EA]|[\u07F4\u07F5\u07FA\u0800-\u0815\u081A\u0824\u0828\u0840-\u0858\u08A0]|[\u08A2-\u08AC\u0904-\u0939\u093D\u0950\u0958-\u0961\u0971-\u0977]|[\u0979-\u097F\u0985-\u098C\u098F\u0990\u0993-\u09A8\u09AA-\u09B0\u09B2]|[\u09B6-\u09B9\u09BD\u09CE\u09DC\u09DD\u09DF-\u09E1\u09F0\u09F1\u0A05-\u0A0A]|[\u0A0F\u0A10\u0A13-\u0A28\u0A2A-\u0A30\u0A32\u0A33\u0A35\u0A36\u0A38\u0A39]|[\u0A59-\u0A5C\u0A5E\u0A72-\u0A74\u0A85-\u0A8D\u0A8F-\u0A91\u0A93-\u0AA8]|[\u0AAA-\u0AB0\u0AB2\u0AB3\u0AB5-\u0AB9\u0ABD\u0AD0\u0AE0\u0AE1\u0B05-\u0B0C]|[\u0B0F\u0B10\u0B13-\u0B28\u0B2A-\u0B30\u0B32\u0B33\u0B35-\u0B39\u0B3D\u0B5C]|[\u0B5D\u0B5F-\u0B61\u0B71\u0B83\u0B85-\u0B8A\u0B8E-\u0B90\u0B92-\u0B95\u0B99]|[\u0B9A\u0B9C\u0B9E\u0B9F\u0BA3\u0BA4\u0BA8-\u0BAA\u0BAE-\u0BB9\u0BD0]|[\u0C05-\u0C0C\u0C0E-\u0C10\u0C12-\u0C28\u0C2A-\u0C33\u0C35-\u0C39\u0C3D]|[\u0C58\u0C59\u0C60\u0C61\u0C85-\u0C8C\u0C8E-\u0C90\u0C92-\u0CA8\u0CAA-\u0CB3]|[\u0CB5-\u0CB9\u0CBD\u0CDE\u0CE0\u0CE1\u0CF1\u0CF2\u0D05-\u0D0C\u0D0E-\u0D10]|[\u0D12-\u0D3A\u0D3D\u0D4E\u0D60\u0D61\u0D7A-\u0D7F\u0D85-\u0D96\u0D9A-\u0DB1]|[\u0DB3-\u0DBB\u0DBD\u0DC0-\u0DC6\u0E01-\u0E30\u0E32\u0E33\u0E40-\u0E46\u0E81]|[\u0E82\u0E84\u0E87\u0E88\u0E8A\u0E8D\u0E94-\u0E97\u0E99-\u0E9F\u0EA1-\u0EA3]|[\u0EA5\u0EA7\u0EAA\u0EAB\u0EAD-\u0EB0\u0EB2\u0EB3\u0EBD\u0EC0-\u0EC4\u0EC6]|[\u0EDC-\u0EDF\u0F00\u0F40-\u0F47\u0F49-\u0F6C\u0F88-\u0F8C\u1000-\u102A]|[\u103F\u1050-\u1055\u105A-\u105D\u1061\u1065\u1066\u106E-\u1070\u1075-\u1081]|[\u108E\u10A0-\u10C5\u10C7\u10CD\u10D0-\u10FA\u10FC-\u1248\u124A-\u124D]|[\u1250-\u1256\u1258\u125A-\u125D\u1260-\u1288\u128A-\u128D\u1290-\u12B0]|[\u12B2-\u12B5\u12B8-\u12BE\u12C0\u12C2-\u12C5\u12C8-\u12D6\u12D8-\u1310]|[\u1312-\u1315\u1318-\u135A\u1380-\u138F\u13A0-\u13F4\u1401-\u166C]|[\u166F-\u167F\u1681-\u169A\u16A0-\u16EA\u1700-\u170C\u170E-\u1711]|[\u1720-\u1731\u1740-\u1751\u1760-\u176C\u176E-\u1770\u1780-\u17B3\u17D7]|[\u17DC\u1820-\u1877\u1880-\u18A8\u18AA\u18B0-\u18F5\u1900-\u191C]|[\u1950-\u196D\u1970-\u1974\u1980-\u19AB\u19C1-\u19C7\u1A00-\u1A16]|[\u1A20-\u1A54\u1AA7\u1B05-\u1B33\u1B45-\u1B4B\u1B83-\u1BA0\u1BAE\u1BAF]|[\u1BBA-\u1BE5\u1C00-\u1C23\u1C4D-\u1C4F\u1C5A-\u1C7D\u1CE9-\u1CEC]|[\u1CEE-\u1CF1\u1CF5\u1CF6\u1D00-\u1DBF\u1E00-\u1F15\u1F18-\u1F1D]|[\u1F20-\u1F45\u1F48-\u1F4D\u1F50-\u1F57\u1F59\u1F5B\u1F5D\u1F5F-\u1F7D]|[\u1F80-\u1FB4\u1FB6-\u1FBC\u1FBE\u1FC2-\u1FC4\u1FC6-\u1FCC\u1FD0-\u1FD3]|[\u1FD6-\u1FDB\u1FE0-\u1FEC\u1FF2-\u1FF4\u1FF6-\u1FFC\u2071\u207F]|[\u2090-\u209C\u2102\u2107\u210A-\u2113\u2115\u2119-\u211D\u2124\u2126\u2128]|[\u212A-\u212D\u212F-\u2139\u213C-\u213F\u2145-\u2149\u214E\u2183\u2184]|[\u2C00-\u2C2E\u2C30-\u2C5E\u2C60-\u2CE4\u2CEB-\u2CEE\u2CF2\u2CF3]|[\u2D00-\u2D25\u2D27\u2D2D\u2D30-\u2D67\u2D6F\u2D80-\u2D96\u2DA0-\u2DA6]|[\u2DA8-\u2DAE\u2DB0-\u2DB6\u2DB8-\u2DBE\u2DC0-\u2DC6\u2DC8-\u2DCE]|[\u2DD0-\u2DD6\u2DD8-\u2DDE\u2E2F\u3005\u3006\u3031-\u3035\u303B\u303C]|[\u3041-\u3096\u309D-\u309F\u30A1-\u30FA\u30FC-\u30FF\u3105-\u312D]|[\u3131-\u318E\u31A0-\u31BA\u31F0-\u31FF\u3400-\u4DB5\u4E00-\u9FCC]|[\uA000-\uA48C\uA4D0-\uA4FD\uA500-\uA60C\uA610-\uA61F\uA62A\uA62B]|[\uA640-\uA66E\uA67F-\uA697\uA6A0-\uA6E5\uA717-\uA71F\uA722-\uA788]|[\uA78B-\uA78E\uA790-\uA793\uA7A0-\uA7AA\uA7F8-\uA801\uA803-\uA805]|[\uA807-\uA80A\uA80C-\uA822\uA840-\uA873\uA882-\uA8B3\uA8F2-\uA8F7\uA8FB]|[\uA90A-\uA925\uA930-\uA946\uA960-\uA97C\uA984-\uA9B2\uA9CF\uAA00-\uAA28]|[\uAA40-\uAA42\uAA44-\uAA4B\uAA60-\uAA76\uAA7A\uAA80-\uAAAF\uAAB1\uAAB5]|[\uAAB6\uAAB9-\uAABD\uAAC0\uAAC2\uAADB-\uAADD\uAAE0-\uAAEA\uAAF2-\uAAF4]|[\uAB01-\uAB06\uAB09-\uAB0E\uAB11-\uAB16\uAB20-\uAB26\uAB28-\uAB2E]|[\uABC0-\uABE2\uAC00-\uD7A3\uD7B0-\uD7C6\uD7CB-\uD7FB\uF900-\uFA6D]|[\uFA70-\uFAD9\uFB00-\uFB06\uFB13-\uFB17\uFB1D\uFB1F-\uFB28\uFB2A-\uFB36]|[\uFB38-\uFB3C\uFB3E\uFB40\uFB41\uFB43\uFB44\uFB46-\uFBB1\uFBD3-\uFD3D]|[\uFD50-\uFD8F\uFD92-\uFDC7\uFDF0-\uFDFB\uFE70-\uFE74\uFE76-\uFEFC]|[\uFF21-\uFF3A\uFF41-\uFF5A\uFF66-\uFFBE\uFFC2-\uFFC7\uFFCA-\uFFCF]|[\uFFD2-\uFFD7\uFFDA-\uFFDC])/,/^(?:\s)/,/^(?:$)/],conditions:{string:{rules:[10,11],inclusive:!1},struct:{rules:[5,6,7],inclusive:!1},INITIAL:{rules:[0,1,2,3,4,8,9,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32],inclusive:!0}}};return t}();return w.lexer=x,t.prototype=w,w.Parser=t,new t}();"undefined"!=typeof t&&"undefined"!=typeof r&&(r.parser=i,r.Parser=i.Parser,r.parse=function(){return i.parse.apply(i,arguments)},r.main=function(e){e[1]||(console.log("Usage: "+e[0]+" FILE"),n.exit(1));var i=t("fs").readFileSync(t("path").normalize(e[1]),"utf8");return r.parser.parse(i)},"undefined"!=typeof e&&t.main===e&&r.main(n.argv.slice(1)))}).call(this,t("_process"))},{_process:3,fs:1,path:2}],111:[function(t,e,r){(function(e){"use strict";var n=t("../../logger"),i=new n.Log,a="",s=!1;r.setMessage=function(t){i.debug("Setting message to: "+t),a=t},r.getMessage=function(){return a},r.setInfo=function(t){s=t},r.getInfo=function(){return s},r.parseError=function(t,r){e.mermaidAPI.parseError(t,r)}}).call(this,"undefined"!=typeof global?global:"undefined"!=typeof self?self:"undefined"!=typeof window?window:{})},{"../../logger":126}],112:[function(t,e,r){"use strict";var n=t("./exampleDb"),i=t("./parser/example.js"),a=t("../../d3"),s=t("../../logger"),o=new s.Log;r.draw=function(t,e,r){var s;s=i.parser,s.yy=n,o.debug("Renering example diagram"),s.parse(t);var u=a.select("#"+e),c=u.append("g");c.append("text").attr("x",100).attr("y",40).attr("class","version").attr("font-size","32px").style("text-anchor","middle").text("mermaid "+r),u.attr("height",100),u.attr("width",400)}},{"../../d3":107,"../../logger":126,"./exampleDb":111,"./parser/example.js":113}],113:[function(t,e,r){(function(n){"use strict";var i=function(){function t(){this.yy={}}var e=function(t,e,r,n){for(r=r||{},n=t.length;n--;r[t[n]]=e);return r},r=[6,9,10,12],n={trace:function(){},yy:{},symbols_:{error:2,start:3,info:4,document:5,EOF:6,line:7,statement:8,NL:9,showInfo:10,message:11,say:12,TXT:13,$accept:0,$end:1},terminals_:{2:"error",4:"info",6:"EOF",9:"NL",10:"showInfo",12:"say",13:"TXT"},productions_:[0,[3,3],[5,0],[5,2],[7,1],[7,1],[8,1],[8,1],[11,2]],performAction:function(t,e,r,n,i,a,s){var o=a.length-1;switch(i){case 1:return n;case 4:break;case 6:n.setInfo(!0);break;case 7:n.setMessage(a[o]);break;case 8:this.$=a[o-1].substring(1).trim().replace(/\\n/gm,"\n")}},table:[{3:1,4:[1,2]},{1:[3]},e(r,[2,2],{5:3}),{6:[1,4],7:5,8:6,9:[1,7],10:[1,8],11:9,12:[1,10]},{1:[2,1]},e(r,[2,3]),e(r,[2,4]),e(r,[2,5]),e(r,[2,6]),e(r,[2,7]),{13:[1,11]},e(r,[2,8])],defaultActions:{4:[2,1]},parseError:function(t,e){if(!e.recoverable){var r=function(t,e){this.message=t,this.hash=e};throw r.prototype=new Error,new r(t,e)}this.trace(t)},parse:function(t){var e=this,r=[0],n=[null],i=[],a=this.table,s="",o=0,u=0,c=0,l=2,h=1,d=i.slice.call(arguments,1),f=Object.create(this.lexer),p={yy:{}};for(var g in this.yy)Object.prototype.hasOwnProperty.call(this.yy,g)&&(p.yy[g]=this.yy[g]);f.setInput(t,p.yy),p.yy.lexer=f,p.yy.parser=this,"undefined"==typeof f.yylloc&&(f.yylloc={});var m=f.yylloc;i.push(m);var y=f.options&&f.options.ranges;"function"==typeof p.yy.parseError?this.parseError=p.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;for(var v,b,_,A,w,x,E,k,D,C=function(){var t;return t=f.lex()||h,"number"!=typeof t&&(t=e.symbols_[t]||t),t},F={};;){if(_=r[r.length-1],this.defaultActions[_]?A=this.defaultActions[_]:((null===v||"undefined"==typeof v)&&(v=C()),A=a[_]&&a[_][v]),"undefined"==typeof A||!A.length||!A[0]){var T="";D=[];for(x in a[_])this.terminals_[x]&&x>l&&D.push("'"+this.terminals_[x]+"'");T=f.showPosition?"Parse error on line "+(o+1)+":\n"+f.showPosition()+"\nExpecting "+D.join(", ")+", got '"+(this.terminals_[v]||v)+"'":"Parse error on line "+(o+1)+": Unexpected "+(v==h?"end of input":"'"+(this.terminals_[v]||v)+"'"),this.parseError(T,{text:f.match,token:this.terminals_[v]||v,line:f.yylineno,loc:m,expected:D})}if(A[0]instanceof Array&&A.length>1)throw new Error("Parse Error: multiple actions possible at state: "+_+", token: "+v);switch(A[0]){case 1:r.push(v),n.push(f.yytext),i.push(f.yylloc),r.push(A[1]),v=null,b?(v=b,b=null):(u=f.yyleng,s=f.yytext,o=f.yylineno,m=f.yylloc,c>0&&c--);break;case 2:if(E=this.productions_[A[1]][1],F.$=n[n.length-E],F._$={first_line:i[i.length-(E||1)].first_line,last_line:i[i.length-1].last_line,first_column:i[i.length-(E||1)].first_column,last_column:i[i.length-1].last_column},y&&(F._$.range=[i[i.length-(E||1)].range[0],i[i.length-1].range[1]]),w=this.performAction.apply(F,[s,u,o,p.yy,A[1],n,i].concat(d)),"undefined"!=typeof w)return 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e=t.length,r=t.split(/(?:\r\n?|\n)/g);this._input=t+this._input,this.yytext=this.yytext.substr(0,this.yytext.length-e),this.offset-=e;var n=this.match.split(/(?:\r\n?|\n)/g);this.match=this.match.substr(0,this.match.length-1),this.matched=this.matched.substr(0,this.matched.length-1),r.length-1&&(this.yylineno-=r.length-1);var i=this.yylloc.range;return this.yylloc={first_line:this.yylloc.first_line,last_line:this.yylineno+1,first_column:this.yylloc.first_column,last_column:r?(r.length===n.length?this.yylloc.first_column:0)+n[n.length-r.length].length-r[0].length:this.yylloc.first_column-e},this.options.ranges&&(this.yylloc.range=[i[0],i[0]+this.yyleng-e]),this.yyleng=this.yytext.length,this},more:function(){return this._more=!0,this},reject:function(){return this.options.backtrack_lexer?(this._backtrack=!0,this):this.parseError("Lexical error on line "+(this.yylineno+1)+". You can only invoke reject() in the lexer when the lexer is of the backtracking persuasion (options.backtrack_lexer = true).\n"+this.showPosition(),{text:"",token:null,line:this.yylineno})},less:function(t){this.unput(this.match.slice(t))},pastInput:function(){var t=this.matched.substr(0,this.matched.length-this.match.length);return(t.length>20?"...":"")+t.substr(-20).replace(/\n/g,"")},upcomingInput:function(){var t=this.match;return t.length<20&&(t+=this._input.substr(0,20-t.length)),(t.substr(0,20)+(t.length>20?"...":"")).replace(/\n/g,"")},showPosition:function(){var t=this.pastInput(),e=new Array(t.length+1).join("-");return t+this.upcomingInput()+"\n"+e+"^"},test_match:function(t,e){var r,n,i;if(this.options.backtrack_lexer&&(i={yylineno:this.yylineno,yylloc:{first_line:this.yylloc.first_line,last_line:this.last_line,first_column:this.yylloc.first_column,last_column:this.yylloc.last_column},yytext:this.yytext,match:this.match,matches:this.matches,matched:this.matched,yyleng:this.yyleng,offset:this.offset,_more:this._more,_input:this._input,yy:this.yy,conditionStack:this.conditionStack.slice(0),done:this.done},this.options.ranges&&(i.yylloc.range=this.yylloc.range.slice(0))),n=t[0].match(/(?:\r\n?|\n).*/g),n&&(this.yylineno+=n.length),this.yylloc={first_line:this.yylloc.last_line,last_line:this.yylineno+1,first_column:this.yylloc.last_column,last_column:n?n[n.length-1].length-n[n.length-1].match(/\r?\n?/)[0].length:this.yylloc.last_column+t[0].length},this.yytext+=t[0],this.match+=t[0],this.matches=t,this.yyleng=this.yytext.length,this.options.ranges&&(this.yylloc.range=[this.offset,this.offset+=this.yyleng]),this._more=!1,this._backtrack=!1,this._input=this._input.slice(t[0].length),this.matched+=t[0],r=this.performAction.call(this,this.yy,this,e,this.conditionStack[this.conditionStack.length-1]),this.done&&this._input&&(this.done=!1),r)return r;if(this._backtrack){for(var a in i)this[a]=i[a];return!1}return!1},next:function(){if(this.done)return this.EOF;this._input||(this.done=!0);var t,e,r,n;this._more||(this.yytext="",this.match="");for(var i=this._currentRules(),a=0;ae[0].length)){if(e=r,n=a,this.options.backtrack_lexer){if(t=this.test_match(r,i[a]),t!==!1)return t;if(this._backtrack){e=!1;continue}return!1}if(!this.options.flex)break}return e?(t=this.test_match(e,i[n]),t!==!1?t:!1):""===this._input?this.EOF:this.parseError("Lexical error on line "+(this.yylineno+1)+". Unrecognized text.\n"+this.showPosition(),{text:"",token:null,line:this.yylineno})},lex:function(){var t=this.next();return t?t:this.lex()},begin:function(t){this.conditionStack.push(t)},popState:function(){var t=this.conditionStack.length-1;return t>0?this.conditionStack.pop():this.conditionStack[0]},_currentRules:function(){return this.conditionStack.length&&this.conditionStack[this.conditionStack.length-1]?this.conditions[this.conditionStack[this.conditionStack.length-1]].rules:this.conditions.INITIAL.rules},topState:function(t){return t=this.conditionStack.length-1-Math.abs(t||0),t>=0?this.conditionStack[t]:"INITIAL"},pushState:function(t){this.begin(t)},stateStackSize:function(){return this.conditionStack.length},options:{"case-insensitive":!0},performAction:function(t,e,r,n){switch(r){case 0:return 9;case 1:return 10;case 2:return 4;case 3:return 12;case 4:return 13;case 5:return 6;case 6:return"INVALID"}},rules:[/^(?:[\n]+)/i,/^(?:showInfo\b)/i,/^(?:info\b)/i,/^(?:say\b)/i,/^(?::[^#\n;]+)/i,/^(?:$)/i,/^(?:.)/i],conditions:{INITIAL:{rules:[0,1,2,3,4,5,6],inclusive:!0}}};return t}();return n.lexer=i,t.prototype=n,n.Parser=t,new t}();"undefined"!=typeof t&&"undefined"!=typeof r&&(r.parser=i,r.Parser=i.Parser,r.parse=function(){return i.parse.apply(i,arguments)},r.main=function(e){e[1]||(console.log("Usage: "+e[0]+" FILE"),n.exit(1));var i=t("fs").readFileSync(t("path").normalize(e[1]),"utf8");return r.parser.parse(i)},"undefined"!=typeof e&&t.main===e&&r.main(n.argv.slice(1)))}).call(this,t("_process"))},{_process:3,fs:1,path:2}],114:[function(t,e,r){"use strict";var n,i=t("../../logger"),a=new i.Log;if(t)try{n=t("dagre-d3")}catch(s){a.debug("Could not load dagre-d3")}n||(n=window.dagreD3),e.exports=n},{"../../logger":126,"dagre-d3":4}],115:[function(t,e,r){"use strict";var n=t("./graphDb"),i=t("./parser/flow"),a=t("./parser/dot"),s=t("../../d3"),o=t("./dagre-d3"),u=t("../../logger"),c=new u.Log,l={};e.exports.setConf=function(t){var e,r=Object.keys(t);for(e=0;e0&&(s=a.classes.join(" "));var o="";o=n(o,a.styles),i="undefined"==typeof a.text?a.id:a.text;var u="";l.htmlLabels?(u="html",i=i.replace(/fa:fa[\w\-]+/g,function(t){return''})):(i=i.replace(/
    /g,"\n"),u="text");var c=0,h="";switch(a.type){case"round":c=5,h="rect";break;case"square":h="rect";break;case"diamond":h="question";break;case"odd":h="rect_left_inv_arrow";break;case"odd_right":h="rect_left_inv_arrow";break;case"circle":h="circle";break;case"ellipse":h="ellipse";break;case"group":h="rect",i="";break;default:h="rect"}e.setNode(a.id,{labelType:u,shape:h,label:i,rx:c,ry:c,"class":s,style:o,id:a.id})})},r.addEdges=function(t,e){var r,n,i=0;"undefined"!=typeof t.defaultStyle&&(n=t.defaultStyle.toString().replace(/,/g,";")),t.forEach(function(t){i++,r="arrow_open"===t.type?"none":"normal";var a="";if("undefined"!=typeof t.style)t.style.forEach(function(t){a=a+t+";"});else switch(t.stroke){case"normal":a="fill:none","undefined"!=typeof n&&(a=n);break;case"dotted":a="stroke: #333; fill:none;stroke-width:2px;stroke-dasharray:3;";break;case"thick":a="stroke: #333; stroke-width: 3.5px;fill:none"}if("undefined"==typeof t.text)"undefined"==typeof t.style?e.setEdge(t.start,t.end,{style:a,arrowhead:r},i):e.setEdge(t.start,t.end,{style:a,arrowheadStyle:"fill: #333",arrowhead:r},i);else{var s=t.text.replace(/
    /g,"\n");"undefined"==typeof t.style?l.htmlLabels?e.setEdge(t.start,t.end,{labelType:"html",style:a,labelpos:"c",label:''+t.text+"",arrowheadStyle:"fill: #333",arrowhead:r},i):e.setEdge(t.start,t.end,{labelType:"text",style:"stroke: #333; stroke-width: 1.5px;fill:none",labelpos:"c",label:s,arrowheadStyle:"fill: #333",arrowhead:r},i):e.setEdge(t.start,t.end,{labelType:"text",style:a,arrowheadStyle:"fill: #333",label:s,arrowhead:r},i)}})},r.getClasses=function(t,e){var r;n.clear(),r=e?a.parser:i.parser,r.yy=n,r.parse(t);var s=n.getClasses();return"undefined"==typeof s["default"]&&(s["default"]={id:"default"},s["default"].styles=[],s["default"].clusterStyles=["rx:4px","fill: rgb(255, 255, 222)","rx: 4px","stroke: rgb(170, 170, 51)","stroke-width: 1px"],s["default"].nodeLabelStyles=["fill:#000","stroke:none","font-weight:300",'font-family:"Helvetica Neue",Helvetica,Arial,sans-serf',"font-size:14px"],s["default"].edgeLabelStyles=["fill:#000","stroke:none","font-weight:300",'font-family:"Helvetica Neue",Helvetica,Arial,sans-serf',"font-size:14px"]), +s},r.draw=function(t,e,u){c.debug("Drawing flowchart");var h;n.clear(),h=u?a.parser:i.parser,h.yy=n;try{h.parse(t)}catch(d){c.debug("Parsing failed")}var f;f=n.getDirection(),"undefined"==typeof f&&(f="TD");var p,g=new o.graphlib.Graph({multigraph:!0,compound:!0}).setGraph({rankdir:f,marginx:20,marginy:20}).setDefaultEdgeLabel(function(){return{}}),m=n.getSubGraphs(),y=0;for(y=m.length-1;y>=0;y--)p=m[y],n.addVertex(p.id,p.title,"group",void 0);var v=n.getVertices(),b=n.getEdges();y=0;var _;for(y=m.length-1;y>=0;y--)for(p=m[y],s.selectAll("cluster").append("text"),_=0;_0?t.split(",").forEach(function(t){"undefined"!=typeof vertices[t]&&vertices[t].classes.push(e)}):"undefined"!=typeof vertices[t]&&vertices[t].classes.push(e)};var setTooltip=function(t,e){"undefined"!=typeof e&&(tooltips[t]=e)},setClickFun=function setClickFun(id,functionName){"undefined"!=typeof functionName&&"undefined"!=typeof vertices[id]&&funs.push(function(element){var elem=d3.select(element).select("#"+id);null!==elem&&elem.on("click",function(){eval(functionName+"('"+id+"')")})})},setLink=function(t,e){"undefined"!=typeof e&&"undefined"!=typeof vertices[t]&&funs.push(function(r){var n=d3.select(r).select("#"+t);null!==n&&n.on("click",function(){window.open(e,"newTab")})})};exports.getTooltip=function(t){return tooltips[t]},exports.setClickEvent=function(t,e,r,n){t.indexOf(",")>0?t.split(",").forEach(function(t){setTooltip(t,n),setClickFun(t,e),setLink(t,r)}):(setTooltip(t,n),setClickFun(t,e),setLink(t,r))},exports.bindFunctions=function(t){funs.forEach(function(e){e(t)})},exports.getDirection=function(){return direction},exports.getVertices=function(){return vertices},exports.getEdges=function(){return edges},exports.getClasses=function(){return classes};var setupToolTips=function(t){var e=d3.select(".mermaidTooltip");null===e[0][0]&&(e=d3.select("body").append("div").attr("class","mermaidTooltip").style("opacity",0));var r=d3.select(t).select("svg"),n=r.selectAll("g.node");n.on("mouseover",function(){var t=d3.select(this),r=t.attr("title");if(null!==r){var n=this.getBoundingClientRect();e.transition().duration(200).style("opacity",".9"),e.html(t.attr("title")).style("left",n.left+(n.right-n.left)/2+"px").style("top",n.top-14+document.body.scrollTop+"px"),t.classed("hover",!0)}}).on("mouseout",function(){e.transition().duration(500).style("opacity",0);var t=d3.select(this);t.classed("hover",!1)})};funs.push(setupToolTips),exports.clear=function(){vertices={},classes={},edges=[],funs=[],funs.push(setupToolTips),subGraphs=[],subCount=0,tooltips=[]},exports.defaultStyle=function(){return"fill:#ffa;stroke: #f66; stroke-width: 3px; stroke-dasharray: 5, 5;fill:#ffa;stroke: #666;"},exports.addSubGraph=function(t,e){function r(t){var e={"boolean":{},number:{},string:{}},r=[];return t.filter(function(t){var n=typeof t;return" "===t?!1:n in e?e[n].hasOwnProperty(t)?!1:e[n][t]=!0:r.indexOf(t)>=0?!1:r.push(t)})}var n=[];n=r(n.concat.apply(n,t));var i={id:"subGraph"+subCount,nodes:n,title:e};return subGraphs.push(i),subCount+=1,i.id};var getPosForId=function(t){var e;for(e=0;e2e3)){if(posCrossRef[secCount]=r,subGraphs[r].id===e)return{result:!0,count:0};for(var i=0,a=1;i=0){var o=t(e,s);if(o.result)return{result:!0,count:a+o.count};a+=o.count}i+=1}return{result:!1,count:a}}};exports.getDepthFirstPos=function(t){return posCrossRef[t]},exports.indexNodes=function(){secCount=-1,subGraphs.length>0&&indexNodes("none",subGraphs.length-1,0)},exports.getSubGraphs=function(){return subGraphs},exports.parseError=function(t,e){global.mermaidAPI.parseError(t,e)}}).call(this,"undefined"!=typeof global?global:"undefined"!=typeof self?self:"undefined"!=typeof window?window:{})},{"../../d3":107,"../../logger":126}],117:[function(t,e,r){(function(n){"use strict";var i=function(){function t(){this.yy={}}var e=function(t,e,r,n){for(r=r||{},n=t.length;n--;r[t[n]]=e);return r},r=[1,5],n=[1,6],i=[1,12],a=[1,13],s=[1,14],o=[1,15],u=[1,16],c=[1,17],l=[1,18],h=[1,19],d=[1,20],f=[1,21],p=[1,22],g=[8,16,17,18,19,20,21,22,23,24,25,26],m=[1,37],y=[1,33],v=[1,34],b=[1,35],_=[1,36],A=[8,10,16,17,18,19,20,21,22,23,24,25,26,28,32,37,39,40,45,57,58],w=[10,28],x=[10,28,37,57,58],E=[2,49],k=[1,45],D=[1,48],C=[1,49],F=[1,52],T=[2,65],S=[1,65],B=[1,66],L=[1,67],O=[1,68],I=[1,69],N=[1,70],M=[1,71],R=[1,72],P=[1,73],q=[8,16,17,18,19,20,21,22,23,24,25,26,47],j=[10,28,37],U={trace:function(){},yy:{},symbols_:{error:2,expressions:3,graph:4,EOF:5,graphStatement:6,idStatement:7,"{":8,stmt_list:9,"}":10,strict:11,GRAPH:12,DIGRAPH:13,textNoTags:14,textNoTagsToken:15,ALPHA:16,NUM:17,COLON:18,PLUS:19,EQUALS:20,MULT:21,DOT:22,BRKT:23,SPACE:24,MINUS:25,keywords:26,stmt:27,";":28,node_stmt:29,edge_stmt:30,attr_stmt:31,"=":32,subgraph:33,attr_list:34,NODE:35,EDGE:36,"[":37,a_list:38,"]":39,",":40,edgeRHS:41,node_id:42,edgeop:43,port:44,":":45,compass_pt:46,SUBGRAPH:47,n:48,ne:49,e:50,se:51,s:52,sw:53,w:54,nw:55,c:56,ARROW_POINT:57,ARROW_OPEN:58,$accept:0,$end:1},terminals_:{2:"error",5:"EOF",8:"{",10:"}",11:"strict",12:"GRAPH",13:"DIGRAPH",16:"ALPHA",17:"NUM",18:"COLON",19:"PLUS",20:"EQUALS",21:"MULT",22:"DOT",23:"BRKT",24:"SPACE",25:"MINUS",26:"keywords",28:";",32:"=",35:"NODE",36:"EDGE",37:"[",39:"]",40:",",45:":",47:"SUBGRAPH",48:"n",49:"ne",50:"e",51:"se",52:"s",53:"sw",54:"w",55:"nw",56:"c",57:"ARROW_POINT",58:"ARROW_OPEN"},productions_:[0,[3,2],[4,5],[4,6],[4,4],[6,1],[6,1],[7,1],[14,1],[14,2],[15,1],[15,1],[15,1],[15,1],[15,1],[15,1],[15,1],[15,1],[15,1],[15,1],[15,1],[9,1],[9,3],[27,1],[27,1],[27,1],[27,3],[27,1],[31,2],[31,2],[31,2],[34,4],[34,3],[34,3],[34,2],[38,5],[38,5],[38,3],[30,3],[30,3],[30,2],[30,2],[41,3],[41,3],[41,2],[41,2],[29,2],[29,1],[42,2],[42,1],[44,4],[44,2],[44,2],[33,5],[33,4],[33,3],[46,1],[46,1],[46,1],[46,1],[46,1],[46,1],[46,1],[46,1],[46,1],[46,0],[43,1],[43,1]],performAction:function(t,e,r,n,i,a,s){var o=a.length-1;switch(i){case 1:this.$=a[o-1];break;case 2:this.$=a[o-4];break;case 3:this.$=a[o-5];break;case 4:this.$=a[o-3];break;case 8:case 10:case 11:this.$=a[o];break;case 9:this.$=a[o-1]+""+a[o];break;case 12:case 13:case 14:case 15:case 16:case 18:case 19:case 20:this.$=a[o];break;case 17:this.$="
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this.yylloc={first_line:this.yylloc.first_line,last_line:this.yylineno+1,first_column:this.yylloc.first_column,last_column:r?(r.length===n.length?this.yylloc.first_column:0)+n[n.length-r.length].length-r[0].length:this.yylloc.first_column-e},this.options.ranges&&(this.yylloc.range=[i[0],i[0]+this.yyleng-e]),this.yyleng=this.yytext.length,this},more:function(){return this._more=!0,this},reject:function(){return this.options.backtrack_lexer?(this._backtrack=!0,this):this.parseError("Lexical error on line "+(this.yylineno+1)+". 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a[_])this.terminals_[x]&&x>l&&D.push("'"+this.terminals_[x]+"'");T=f.showPosition?"Parse error on line "+(o+1)+":\n"+f.showPosition()+"\nExpecting "+D.join(", ")+", got '"+(this.terminals_[v]||v)+"'":"Parse error on line "+(o+1)+": Unexpected "+(v==h?"end of input":"'"+(this.terminals_[v]||v)+"'"),this.parseError(T,{text:f.match,token:this.terminals_[v]||v,line:f.yylineno,loc:m,expected:D})}if(A[0]instanceof Array&&A.length>1)throw new Error("Parse Error: multiple actions possible at state: "+_+", token: "+v);switch(A[0]){case 1:r.push(v),n.push(f.yytext),i.push(f.yylloc),r.push(A[1]),v=null,b?(v=b,b=null):(u=f.yyleng,s=f.yytext,o=f.yylineno,m=f.yylloc,c>0&&c--);break;case 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this.yy=e||this.yy||{},this._input=t,this._more=this._backtrack=this.done=!1,this.yylineno=this.yyleng=0,this.yytext=this.matched=this.match="",this.conditionStack=["INITIAL"],this.yylloc={first_line:1,first_column:0,last_line:1,last_column:0},this.options.ranges&&(this.yylloc.range=[0,0]),this.offset=0,this},input:function(){var t=this._input[0];this.yytext+=t,this.yyleng++,this.offset++,this.match+=t,this.matched+=t;var e=t.match(/(?:\r\n?|\n).*/g);return e?(this.yylineno++,this.yylloc.last_line++):this.yylloc.last_column++,this.options.ranges&&this.yylloc.range[1]++,this._input=this._input.slice(1),t},unput:function(t){var e=t.length,r=t.split(/(?:\r\n?|\n)/g);this._input=t+this._input,this.yytext=this.yytext.substr(0,this.yytext.length-e),this.offset-=e;var n=this.match.split(/(?:\r\n?|\n)/g);this.match=this.match.substr(0,this.match.length-1),this.matched=this.matched.substr(0,this.matched.length-1),r.length-1&&(this.yylineno-=r.length-1);var i=this.yylloc.range;return this.yylloc={first_line:this.yylloc.first_line,last_line:this.yylineno+1,first_column:this.yylloc.first_column,last_column:r?(r.length===n.length?this.yylloc.first_column:0)+n[n.length-r.length].length-r[0].length:this.yylloc.first_column-e},this.options.ranges&&(this.yylloc.range=[i[0],i[0]+this.yyleng-e]),this.yyleng=this.yytext.length,this},more:function(){return this._more=!0,this},reject:function(){return this.options.backtrack_lexer?(this._backtrack=!0,this):this.parseError("Lexical error on line "+(this.yylineno+1)+". You can only invoke reject() in the lexer when the lexer is of the backtracking persuasion (options.backtrack_lexer = true).\n"+this.showPosition(),{text:"",token:null,line:this.yylineno})},less:function(t){this.unput(this.match.slice(t))},pastInput:function(){var t=this.matched.substr(0,this.matched.length-this.match.length);return(t.length>20?"...":"")+t.substr(-20).replace(/\n/g,"")},upcomingInput:function(){var t=this.match;return t.length<20&&(t+=this._input.substr(0,20-t.length)),(t.substr(0,20)+(t.length>20?"...":"")).replace(/\n/g,"")},showPosition:function(){var t=this.pastInput(),e=new Array(t.length+1).join("-");return t+this.upcomingInput()+"\n"+e+"^"},test_match:function(t,e){var r,n,i;if(this.options.backtrack_lexer&&(i={yylineno:this.yylineno,yylloc:{first_line:this.yylloc.first_line,last_line:this.last_line,first_column:this.yylloc.first_column,last_column:this.yylloc.last_column},yytext:this.yytext,match:this.match,matches:this.matches,matched:this.matched,yyleng:this.yyleng,offset:this.offset,_more:this._more,_input:this._input,yy:this.yy,conditionStack:this.conditionStack.slice(0),done:this.done},this.options.ranges&&(i.yylloc.range=this.yylloc.range.slice(0))),n=t[0].match(/(?:\r\n?|\n).*/g),n&&(this.yylineno+=n.length),this.yylloc={first_line:this.yylloc.last_line,last_line:this.yylineno+1,first_column:this.yylloc.last_column,last_column:n?n[n.length-1].length-n[n.length-1].match(/\r?\n?/)[0].length:this.yylloc.last_column+t[0].length},this.yytext+=t[0],this.match+=t[0],this.matches=t,this.yyleng=this.yytext.length,this.options.ranges&&(this.yylloc.range=[this.offset,this.offset+=this.yyleng]),this._more=!1,this._backtrack=!1,this._input=this._input.slice(t[0].length),this.matched+=t[0],r=this.performAction.call(this,this.yy,this,e,this.conditionStack[this.conditionStack.length-1]),this.done&&this._input&&(this.done=!1),r)return r;if(this._backtrack){for(var a in i)this[a]=i[a];return!1}return!1},next:function(){if(this.done)return this.EOF;this._input||(this.done=!0);var t,e,r,n;this._more||(this.yytext="",this.match="");for(var i=this._currentRules(),a=0;ae[0].length)){if(e=r,n=a,this.options.backtrack_lexer){if(t=this.test_match(r,i[a]),t!==!1)return t;if(this._backtrack){e=!1;continue}return!1}if(!this.options.flex)break}return e?(t=this.test_match(e,i[n]),t!==!1?t:!1):""===this._input?this.EOF:this.parseError("Lexical error on line "+(this.yylineno+1)+". Unrecognized text.\n"+this.showPosition(),{text:"",token:null,line:this.yylineno})},lex:function(){var t=this.next();return t?t:this.lex()},begin:function(t){this.conditionStack.push(t)},popState:function(){var t=this.conditionStack.length-1;return t>0?this.conditionStack.pop():this.conditionStack[0]},_currentRules:function(){return this.conditionStack.length&&this.conditionStack[this.conditionStack.length-1]?this.conditions[this.conditionStack[this.conditionStack.length-1]].rules:this.conditions.INITIAL.rules},topState:function(t){return t=this.conditionStack.length-1-Math.abs(t||0),t>=0?this.conditionStack[t]:"INITIAL"},pushState:function(t){this.begin(t)},stateStackSize:function(){return this.conditionStack.length},options:{},performAction:function(t,e,r,n){switch(r){case 0:break;case 1:this.begin("string");break;case 2:this.popState();break;case 3:return"STR";case 4:return 71;case 5:return 78;case 6:return 72;case 7:return 73;case 8:return 74;case 9:return 75;case 10:return 12;case 11:return 30;case 12:return 32;case 13:return 13;case 14:return 13;case 15:return 13;case 16:return 13;case 17:return 13;case 18:return 13;case 19:return 81;case 20:return 90;case 21:return 88;case 22:return 8;case 23:return 85;case 24:return 97;case 25:return 16;case 26:return 15;case 27:return 17;case 28:return 18;case 29:return 53;case 30:return 51;case 31:return 52;case 32:return 54;case 33:return 58;case 34:return 56;case 35:return 57;case 36:return 59;case 37:return 58;case 38:return 56;case 39:return 57;case 40:return 59;case 41:return 63;case 42:return 61;case 43:return 62;case 44:return 64;case 45:return 50;case 46:return 55;case 47:return 60;case 48:return 40;case 49:return 41;case 50:return 46;case 51:return 91;case 52:return 95;case 53:return 83;case 54:return 96;case 55:return 96;case 56:return 87;case 57:return 93;case 58:return 94;case 59:return 65;case 60:return 38;case 61:return 39;case 62:return 36;case 63:return 37;case 64:return 42;case 65:return 43;case 66:return 100;case 67:return 9;case 68:return 10;case 69:return 11}},rules:[/^(?:%%[^\n]*)/,/^(?:["])/,/^(?:["])/,/^(?:[^"]*)/,/^(?:style\b)/,/^(?:default\b)/,/^(?:linkStyle\b)/,/^(?:classDef\b)/,/^(?:class\b)/,/^(?:click\b)/,/^(?:graph\b)/,/^(?:subgraph\b)/,/^(?:end\b\s*)/,/^(?:LR\b)/,/^(?:RL\b)/,/^(?:TB\b)/,/^(?:BT\b)/,/^(?:TD\b)/,/^(?:BR\b)/,/^(?:[0-9]+)/,/^(?:#)/,/^(?::)/,/^(?:;)/,/^(?:,)/,/^(?:\*)/,/^(?:<)/,/^(?:>)/,/^(?:\^)/,/^(?:v\b)/,/^(?:\s*--[x]\s*)/,/^(?:\s*-->\s*)/,/^(?:\s*--[o]\s*)/,/^(?:\s*---\s*)/,/^(?:\s*-\.-[x]\s*)/,/^(?:\s*-\.->\s*)/,/^(?:\s*-\.-[o]\s*)/,/^(?:\s*-\.-\s*)/,/^(?:\s*.-[x]\s*)/,/^(?:\s*\.->\s*)/,/^(?:\s*\.-[o]\s*)/,/^(?:\s*\.-\s*)/,/^(?:\s*==[x]\s*)/,/^(?:\s*==>\s*)/,/^(?:\s*==[o]\s*)/,/^(?:\s*==[\=]\s*)/,/^(?:\s*--\s*)/,/^(?:\s*-\.\s*)/,/^(?:\s*==\s*)/,/^(?:\(-)/,/^(?:-\))/,/^(?:-)/,/^(?:\.)/,/^(?:\+)/,/^(?:%)/,/^(?:=)/,/^(?:=)/,/^(?:[A-Za-z]+)/,/^(?:[!"#$%&'*+,-.`?\\_\/])/,/^(?:[\u00AA\u00B5\u00BA\u00C0-\u00D6\u00D8-\u00F6]|[\u00F8-\u02C1\u02C6-\u02D1\u02E0-\u02E4\u02EC\u02EE\u0370-\u0374\u0376\u0377]|[\u037A-\u037D\u0386\u0388-\u038A\u038C\u038E-\u03A1\u03A3-\u03F5]|[\u03F7-\u0481\u048A-\u0527\u0531-\u0556\u0559\u0561-\u0587\u05D0-\u05EA]|[\u05F0-\u05F2\u0620-\u064A\u066E\u066F\u0671-\u06D3\u06D5\u06E5\u06E6\u06EE]|[\u06EF\u06FA-\u06FC\u06FF\u0710\u0712-\u072F\u074D-\u07A5\u07B1\u07CA-\u07EA]|[\u07F4\u07F5\u07FA\u0800-\u0815\u081A\u0824\u0828\u0840-\u0858\u08A0]|[\u08A2-\u08AC\u0904-\u0939\u093D\u0950\u0958-\u0961\u0971-\u0977]|[\u0979-\u097F\u0985-\u098C\u098F\u0990\u0993-\u09A8\u09AA-\u09B0\u09B2]|[\u09B6-\u09B9\u09BD\u09CE\u09DC\u09DD\u09DF-\u09E1\u09F0\u09F1\u0A05-\u0A0A]|[\u0A0F\u0A10\u0A13-\u0A28\u0A2A-\u0A30\u0A32\u0A33\u0A35\u0A36\u0A38\u0A39]|[\u0A59-\u0A5C\u0A5E\u0A72-\u0A74\u0A85-\u0A8D\u0A8F-\u0A91\u0A93-\u0AA8]|[\u0AAA-\u0AB0\u0AB2\u0AB3\u0AB5-\u0AB9\u0ABD\u0AD0\u0AE0\u0AE1\u0B05-\u0B0C]|[\u0B0F\u0B10\u0B13-\u0B28\u0B2A-\u0B30\u0B32\u0B33\u0B35-\u0B39\u0B3D\u0B5C]|[\u0B5D\u0B5F-\u0B61\u0B71\u0B83\u0B85-\u0B8A\u0B8E-\u0B90\u0B92-\u0B95\u0B99]|[\u0B9A\u0B9C\u0B9E\u0B9F\u0BA3\u0BA4\u0BA8-\u0BAA\u0BAE-\u0BB9\u0BD0]|[\u0C05-\u0C0C\u0C0E-\u0C10\u0C12-\u0C28\u0C2A-\u0C33\u0C35-\u0C39\u0C3D]|[\u0C58\u0C59\u0C60\u0C61\u0C85-\u0C8C\u0C8E-\u0C90\u0C92-\u0CA8\u0CAA-\u0CB3]|[\u0CB5-\u0CB9\u0CBD\u0CDE\u0CE0\u0CE1\u0CF1\u0CF2\u0D05-\u0D0C\u0D0E-\u0D10]|[\u0D12-\u0D3A\u0D3D\u0D4E\u0D60\u0D61\u0D7A-\u0D7F\u0D85-\u0D96\u0D9A-\u0DB1]|[\u0DB3-\u0DBB\u0DBD\u0DC0-\u0DC6\u0E01-\u0E30\u0E32\u0E33\u0E40-\u0E46\u0E81]|[\u0E82\u0E84\u0E87\u0E88\u0E8A\u0E8D\u0E94-\u0E97\u0E99-\u0E9F\u0EA1-\u0EA3]|[\u0EA5\u0EA7\u0EAA\u0EAB\u0EAD-\u0EB0\u0EB2\u0EB3\u0EBD\u0EC0-\u0EC4\u0EC6]|[\u0EDC-\u0EDF\u0F00\u0F40-\u0F47\u0F49-\u0F6C\u0F88-\u0F8C\u1000-\u102A]|[\u103F\u1050-\u1055\u105A-\u105D\u1061\u1065\u1066\u106E-\u1070\u1075-\u1081]|[\u108E\u10A0-\u10C5\u10C7\u10CD\u10D0-\u10FA\u10FC-\u1248\u124A-\u124D]|[\u1250-\u1256\u1258\u125A-\u125D\u1260-\u1288\u128A-\u128D\u1290-\u12B0]|[\u12B2-\u12B5\u12B8-\u12BE\u12C0\u12C2-\u12C5\u12C8-\u12D6\u12D8-\u1310]|[\u1312-\u1315\u1318-\u135A\u1380-\u138F\u13A0-\u13F4\u1401-\u166C]|[\u166F-\u167F\u1681-\u169A\u16A0-\u16EA\u1700-\u170C\u170E-\u1711]|[\u1720-\u1731\u1740-\u1751\u1760-\u176C\u176E-\u1770\u1780-\u17B3\u17D7]|[\u17DC\u1820-\u1877\u1880-\u18A8\u18AA\u18B0-\u18F5\u1900-\u191C]|[\u1950-\u196D\u1970-\u1974\u1980-\u19AB\u19C1-\u19C7\u1A00-\u1A16]|[\u1A20-\u1A54\u1AA7\u1B05-\u1B33\u1B45-\u1B4B\u1B83-\u1BA0\u1BAE\u1BAF]|[\u1BBA-\u1BE5\u1C00-\u1C23\u1C4D-\u1C4F\u1C5A-\u1C7D\u1CE9-\u1CEC]|[\u1CEE-\u1CF1\u1CF5\u1CF6\u1D00-\u1DBF\u1E00-\u1F15\u1F18-\u1F1D]|[\u1F20-\u1F45\u1F48-\u1F4D\u1F50-\u1F57\u1F59\u1F5B\u1F5D\u1F5F-\u1F7D]|[\u1F80-\u1FB4\u1FB6-\u1FBC\u1FBE\u1FC2-\u1FC4\u1FC6-\u1FCC\u1FD0-\u1FD3]|[\u1FD6-\u1FDB\u1FE0-\u1FEC\u1FF2-\u1FF4\u1FF6-\u1FFC\u2071\u207F]|[\u2090-\u209C\u2102\u2107\u210A-\u2113\u2115\u2119-\u211D\u2124\u2126\u2128]|[\u212A-\u212D\u212F-\u2139\u213C-\u213F\u2145-\u2149\u214E\u2183\u2184]|[\u2C00-\u2C2E\u2C30-\u2C5E\u2C60-\u2CE4\u2CEB-\u2CEE\u2CF2\u2CF3]|[\u2D00-\u2D25\u2D27\u2D2D\u2D30-\u2D67\u2D6F\u2D80-\u2D96\u2DA0-\u2DA6]|[\u2DA8-\u2DAE\u2DB0-\u2DB6\u2DB8-\u2DBE\u2DC0-\u2DC6\u2DC8-\u2DCE]|[\u2DD0-\u2DD6\u2DD8-\u2DDE\u2E2F\u3005\u3006\u3031-\u3035\u303B\u303C]|[\u3041-\u3096\u309D-\u309F\u30A1-\u30FA\u30FC-\u30FF\u3105-\u312D]|[\u3131-\u318E\u31A0-\u31BA\u31F0-\u31FF\u3400-\u4DB5\u4E00-\u9FCC]|[\uA000-\uA48C\uA4D0-\uA4FD\uA500-\uA60C\uA610-\uA61F\uA62A\uA62B]|[\uA640-\uA66E\uA67F-\uA697\uA6A0-\uA6E5\uA717-\uA71F\uA722-\uA788]|[\uA78B-\uA78E\uA790-\uA793\uA7A0-\uA7AA\uA7F8-\uA801\uA803-\uA805]|[\uA807-\uA80A\uA80C-\uA822\uA840-\uA873\uA882-\uA8B3\uA8F2-\uA8F7\uA8FB]|[\uA90A-\uA925\uA930-\uA946\uA960-\uA97C\uA984-\uA9B2\uA9CF\uAA00-\uAA28]|[\uAA40-\uAA42\uAA44-\uAA4B\uAA60-\uAA76\uAA7A\uAA80-\uAAAF\uAAB1\uAAB5]|[\uAAB6\uAAB9-\uAABD\uAAC0\uAAC2\uAADB-\uAADD\uAAE0-\uAAEA\uAAF2-\uAAF4]|[\uAB01-\uAB06\uAB09-\uAB0E\uAB11-\uAB16\uAB20-\uAB26\uAB28-\uAB2E]|[\uABC0-\uABE2\uAC00-\uD7A3\uD7B0-\uD7C6\uD7CB-\uD7FB\uF900-\uFA6D]|[\uFA70-\uFAD9\uFB00-\uFB06\uFB13-\uFB17\uFB1D\uFB1F-\uFB28\uFB2A-\uFB36]|[\uFB38-\uFB3C\uFB3E\uFB40\uFB41\uFB43\uFB44\uFB46-\uFBB1\uFBD3-\uFD3D]|[\uFD50-\uFD8F\uFD92-\uFDC7\uFDF0-\uFDFB\uFE70-\uFE74\uFE76-\uFEFC]|[\uFF21-\uFF3A\uFF41-\uFF5A\uFF66-\uFFBE\uFFC2-\uFFC7\uFFCA-\uFFCF]|[\uFFD2-\uFFD7\uFFDA-\uFFDC])/,/^(?:\|)/,/^(?:\()/,/^(?:\))/,/^(?:\[)/,/^(?:\])/,/^(?:\{)/,/^(?:\})/,/^(?:")/,/^(?:\n+)/,/^(?:\s)/,/^(?:$)/],conditions:{string:{rules:[2,3],inclusive:!1},INITIAL:{rules:[0,1,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69],inclusive:!0}}};return t}();return Dt.lexer=Ct,t.prototype=Dt,Dt.Parser=t,new t}();"undefined"!=typeof t&&"undefined"!=typeof r&&(r.parser=i,r.Parser=i.Parser,r.parse=function(){return i.parse.apply(i,arguments)},r.main=function(e){e[1]||(console.log("Usage: "+e[0]+" FILE"),n.exit(1));var i=t("fs").readFileSync(t("path").normalize(e[1]),"utf8");return r.parser.parse(i)},"undefined"!=typeof e&&t.main===e&&r.main(n.argv.slice(1)))}).call(this,t("_process"))},{_process:3,fs:1,path:2}],119:[function(t,e,r){(function(e){"use strict";var n=t("moment"),i=t("../../logger"),a=new i.Log,s="",o="",u=[],c=[],l="";r.clear=function(){u=[],c=[],l="",o="",g=0,h=void 0,d=void 0,b=[]},r.setDateFormat=function(t){s=t},r.getDateFormat=function(){return s},r.setTitle=function(t){o=t},r.getTitle=function(){return o},r.addSection=function(t){l=t,u.push(t)},r.getTasks=function(){for(var t=A(),e=10,r=0;!t&&e>r;)t=A(),r++;return c=b};var h,d,f=function(t,e,i){i=i.trim();var s=/^after\s+([\d\w\-]+)/,o=s.exec(i.trim());if(null!==o){var u=r.findTaskById(o[1]);if("undefined"==typeof u){var c=new Date;return c.setHours(0,0,0,0),c}return u.endTime}return n(i,e.trim(),!0).isValid()?n(i,e.trim(),!0).toDate():(a.debug("Invalid date:"+i),a.debug("With date format:"+e.trim()),new Date)},p=function(t,e,r){if(r=r.trim(),n(r,e.trim(),!0).isValid())return n(r,e.trim()).toDate();var i=n(t),a=/^([\d]+)([wdhms])/,s=a.exec(r.trim());if(null!==s){switch(s[2]){case"s":i.add(s[1],"seconds");break;case"m":i.add(s[1],"minutes");break;case"h":i.add(s[1],"hours");break;case"d":i.add(s[1],"days");break;case"w":i.add(s[1],"weeks")}return i.toDate()}return i.toDate()},g=0,m=function(t){return"undefined"==typeof t?(g+=1,"task"+g):t},y=function(t,e){var n;n=":"===e.substr(0,1)?e.substr(1,e.length):e;for(var i=n.split(","),a={},s=r.getDateFormat(),o=!0;o;)o=!1,i[0].match(/^\s*active\s*$/)&&(a.active=!0,i.shift(1),o=!0),i[0].match(/^\s*done\s*$/)&&(a.done=!0,i.shift(1),o=!0),i[0].match(/^\s*crit\s*$/)&&(a.crit=!0,i.shift(1),o=!0);var 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r=function(t,e){this.message=t,this.hash=e};throw r.prototype=new Error,new r(t,e)}this.trace(t)},parse:function(t){var e=this,r=[0],n=[null],i=[],a=this.table,s="",o=0,u=0,c=0,l=2,h=1,d=i.slice.call(arguments,1),f=Object.create(this.lexer),p={yy:{}};for(var g in this.yy)Object.prototype.hasOwnProperty.call(this.yy,g)&&(p.yy[g]=this.yy[g]);f.setInput(t,p.yy),p.yy.lexer=f,p.yy.parser=this,"undefined"==typeof f.yylloc&&(f.yylloc={});var m=f.yylloc;i.push(m);var y=f.options&&f.options.ranges;"function"==typeof p.yy.parseError?this.parseError=p.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;for(var v,b,_,A,w,x,E,k,D,C=function(){var t;return t=f.lex()||h,"number"!=typeof t&&(t=e.symbols_[t]||t),t},F={};;){if(_=r[r.length-1],this.defaultActions[_]?A=this.defaultActions[_]:((null===v||"undefined"==typeof v)&&(v=C()),A=a[_]&&a[_][v]),"undefined"==typeof A||!A.length||!A[0]){var T="";D=[];for(x in a[_])this.terminals_[x]&&x>l&&D.push("'"+this.terminals_[x]+"'");T=f.showPosition?"Parse error on line "+(o+1)+":\n"+f.showPosition()+"\nExpecting "+D.join(", ")+", got '"+(this.terminals_[v]||v)+"'":"Parse error on line "+(o+1)+": Unexpected "+(v==h?"end of input":"'"+(this.terminals_[v]||v)+"'"),this.parseError(T,{text:f.match,token:this.terminals_[v]||v,line:f.yylineno,loc:m,expected:D})}if(A[0]instanceof Array&&A.length>1)throw new Error("Parse Error: multiple actions possible at state: "+_+", token: "+v);switch(A[0]){case 1:r.push(v),n.push(f.yytext),i.push(f.yylloc),r.push(A[1]),v=null,b?(v=b,b=null):(u=f.yyleng,s=f.yytext,o=f.yylineno,m=f.yylloc,c>0&&c--);break;case 2:if(E=this.productions_[A[1]][1],F.$=n[n.length-E],F._$={first_line:i[i.length-(E||1)].first_line,last_line:i[i.length-1].last_line,first_column:i[i.length-(E||1)].first_column,last_column:i[i.length-1].last_column},y&&(F._$.range=[i[i.length-(E||1)].range[0],i[i.length-1].range[1]]),w=this.performAction.apply(F,[s,u,o,p.yy,A[1],n,i].concat(d)),"undefined"!=typeof w)return w;E&&(r=r.slice(0,-1*E*2),n=n.slice(0,-1*E),i=i.slice(0,-1*E)),r.push(this.productions_[A[1]][0]),n.push(F.$),i.push(F._$),k=a[r[r.length-2]][r[r.length-1]],r.push(k);break;case 3:return!0}}return!0}},m=function(){var t={EOF:1,parseError:function(t,e){if(!this.yy.parser)throw new Error(t);this.yy.parser.parseError(t,e)},setInput:function(t,e){return this.yy=e||this.yy||{},this._input=t,this._more=this._backtrack=this.done=!1,this.yylineno=this.yyleng=0,this.yytext=this.matched=this.match="",this.conditionStack=["INITIAL"],this.yylloc={first_line:1,first_column:0,last_line:1,last_column:0},this.options.ranges&&(this.yylloc.range=[0,0]),this.offset=0,this},input:function(){var t=this._input[0];this.yytext+=t,this.yyleng++,this.offset++,this.match+=t,this.matched+=t;var e=t.match(/(?:\r\n?|\n).*/g);return e?(this.yylineno++,this.yylloc.last_line++):this.yylloc.last_column++,this.options.ranges&&this.yylloc.range[1]++,this._input=this._input.slice(1),t},unput:function(t){var e=t.length,r=t.split(/(?:\r\n?|\n)/g);this._input=t+this._input,this.yytext=this.yytext.substr(0,this.yytext.length-e),this.offset-=e;var n=this.match.split(/(?:\r\n?|\n)/g);this.match=this.match.substr(0,this.match.length-1),this.matched=this.matched.substr(0,this.matched.length-1),r.length-1&&(this.yylineno-=r.length-1);var i=this.yylloc.range;return this.yylloc={first_line:this.yylloc.first_line,last_line:this.yylineno+1,first_column:this.yylloc.first_column,last_column:r?(r.length===n.length?this.yylloc.first_column:0)+n[n.length-r.length].length-r[0].length:this.yylloc.first_column-e},this.options.ranges&&(this.yylloc.range=[i[0],i[0]+this.yyleng-e]),this.yyleng=this.yytext.length,this},more:function(){return this._more=!0,this},reject:function(){return this.options.backtrack_lexer?(this._backtrack=!0,this):this.parseError("Lexical error on line "+(this.yylineno+1)+". You can only invoke reject() in the lexer when the lexer is of the backtracking persuasion (options.backtrack_lexer = true).\n"+this.showPosition(),{text:"",token:null,line:this.yylineno})},less:function(t){this.unput(this.match.slice(t))},pastInput:function(){var t=this.matched.substr(0,this.matched.length-this.match.length);return(t.length>20?"...":"")+t.substr(-20).replace(/\n/g,"")},upcomingInput:function(){var t=this.match;return t.length<20&&(t+=this._input.substr(0,20-t.length)),(t.substr(0,20)+(t.length>20?"...":"")).replace(/\n/g,"")},showPosition:function(){var t=this.pastInput(),e=new Array(t.length+1).join("-");return t+this.upcomingInput()+"\n"+e+"^"},test_match:function(t,e){var r,n,i;if(this.options.backtrack_lexer&&(i={yylineno:this.yylineno,yylloc:{first_line:this.yylloc.first_line,last_line:this.last_line,first_column:this.yylloc.first_column,last_column:this.yylloc.last_column},yytext:this.yytext,match:this.match,matches:this.matches,matched:this.matched,yyleng:this.yyleng,offset:this.offset,_more:this._more,_input:this._input,yy:this.yy,conditionStack:this.conditionStack.slice(0),done:this.done},this.options.ranges&&(i.yylloc.range=this.yylloc.range.slice(0))),n=t[0].match(/(?:\r\n?|\n).*/g),n&&(this.yylineno+=n.length),this.yylloc={first_line:this.yylloc.last_line,last_line:this.yylineno+1,first_column:this.yylloc.last_column,last_column:n?n[n.length-1].length-n[n.length-1].match(/\r?\n?/)[0].length:this.yylloc.last_column+t[0].length},this.yytext+=t[0],this.match+=t[0],this.matches=t,this.yyleng=this.yytext.length,this.options.ranges&&(this.yylloc.range=[this.offset,this.offset+=this.yyleng]),this._more=!1,this._backtrack=!1,this._input=this._input.slice(t[0].length),this.matched+=t[0],r=this.performAction.call(this,this.yy,this,e,this.conditionStack[this.conditionStack.length-1]),this.done&&this._input&&(this.done=!1),r)return r;if(this._backtrack){for(var a in i)this[a]=i[a];return!1}return!1},next:function(){if(this.done)return this.EOF;this._input||(this.done=!0);var t,e,r,n;this._more||(this.yytext="",this.match="");for(var i=this._currentRules(),a=0;ae[0].length)){if(e=r,n=a,this.options.backtrack_lexer){if(t=this.test_match(r,i[a]),t!==!1)return t;if(this._backtrack){e=!1;continue}return!1}if(!this.options.flex)break}return e?(t=this.test_match(e,i[n]),t!==!1?t:!1):""===this._input?this.EOF:this.parseError("Lexical error on line "+(this.yylineno+1)+". Unrecognized text.\n"+this.showPosition(),{text:"",token:null,line:this.yylineno})},lex:function(){var t=this.next();return t?t:this.lex()},begin:function(t){this.conditionStack.push(t)},popState:function(){var t=this.conditionStack.length-1;return t>0?this.conditionStack.pop():this.conditionStack[0]},_currentRules:function(){return this.conditionStack.length&&this.conditionStack[this.conditionStack.length-1]?this.conditions[this.conditionStack[this.conditionStack.length-1]].rules:this.conditions.INITIAL.rules},topState:function(t){return t=this.conditionStack.length-1-Math.abs(t||0),t>=0?this.conditionStack[t]:"INITIAL"},pushState:function(t){this.begin(t)},stateStackSize:function(){return this.conditionStack.length},options:{"case-insensitive":!0},performAction:function(t,e,r,n){switch(r){case 0:return 9;case 1:break;case 2:break;case 3:break;case 4:break;case 5:return this.begin("ID"),10;case 6:return this.begin("ALIAS"),33;case 7:return this.popState(),this.popState(),this.begin("LINE"),12;case 8:return this.popState(),this.popState(),9;case 9:return this.begin("LINE"),18;case 10:return this.begin("LINE"),20;case 11:return this.begin("LINE"),21;case 12:return this.begin("LINE"),22;case 13:return this.popState(),13;case 14:return 19;case 15:return 30;case 16:return 31;case 17:return 26;case 18:return 23;case 19:return 16;case 20:return 4;case 21:return 29;case 22:return 9;case 23:return 33;case 24:return 36;case 25:return 37;case 26:return 34;case 27:return 35;case 28:return 38;case 29:return 39;case 30:return 40;case 31:return 9;case 32:return"INVALID"}},rules:[/^(?:[\n]+)/i,/^(?:\s+)/i,/^(?:((?!\n)\s)+)/i,/^(?:#[^\n]*)/i,/^(?:%[^\n]*)/i,/^(?:participant\b)/i,/^(?:[^\->:\n,;]+?(?=((?!\n)\s)+as(?!\n)\s|[#\n;]|$))/i,/^(?:as\b)/i,/^(?:(?:))/i,/^(?:loop\b)/i,/^(?:opt\b)/i,/^(?:alt\b)/i,/^(?:else\b)/i,/^(?:[^#\n;]*)/i,/^(?:end\b)/i,/^(?:left of\b)/i,/^(?:right of\b)/i,/^(?:over\b)/i,/^(?:note\b)/i,/^(?:title\b)/i,/^(?:sequenceDiagram\b)/i,/^(?:,)/i,/^(?:;)/i,/^(?:[^\->:\n,;]+)/i,/^(?:->>)/i,/^(?:-->>)/i,/^(?:->)/i,/^(?:-->)/i,/^(?:-[x])/i,/^(?:--[x])/i,/^(?::[^#\n;]+)/i,/^(?:$)/i,/^(?:.)/i],conditions:{LINE:{rules:[2,3,13],inclusive:!1},ALIAS:{rules:[2,3,7,8],inclusive:!1},ID:{rules:[2,3,6],inclusive:!1},INITIAL:{rules:[0,1,3,4,5,9,10,11,12,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32],inclusive:!0}}};return t}();return g.lexer=m,t.prototype=g,g.Parser=t,new t}();"undefined"!=typeof t&&"undefined"!=typeof r&&(r.parser=i,r.Parser=i.Parser,r.parse=function(){return i.parse.apply(i,arguments)},r.main=function(e){e[1]||(console.log("Usage: "+e[0]+" FILE"),n.exit(1));var i=t("fs").readFileSync(t("path").normalize(e[1]),"utf8");return r.parser.parse(i)},"undefined"!=typeof e&&t.main===e&&r.main(n.argv.slice(1)))}).call(this,t("_process"))},{_process:3,fs:1,path:2}],123:[function(t,e,r){(function(e){"use strict";var n={},i=[],a=[],s=t("../../logger"),o=new s.Log;r.addActor=function(t,e,r){var i=n[t];i&&e===i.name&&null==r||(null==r&&(r=e),n[t]={name:e,description:r})},r.addMessage=function(t,e,r,n){i.push({from:t,to:e,message:r,answer:n})},r.addSignal=function(t,e,r,n){o.debug("Adding message from="+t+" to="+e+" message="+r+" type="+n),i.push({from:t,to:e,message:r,type:n})},r.getMessages=function(){return i},r.getActors=function(){return n},r.getActor=function(t){return n[t]},r.getActorKeys=function(){return Object.keys(n)},r.clear=function(){n={},i=[]},r.LINETYPE={SOLID:0,DOTTED:1,NOTE:2,SOLID_CROSS:3,DOTTED_CROSS:4,SOLID_OPEN:5,DOTTED_OPEN:6,LOOP_START:10,LOOP_END:11,ALT_START:12,ALT_ELSE:13,ALT_END:14,OPT_START:15,OPT_END:16},r.ARROWTYPE={FILLED:0,OPEN:1},r.PLACEMENT={LEFTOF:0,RIGHTOF:1,OVER:2},r.addNote=function(t,e,n){var s={actor:t,placement:e,message:n},o=[].concat(t,t);a.push(s),i.push({from:o[0],to:o[1],message:n,type:r.LINETYPE.NOTE,placement:e})},r.parseError=function(t,r){e.mermaidAPI.parseError(t,r)},r.apply=function(t){if(t instanceof Array)t.forEach(function(t){r.apply(t)});else switch(t.type){case"addActor":r.addActor(t.actor,t.actor,t.description);break;case"addNote":r.addNote(t.actor,t.placement,t.text);break;case"addMessage":r.addSignal(t.from,t.to,t.msg,t.signalType);break;case"loopStart":r.addSignal(void 0,void 0,t.loopText,t.signalType);break;case"loopEnd":r.addSignal(void 0,void 0,void 0,t.signalType);break;case"optStart":r.addSignal(void 0,void 0,t.optText,t.signalType);break;case"optEnd":r.addSignal(void 0,void 0,void 0,t.signalType);break;case"altStart":r.addSignal(void 0,void 0,t.altText,t.signalType);break;case"else":r.addSignal(void 0,void 0,t.altText,t.signalType);break;case"altEnd":r.addSignal(void 0,void 0,void 0,t.signalType)}}}).call(this,"undefined"!=typeof global?global:"undefined"!=typeof self?self:"undefined"!=typeof window?window:{})},{"../../logger":126}],124:[function(t,e,r){"use strict";var n=t("./parser/sequenceDiagram").parser;n.yy=t("./sequenceDb");var i=t("./svgDraw"),a=t("../../d3"),s=t("../../logger"),o=new s.Log,u={diagramMarginX:50,diagramMarginY:10,actorMargin:50,width:150,height:65,boxMargin:10,boxTextMargin:5,noteMargin:10,messageMargin:35,mirrorActors:!1,bottomMarginAdj:1};r.bounds={data:{startx:void 0,stopx:void 0,starty:void 0,stopy:void 0},verticalPos:0,list:[],init:function(){this.list=[],this.data={startx:void 0,stopx:void 0,starty:void 0,stopy:void 0},this.verticalPos=0},updateVal:function(t,e,r,n){"undefined"==typeof t[e]?t[e]=r:t[e]=n(r,t[e])},updateLoops:function(t,e,n,i){var a=this,s=0;this.list.forEach(function(o){s++;var c=a.list.length-s+1;a.updateVal(o,"startx",t-c*u.boxMargin,Math.min),a.updateVal(o,"starty",e-c*u.boxMargin,Math.min),a.updateVal(o,"stopx",n+c*u.boxMargin,Math.max),a.updateVal(o,"stopy",i+c*u.boxMargin,Math.max),a.updateVal(r.bounds.data,"startx",t-c*u.boxMargin,Math.min),a.updateVal(r.bounds.data,"starty",e-c*u.boxMargin,Math.min),a.updateVal(r.bounds.data,"stopx",n+c*u.boxMargin,Math.max),a.updateVal(r.bounds.data,"stopy",i+c*u.boxMargin,Math.max)})},insert:function(t,e,n,i){var a,s,o,u;a=Math.min(t,n),o=Math.max(t,n),s=Math.min(e,i),u=Math.max(e,i),this.updateVal(r.bounds.data,"startx",a,Math.min),this.updateVal(r.bounds.data,"starty",s,Math.min),this.updateVal(r.bounds.data,"stopx",o,Math.max), +this.updateVal(r.bounds.data,"stopy",u,Math.max),this.updateLoops(a,s,o,u)},newLoop:function(t){this.list.push({startx:void 0,starty:this.verticalPos,stopx:void 0,stopy:void 0,title:t})},endLoop:function(){var t=this.list.pop();return t},addElseToLoop:function(t){var e=this.list.pop();e.elsey=r.bounds.getVerticalPos(),e.elseText=t,this.list.push(e)},bumpVerticalPos:function(t){this.verticalPos=this.verticalPos+t,this.data.stopy=this.verticalPos},getVerticalPos:function(){return this.verticalPos},getBounds:function(){return this.data}};var c=function(t,e,n,a,s){var o=i.getNoteRect();o.x=e,o.y=n,o.width=s||u.width,o["class"]="note";var c=t.append("g"),l=i.drawRect(c,o),h=i.getTextObj();h.x=e-4,h.y=n-13,h.textMargin=u.noteMargin,h.dy="1em",h.text=a.message,h["class"]="noteText";var d=i.drawText(c,h,o.width-u.noteMargin),f=d[0][0].getBBox().height;!s&&f>u.width?(d.remove(),c=t.append("g"),d=i.drawText(c,h,2*o.width-u.noteMargin),f=d[0][0].getBBox().height,l.attr("width",2*o.width),r.bounds.insert(e,n,e+2*o.width,n+2*u.noteMargin+f)):r.bounds.insert(e,n,e+o.width,n+2*u.noteMargin+f),l.attr("height",f+2*u.noteMargin),r.bounds.bumpVerticalPos(f+2*u.noteMargin)},l=function(t,e,i,a,s){var o,c=t.append("g"),l=e+(i-e)/2,h=c.append("text").attr("x",l).attr("y",a-7).style("text-anchor","middle").attr("class","messageText").text(s.message);o="undefined"!=typeof h[0][0].getBBox?h[0][0].getBBox().width:h[0][0].getBoundingClientRect();var d;if(e===i){d=c.append("path").attr("d","M "+e+","+a+" C "+(e+60)+","+(a-10)+" "+(e+60)+","+(a+30)+" "+e+","+(a+20)),r.bounds.bumpVerticalPos(30);var f=Math.max(o/2,100);r.bounds.insert(e-f,r.bounds.getVerticalPos()-10,i+f,r.bounds.getVerticalPos())}else d=c.append("line"),d.attr("x1",e),d.attr("y1",a),d.attr("x2",i),d.attr("y2",a),r.bounds.insert(e,r.bounds.getVerticalPos()-10,i,r.bounds.getVerticalPos());s.type===n.yy.LINETYPE.DOTTED||s.type===n.yy.LINETYPE.DOTTED_CROSS||s.type===n.yy.LINETYPE.DOTTED_OPEN?(d.style("stroke-dasharray","3, 3"),d.attr("class","messageLine1")):d.attr("class","messageLine0");var p="";u.arrowMarkerAbsolute&&(p=window.location.protocol+"//"+window.location.host+window.location.pathname+window.location.search,p=p.replace(/\(/g,"\\("),p=p.replace(/\)/g,"\\)")),d.attr("stroke-width",2),d.attr("stroke","black"),d.style("fill","none"),(s.type===n.yy.LINETYPE.SOLID||s.type===n.yy.LINETYPE.DOTTED)&&d.attr("marker-end","url("+p+"#arrowhead)"),(s.type===n.yy.LINETYPE.SOLID_CROSS||s.type===n.yy.LINETYPE.DOTTED_CROSS)&&d.attr("marker-end","url("+p+"#crosshead)")};e.exports.drawActors=function(t,e,n,a){var s;for(s=0;s/gi," "),i=t.append("text");i.attr("x",e.x),i.attr("y",e.y),i.style("text-anchor",e.anchor),i.attr("fill",e.fill),"undefined"!=typeof e["class"]&&i.attr("class",e["class"]);var a=i.append("tspan");return a.attr("x",e.x+2*e.textMargin),a.text(n),"undefined"!=typeof i.textwrap&&i.textwrap({x:e.x,y:e.y,width:r,height:1800},e.textMargin),i},r.drawLabel=function(t,e){var n=r.getNoteRect();n.x=e.x,n.y=e.y,n.width=50,n.height=20,n.fill="#526e52",n.stroke="none",n["class"]="labelBox",r.drawRect(t,n),e.y=e.y+e.labelMargin,e.x=e.x+.5*e.labelMargin,e.fill="white",r.drawText(t,e)};var n=-1;r.drawActor=function(t,e,i,a,s){var o=e+s.width/2,u=t.append("g");0===i&&(n++,u.append("line").attr("id","actor"+n).attr("x1",o).attr("y1",5).attr("x2",o).attr("y2",2e3).attr("class","actor-line").attr("stroke-width","0.5px").attr("stroke","#999"));var c=r.getNoteRect();c.x=e,c.y=i,c.fill="#eaeaea",c.width=s.width,c.height=s.height,c["class"]="actor",c.rx=3,c.ry=3,r.drawRect(u,c),u.append("text").attr("x",o).attr("y",i+s.height/2+5).attr("class","actor").style("text-anchor","middle").text(a)},r.drawLoop=function(t,e,n,i){var 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    Change log All releases

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    +netrankr 0.1.0

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    • first public release
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    +netrankr 0.0.5

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    • most function reimplemented in C++ for efficiency.
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    • vignettes added: browseVignettes("netrankr") +
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    • added visualization function plot_rank_intervals +
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    • spell checked and extended help
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    +netrankr 0.0.1-0.0.4

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    initial builds, predominantely written in R.

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    Developed by David Schoch.

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    Site built with pkgdown.

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    + +
    +
    + + + diff --git a/docs/pkgdown.css b/docs/pkgdown.css new file mode 100644 index 0000000..209ce57 --- /dev/null +++ b/docs/pkgdown.css @@ -0,0 +1,163 @@ +/* Sticker footer */ +body > .container { + display: flex; + padding-top: 60px; + min-height: calc(100vh); + flex-direction: column; +} + +body > .container .row { + flex: 1; +} + +footer { + margin-top: 45px; + padding: 35px 0 36px; + border-top: 1px solid #e5e5e5; + color: #666; + display: flex; +} +footer p { + margin-bottom: 0; +} +footer div { + flex: 1; +} +footer .pkgdown { + text-align: right; +} +footer p { + margin-bottom: 0; +} + +img.icon { + float: right; +} + +img { + max-width: 100%; +} + +/* Section anchors ---------------------------------*/ + +a.anchor { + margin-left: -30px; + display:inline-block; + width: 30px; + height: 30px; + visibility: hidden; + + background-image: url(./link.svg); + background-repeat: no-repeat; + background-size: 20px 20px; + background-position: center center; +} + +.hasAnchor:hover a.anchor { + visibility: visible; +} + +@media (max-width: 767px) { + .hasAnchor:hover a.anchor { + visibility: hidden; + } +} + + +/* Fixes for fixed navbar --------------------------*/ + +.contents h1, .contents h2, .contents h3, .contents h4 { + padding-top: 60px; + margin-top: -60px; +} + +/* Static header placement on mobile devices */ +@media (max-width: 767px) { + .navbar-fixed-top { + position: absolute; + } + .navbar { + padding: 0; + } +} + + +/* Sidebar --------------------------*/ + +#sidebar { + margin-top: 30px; +} +#sidebar h2 { + font-size: 1.5em; + margin-top: 1em; +} + +#sidebar h2:first-child { + margin-top: 0; +} + +#sidebar .list-unstyled li { + margin-bottom: 0.5em; +} + +/* Reference index & topics ----------------------------------------------- */ + +.ref-index th {font-weight: normal;} +.ref-index h2 {font-size: 20px;} + +.ref-index td {vertical-align: top;} +.ref-index .alias {width: 40%;} +.ref-index .title {width: 60%;} + +.ref-index .alias {width: 40%;} +.ref-index .title {width: 60%;} + +.ref-arguments th {text-align: right; padding-right: 10px;} +.ref-arguments th, .ref-arguments td {vertical-align: top;} +.ref-arguments .name {width: 20%;} +.ref-arguments .desc {width: 80%;} + +/* Nice scrolling for wide elements --------------------------------------- */ + +table { + display: block; + overflow: auto; +} + +/* Syntax highlighting ---------------------------------------------------- */ + +pre { + word-wrap: normal; + word-break: normal; + border: 1px solid #eee; +} + +pre, code { + background-color: #f8f8f8; + color: #333; +} + +pre .img { + margin: 5px 0; +} + +pre .img img { + background-color: #fff; + display: block; + height: auto; +} + +code a, pre a { + color: #375f84; +} + +.fl {color: #1514b5;} +.fu {color: #000000;} /* function */ +.ch,.st {color: #036a07;} /* string */ +.kw {color: #264D66;} /* keyword */ +.co {color: #888888;} /* comment */ + +.message { color: black; font-weight: bolder;} +.error { color: orange; font-weight: bolder;} +.warning { color: #6A0366; font-weight: bolder;} + diff --git a/docs/pkgdown.js b/docs/pkgdown.js new file mode 100644 index 0000000..4b81713 --- /dev/null +++ b/docs/pkgdown.js @@ -0,0 +1,45 @@ +$(function() { + $("#sidebar").stick_in_parent({offset_top: 40}); + $('body').scrollspy({ + target: '#sidebar', + offset: 60 + }); + + var cur_path = paths(location.pathname); + $("#navbar ul li a").each(function(index, value) { + if (value.text == "Home") + return; + if (value.getAttribute("href") === "#") + return; + + var path = paths(value.pathname); + if (is_prefix(cur_path, path)) { + // Add class to parent
  • , and enclosing
  • if in dropdown + var menu_anchor = $(value); + menu_anchor.parent().addClass("active"); + menu_anchor.closest("li.dropdown").addClass("active"); + } + }); +}); + +function paths(pathname) { + var pieces = pathname.split("/"); + pieces.shift(); // always starts with / + + var end = pieces[pieces.length - 1]; + if (end === "index.html" || end === "") + pieces.pop(); + return(pieces); +} + +function is_prefix(needle, haystack) { + if (needle.length > haystack.lengh) + return(false); + + for (var i = 0; i < haystack.length; i++) { + if (needle[i] != haystack[i]) + return(false); + } + + return(true); +} diff --git a/docs/pkgdown.yml b/docs/pkgdown.yml new file mode 100644 index 0000000..f7792e5 --- /dev/null +++ b/docs/pkgdown.yml @@ -0,0 +1,14 @@ +urls: + reference: https://schochastics.github.io/netrankr/reference + article: https://schochastics.github.io/netrankr/articles +articles: + benchmarks: benchmarks.html + centrality_indices: centrality_indices.html + indirect_relations: indirect_relations.html + neighborhood_inclusion: neighborhood_inclusion.html + partial_centrality: partial_centrality.html + positional_dominance: positional_dominance.html + probabilistic_cent: probabilistic_cent.html + threshold_graph: threshold_graph.html + use_case: use_case.html + diff --git a/docs/reference/aggregate_positions.html b/docs/reference/aggregate_positions.html new file mode 100644 index 0000000..0785544 --- /dev/null +++ b/docs/reference/aggregate_positions.html @@ -0,0 +1,236 @@ + + + + + + + + +Quantification of (indirect) relations — aggregate_positions • netrankr + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + +
    + +
    +
    +
    +

    Quantification of (indirect) relations

    +
    + + +

    Function to aggregate positions defined via indirect relations to construct centrality +scores.

    + + + 
    aggregate_positions(tau_x, type = "sum")
    + +

    Arguments

    + + + + + + + + + + +
    tau_x

    Numeric matrix containing indirect relations calculated with indirect_relations.

    type

    String indicating the type of aggregation to be used. See Details for options.

    + +

    Value

    + +

    Scores for the index defined by the indirect relation tau_x and the +used aggregation type.

    + +

    Details

    + +

    The predefined functions are mainly wrappers around base R functions. +type='sum', for instance, is equivalent to rowSums(). A non-base functions is +type='invsum' which calculates the inverse of type='sum'. +type='self' is mostly useful for walk based relations, e.g. to count closed walks. +Other self explanatory options are type='mean', type='min', type='max' and type='prod'.

    + +

    See also

    + +

    indirect_relations, transform_relations

    + + +

    Examples

    + 
    require(igraph)
+require(magrittr)
+
+g <- graph.empty(n=11,directed = FALSE)
+g <- add_edges(g,c(1,11,2,4,3,5,3,11,4,8,5,9,5,11,6,7,6,8,
+                   6,10,6,11,7,9,7,10,7,11,8,9,8,10,9,10))
+#degree
+g %>% indirect_relations(type='identity') %>%
+ aggregate_positions(type='sum')
    #>  [1] 1 1 2 2 3 4 4 4 4 4 5
    
+#closeness centrality
+g %>% indirect_relations(type='geodesic') %>%
+  aggregate_positions(type='invsum')
    #>  [1] 0.03704 0.02941 0.04000 0.04000 0.05000 0.05882 0.05263 0.05556 0.05556
+#> [10] 0.05263 0.05556
    
+#betweenness centrality
+g %>% indirect_relations(type='dependencies') %>%
+  aggregate_positions(type='sum')
    #>  [1]  0.000  0.000  0.000 18.000  7.667 19.667  5.333 32.667 14.667  2.667
+#> [11] 29.333
    
+#eigenvector centrality
+g %>% indirect_relations(type='walks',FUN=walks_limit_prop) %>%
+  aggregate_positions(type='sum')
    #>  [1] 0.27516 0.07864 0.46106 0.29410 0.69521 1.19904 1.21772 1.02121 1.10978
+#> [10] 1.21608 1.02901
    
+#subgraph centrality
+g %>% indirect_relations(type='walks',FUN=walks_exp) %>%
+  aggregate_positions(type='self')
    #>  [1] 1.825 1.595 3.149 2.423 4.387 7.807 7.939 6.673 7.033 8.242 7.390
      
+
    +
    + +
    + +
    +
    +

    Developed by David Schoch.

    +
    + +
    +

    Site built with pkgdown.

    +
    + +
    +
    + + + diff --git a/docs/reference/approx_rank_expected.html b/docs/reference/approx_rank_expected.html new file mode 100644 index 0000000..d37acb9 --- /dev/null +++ b/docs/reference/approx_rank_expected.html @@ -0,0 +1,230 @@ + + + + + + + + +Approximation of expected ranks — approx_rank_expected • netrankr + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + +
    + +
    +
    +
    +

    Approximation of expected ranks

    +
    + + +

    Implements a variety of functions to approximate expected ranks +for partial rankings.

    + + + 
    approx_rank_expected(P, method = "lpom")
    + +

    Arguments

    + + + + + + + + + + +
    P

    A partial ranking as matrix object calculated with neighborhood_inclusion +or positional_dominance.

    method

    String indicating which method to be used. see Details.

    + +

    Value

    + +

    A vector containing approximated expected ranks.

    + +

    Details

    + +

    The method parameter can be set to

    +
    lpom

    local partial order model

    +
    glpom

    extension of the local partial order model.

    +
    loof1

    based on a connection with relative rank probabilities.

    +
    loof2

    extension of the previous method.

    +

    Which of the above methods performs best depends on the structure and size of the partial +ranking. See vignette("benchmarks",package="netrankr") for more details.

    + +

    References

    + +

    Brüggemann R., Simon, U., and Mey,S, 2005. Estimation of averaged +ranks by extended local partial order models. MATCH Commun. Math. +Comput. Chem., 54:489-518.

    +

    Brüggemann, R. and Carlsen, L., 2011. An improved estimation of averaged ranks +of partial orders. MATCH Commun. Math. Comput. Chem., +65(2):383-414.

    +

    De Loof, L., De Baets, B., and De Meyer, H., 2011. Approximation of Average +Ranks in Posets. MATCH Commun. Math. Comput. Chem., 66:219-229.

    + +

    See also

    + +

    approx_rank_relative, exact_rank_prob, mcmc_rank_prob

    + + +

    Examples

    + 
    P <- matrix(c(0,0,1,1,1,0,0,0,1,0,0,0,0,0,1,rep(0,10)),5,5,byrow=TRUE)
+#Exact result
+exact_rank_prob(P)$expected.rank
    #> [1] 1.333 2.111 2.889 4.222 4.444
    
+approx_rank_expected(P,method = 'lpom')
    #> [1] 1.2 2.0 3.0 4.5 4.5
    approx_rank_expected(P,method = 'glpom')
    #> [1] 1.250 2.167 2.833 4.333 4.417
    +
    + +
    + +
    +
    +

    Developed by David Schoch.

    +
    + +
    +

    Site built with pkgdown.

    +
    + +
    +
    + + + diff --git a/docs/reference/approx_rank_relative.html b/docs/reference/approx_rank_relative.html new file mode 100644 index 0000000..046f0ca --- /dev/null +++ b/docs/reference/approx_rank_relative.html @@ -0,0 +1,243 @@ + + + + + + + + +Approximation of relative rank probabilities — approx_rank_relative • netrankr + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + +
    + +
    +
    +
    +

    Approximation of relative rank probabilities

    +
    + + +

    Approximate relative rank probabilities \(P(rk(u)<rk(v))\). +In a network context, \(P(rk(u)<rk(v))\) is the probability that u is +less central than v, given the partial ranking P.

    + + + 
    approx_rank_relative(P, iterative = TRUE, num.iter = 10)
    + +

    Arguments

    + + + + + + + + + + + + + + +
    P

    A partial ranking as matrix object calculated with neighborhood_inclusion +or positional_dominance.

    iterative

    Logical scalar if iterative approximation should be used.

    num.iter

    Number of iterations to be used. defaults to 10 (see Details).

    + +

    Value

    + +

    a matrix containing approximation of mutual rank probabilities. +relative.rank[i,j] is the probability that i is ranked lower than j

    + +

    Details

    + +

    The iterative approach generally gives better approximations +than the non iterative, if only slightly. The default number of iterations +is based on the observation, that the approximation does not improve +significantly beyond this value. This observation, however, is based on +very small networks such that increasing it for large network may yield +better results. See vignette("benchmarks",package="netrankr") for more details.

    + +

    References

    + +

    De Loof, K. and De Baets, B and De Meyer, H., 2008. Properties of mutual +rank probabilities in partially ordered sets. In Multicriteria Ordering and +Ranking: Partial Orders, Ambiguities and Applied Issues, 145-165.

    + +

    See also

    + +

    approx_rank_expected, exact_rank_prob, mcmc_rank_prob

    + + +

    Examples

    + 
    P <- matrix(c(0,0,1,1,1,0,0,0,1,0,0,0,0,0,1,rep(0,10)),5,5,byrow=TRUE)
+P
    #>      [,1] [,2] [,3] [,4] [,5]
+#> [1,]    0    0    1    1    1
+#> [2,]    0    0    0    1    0
+#> [3,]    0    0    0    0    1
+#> [4,]    0    0    0    0    0
+#> [5,]    0    0    0    0    0
    approx_rank_relative(P,iterative = FALSE)
    #>        [,1]   [,2]   [,3] [,4]   [,5]
+#> [1,] 0.0000 0.3333 1.0000 1.00 1.0000
+#> [2,] 0.6667 0.0000 0.3333 1.00 0.1429
+#> [3,] 0.0000 0.6667 0.0000 0.25 1.0000
+#> [4,] 0.0000 0.0000 0.7500 0.00 0.5000
+#> [5,] 0.0000 0.8571 0.0000 0.50 0.0000
    approx_rank_relative(P,iterative = TRUE)
    #>        [,1]   [,2]   [,3]   [,4]   [,5]
+#> [1,] 0.0000 0.6858 1.0000 1.0000 1.0000
+#> [2,] 0.3142 0.0000 0.6026 1.0000 0.8104
+#> [3,] 0.0000 0.3974 0.0000 0.7130 1.0000
+#> [4,] 0.0000 0.0000 0.2870 0.0000 0.5314
+#> [5,] 0.0000 0.1896 0.0000 0.4686 0.0000
    +
    + +
    + +
    +
    +

    Developed by David Schoch.

    +
    + +
    +

    Site built with pkgdown.

    +
    + +
    +
    + + + diff --git a/docs/reference/comparable_pairs.html b/docs/reference/comparable_pairs.html new file mode 100644 index 0000000..c9176b3 --- /dev/null +++ b/docs/reference/comparable_pairs.html @@ -0,0 +1,199 @@ + + + + + + + + +Comparable pairs in a partial ranking — comparable_pairs • netrankr + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + +
    + +
    +
    +
    +

    Comparable pairs in a partial ranking

    +
    + + +

    Calculates the fraction of comparable pairs in a partial ranking. +This fraction is identical to the density of the induced undirected graph of +a partial ranking.

    + + + 
    comparable_pairs(P)
    + +

    Arguments

    + + + + + + +
    P

    A partial ranking as matrix object calculated with neighborhood_inclusion +or positional_dominance.

    + +

    Value

    + +

    Fraction of comparable pairs in P.

    + + +

    Examples

    + 
    require(igraph)
+g <- sample_gnp(100,0.1)
+P <- neighborhood_inclusion(g)
+comparable_pairs(P)
    #> [1] 0
    # All pairs of vertices are comparable in a threshold graph
+tg <- threshold_graph(100,0.3)
+P <- neighborhood_inclusion(g)
+comparable_pairs(P)
    #> [1] 0
    +
    + +
    + +
    +
    +

    Developed by David Schoch.

    +
    + +
    +

    Site built with pkgdown.

    +
    + +
    +
    + + + diff --git a/docs/reference/compare_ranks.html b/docs/reference/compare_ranks.html new file mode 100644 index 0000000..2c5ff59 --- /dev/null +++ b/docs/reference/compare_ranks.html @@ -0,0 +1,239 @@ + + + + + + + + +Count occurrences of pairs in rankings — compare_ranks • netrankr + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + +
    + +
    +
    +
    +

    Count occurrences of pairs in rankings

    +
    + + +

    Counts the number of concordant, discordant and (left/right) ties between two rankings.

    + + + 
    compare_ranks(x, y)
    + +

    Arguments

    + + + + + + + + + + +
    x

    A numeric vector.

    y

    A numeric vector with the same length as x.

    + +

    Value

    + +

    A list containing

    +
    concordant

    number of concordant pairs: x[i] > x[j] and y[i] > y[j]

    +
    discordant

    number of discordant pairs: x[i] > x[j] and y[i] < y[j]

    +
    ties

    number of tied pairs: x[i] == x[j] and y[i] == y[j]

    +
    left

    number of left ties: x[i] == x[j] and y[i] != y[j]

    +
    right

    number of right ties: x[i] != x[j] and y[i] == y[j]

    + + +

    Details

    + +

    Explicitly calculating the number of occurring cases is more robust +than using correlation indices as given in the cor function. Especially +left and right ties can significantly alter correlations.

    + + +

    Examples

    + 
    require(igraph)
+tg <- threshold_graph(100,0.2)
+compare_ranks(degree(tg),closeness(tg)) #only concordant pairs
    #> $concordant
+#> [1] 4708
+#> 
+#> $discordant
+#> [1] 0
+#> 
+#> $ties
+#> [1] 242
+#> 
+#> $left
+#> [1] 0
+#> 
+#> $right
+#> [1] 0
+#> 
    compare_ranks(degree(tg),betweenness(tg)) #no discordant pairs
    #> $concordant
+#> [1] 1865
+#> 
+#> $discordant
+#> [1] 0
+#> 
+#> $ties
+#> [1] 242
+#> 
+#> $left
+#> [1] 0
+#> 
+#> $right
+#> [1] 2843
+#> 
    ## Rank Correlation
+cor(degree(tg),closeness(tg),method='kendall') #1
    #> [1] 1
    cor(degree(tg),betweenness(tg),method='kendall') #not 1, although no discordant pairs
    #> [1] 0.6294
    +
    + +
    + +
    +
    +

    Developed by David Schoch.

    +
    + +
    +

    Site built with pkgdown.

    +
    + +
    +
    + + + diff --git a/docs/reference/dominance_graph.html b/docs/reference/dominance_graph.html new file mode 100644 index 0000000..37043a0 --- /dev/null +++ b/docs/reference/dominance_graph.html @@ -0,0 +1,202 @@ + + + + + + + + +Partial ranking as directed graph — dominance_graph • netrankr + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + +
    + +
    +
    +
    +

    Partial ranking as directed graph

    +
    + + +

    Turns a partial ranking into a directed graph. An edge (u,v) is +present if P[u,v]=1, meaning that u is dominated by v.

    + + + 
    dominance_graph(P)
    + +

    Arguments

    + + + + + + +
    P

    A partial ranking as matrix object calculated with neighborhood_inclusion +or positional_dominance.

    + +

    Value

    + +

    Directed graph as an igraph object.

    + + +

    Examples

    + 
    require(igraph)
+g <- threshold_graph(20,0.1)
+P <- neighborhood_inclusion(g)
+d <- dominance_graph(P)
    # NOT RUN {
+plot(d)
+# }
    
+# to reduce overplotting use transitive reduction
+P <- transitive_reduction(P)
+d <- dominance_graph(P)
    # NOT RUN {
+plot(d)
+# }
    +
    + +
    + +
    +
    +

    Developed by David Schoch.

    +
    + +
    +

    Site built with pkgdown.

    +
    + +
    +
    + + + diff --git a/docs/reference/exact_rank_prob.html b/docs/reference/exact_rank_prob.html new file mode 100644 index 0000000..9c73ae6 --- /dev/null +++ b/docs/reference/exact_rank_prob.html @@ -0,0 +1,264 @@ + + + + + + + + +Probabilistic centrality rankings — exact_rank_prob • netrankr + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + +
    + +
    +
    +
    +

    Probabilistic centrality rankings

    +
    + + +

    Performs a complete and exact rank analysis of a given partial ranking. +This includes rank probabilities, relative rank probabilities and expected ranks.

    + + + 
    exact_rank_prob(P, names = "", only.results = T, verbose = F, force = F)
    + +

    Arguments

    + + + + + + + + + + + + + + + + + + + + + + +
    P

    A partial ranking as matrix object calculated with neighborhood_inclusion +or positional_dominance.

    names

    Optional argument for names if P does not have row/column names.

    only.results

    Logical. return only results (default) or additionally +the ideal tree and lattice if FALSE.

    verbose

    Logical. should diagnostics be printed. Defaults to FALSE.

    force

    Logical. If FALSE (default), stops the analysis if the partial +ranking has more than 40 elements and less than 0.4 comparable pairs. +Only change if you know what you are doing.

    + +

    Value

    + + + +
    lin.ext

    Number of possible rankings that extend P.

    +
    mse

    Array giving the equivalence classes of P.

    +
    rank.prob

    Matrix containing rank probabilities: rank.prob[u,k] is the probability that u has rank k.

    +
    relative.rank

    Matrix containing relative rank probabilities: relative.rank[u,v] is the probability that u is ranked lower than v.

    +
    expected.rank

    Expected ranks of nodes in any centrality ranking.

    +
    rank.spread

    Variance of the ranking probabilities.

    +
    topo.order

    Random ranking used to build the lattice of ideals (if only.results=FALSE).

    +
    tree

    igraph object. The tree of ideals (if only.results=FALSE).

    +
    lattice

    igraph object. The lattice of ideals (if only.results=FALSE).

    +
    ideals

    list. order ideals (if only.results=FALSE).

    +In all cases, higher numerical ranks imply a higher position in the ranking. That is, +the lowest ranked node has rank 1. + + +

    Details

    + +

    The function derives rank probabilities from a given partial ranking +(for instance returned by neighborhood_inclusion or positional_dominance). This includes the +calculation of expected ranks, (relative) rank probabilities and the number of possible rankings. +Note that the set of rankings grows exponentially in the number of elements and the exact +calculation becomes infeasible quite quickly and approximations need to be used. +See vignette("benchmarks") for guidelines and approx_rank_relative, +approx_rank_expected, and mcmc_rank_prob for approximative methods.

    + +

    References

    + +

    De Loof, K. 2009. Efficient computation of rank probabilities in posets. +Phd thesis, Ghent University.

    +

    De Loof, K., De Meyer, H. and De Baets, B., 2006. Exploiting the +lattice of ideals representation of a poset. Fundamenta Informaticae, 71(2,3):309-321.

    + +

    See also

    + +

    approx_rank_relative, approx_rank_expected, mcmc_rank_prob

    + + +

    Examples

    + 
    P <- matrix(c(0,0,1,1,1,0,0,0,1,0,0,0,0,0,1,rep(0,10)),5,5,byrow=TRUE)
+P
    #>      [,1] [,2] [,3] [,4] [,5]
+#> [1,]    0    0    1    1    1
+#> [2,]    0    0    0    1    0
+#> [3,]    0    0    0    0    1
+#> [4,]    0    0    0    0    0
+#> [5,]    0    0    0    0    0
    res <- exact_rank_prob(P)
+
+#a warning is displayed if only one ranking is possible
+tg <- threshold_graph(20,0.2)
+P <- neighborhood_inclusion(tg)
+res <- exact_rank_prob(P)
    #> Warning: P is already a ranking.
+#> Expected Ranks correspond to the only possible ranking.
    +
    + +
    + +
    +
    +

    Developed by David Schoch.

    +
    + +
    +

    Site built with pkgdown.

    +
    + +
    +
    + + + diff --git a/docs/reference/florentine_m.html b/docs/reference/florentine_m.html new file mode 100644 index 0000000..312445b --- /dev/null +++ b/docs/reference/florentine_m.html @@ -0,0 +1,179 @@ + + + + + + + + +Florentine family marriage network — florentine_m • netrankr + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + +
    + +
    +
    +
    +

    Florentine family marriage network

    +
    + + +

    Florentine family marriage network

    + + + 
    florentine_m
    + +

    Format

    + +

    An igraph object containing marriage links of florentine families

    + +

    References

    + +

    Padgett, J.F. and Ansell, C.K., 1993. +Robust Action and the Rise of the Medici, 1400-1434. American Journal of Sociology, 98(6), 1259-1319.

    + + +
    + +
    + +
    +
    +

    Developed by David Schoch.

    +
    + +
    +

    Site built with pkgdown.

    +
    + +
    +
    + + + diff --git a/docs/reference/get_rankings.html b/docs/reference/get_rankings.html new file mode 100644 index 0000000..f3949d3 --- /dev/null +++ b/docs/reference/get_rankings.html @@ -0,0 +1,216 @@ + + + + + + + + +Rankings that extend a partial ranking — get_rankings • netrankr + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + +
    + +
    +
    +
    +

    Rankings that extend a partial ranking

    +
    + + +

    Returns all possible rankings that extend a partial ranking.

    + + + 
    get_rankings(data, force = F)
    + +

    Arguments

    + + + + + + + + + + +
    data

    List as returned by exact_rank_prob when run with only.results = FALSE

    force

    Logical scalar. Stops function if the number of rankings is too large. +Only change to TRUE if you know what you are doing

    + +

    Value

    + +

    A matrix containing ranks of nodes in all possible rankings.

    + +

    Details

    + +

    The ith row of the matrix contains the rank of node i in all possible rankings +that are in accordance with the partial ranking P. The lowest rank possible is +associated with 1.

    + + +

    Examples

    + 
    P <- matrix(c(0,0,1,1,1,0,0,0,1,0,0,0,0,0,1,rep(0,10)),5,5,byrow=TRUE)
+P
    #>      [,1] [,2] [,3] [,4] [,5]
+#> [1,]    0    0    1    1    1
+#> [2,]    0    0    0    1    0
+#> [3,]    0    0    0    0    1
+#> [4,]    0    0    0    0    0
+#> [5,]    0    0    0    0    0
    res <- exact_rank_prob(P,only.results = FALSE)
+get_rankings(res)
    #>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
+#> [1,]    1    1    2    1    1    1    2    1    2
+#> [2,]    3    2    1    4    3    2    1    2    1
+#> [3,]    2    3    3    2    2    3    3    4    4
+#> [4,]    5    5    5    5    4    4    4    3    3
+#> [5,]    4    4    4    3    5    5    5    5    5
    
+
    +
    + +
    + +
    +
    +

    Developed by David Schoch.

    +
    + +
    +

    Site built with pkgdown.

    +
    + +
    +
    + + + diff --git a/docs/reference/hyperbolic_index.html b/docs/reference/hyperbolic_index.html new file mode 100644 index 0000000..38f1eae --- /dev/null +++ b/docs/reference/hyperbolic_index.html @@ -0,0 +1,212 @@ + + + + + + + + +Hyperbolic (centrality) index — hyperbolic_index • netrankr + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + +
    + +
    +
    +
    +

    Hyperbolic (centrality) index

    +
    + + +

    The hyperbolic index is an index that considers all closed +walks of even or odd length on induced neighborhoods of a vertex.

    + + + 
    hyperbolic_index(g, type = "odd")
    + +

    Arguments

    + + + + + + + + + + +
    g

    igraph object.

    type

    string. 'even' if only even length walks should be considered. 'odd' (Default) +if only odd length walks should be used.

    + +

    Value

    + +

    A vector containing centrality scores.

    + +

    Details

    + +

    The hyperbolic index is an illustrative index that should +not be used for any serious analysis. Its purpose is to show that with enough mathematical +trickery, any desired result can be obtained when centrality indices are used.

    + + +

    Examples

    + 
    
+require(igraph)
+
+g <- graph.empty(n=11,directed = FALSE)
+g <- add_edges(g,c(1,11,2,4,3,5,3,11,4,8,5,9,5,11,6,7,6,8,
+                   6,10,6,11,7,9,7,10,7,11,8,9,8,10,9,10))
+hyperbolic_index(g,type = "odd")
    #>  [1] 0.000e+00 0.000e+00 1.276e+00 4.219e-15 9.186e-01 3.555e+00 3.555e+00
+#>  [8] 1.926e+00 1.926e+00 5.996e+00 1.501e+00
    hyperbolic_index(g,type = "even")
    #>  [1]  3.086  3.086  6.848  3.571  6.228 11.665 11.665  8.585  8.585 16.292
+#> [11]  7.755
    +
    + +
    + +
    +
    +

    Developed by David Schoch.

    +
    + +
    +

    Site built with pkgdown.

    +
    + +
    +
    + + + diff --git a/docs/reference/index.html b/docs/reference/index.html new file mode 100644 index 0000000..3cbfa10 --- /dev/null +++ b/docs/reference/index.html @@ -0,0 +1,320 @@ + + + + + + + + +Function reference • netrankr + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + +
    + +
    +
    +
    +

    + Reference + version 0.1.0 +

    +
    + +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    All functions

    +

    +
    +

    aggregate_positions

    +

    Quantification of (indirect) relations

    +

    approx_rank_expected

    +

    Approximation of expected ranks

    +

    approx_rank_relative

    +

    Approximation of relative rank probabilities

    +

    comparable_pairs

    +

    Comparable pairs in a partial ranking

    +

    compare_ranks

    +

    Count occurrences of pairs in rankings

    +

    dominance_graph

    +

    Partial ranking as directed graph

    +

    exact_rank_prob

    +

    Probabilistic centrality rankings

    +

    florentine_m

    +

    Florentine family marriage network

    +

    get_rankings

    +

    Rankings that extend a partial ranking

    +

    hyperbolic_index

    +

    Hyperbolic (centrality) index

    +

    indirect_relations

    +

    Indirect relations in a network

    +

    is_preserved

    +

    Check preservation

    +

    majorization_gap

    +

    Majorization gap

    +

    mcmc_rank_prob

    +

    Estimate rank probabilities with Markov Chains

    +

    neighborhood_inclusion

    +

    Neighborhood-inclusion preorder

    +

    +

    netrankr: An R package to analyze partial rankings in networks

    +

    plot_rank_intervals

    +

    Plot rank intervals

    +

    positional_dominance

    +

    Generalized Dominance in Graphs

    +

    rank_intervals

    +

    Rank interval of nodes

    +

    spectral_gap

    +

    Spectral gap of a graph

    +

    threshold_graph

    +

    Random threshold graphs

    +

    dist_2pow dist_inv dist_dpow dist_powd dist_triang walks_limit_prop walks_exp walks_exp_even walks_exp_odd walks_attenuated walks_uptok

    +

    Transform indirect relations

    +

    transitive_reduction

    +

    Transitive Reduction

    +
    +
    + + +
    + +
    +
    +

    Developed by David Schoch.

    +
    + +
    +

    Site built with pkgdown.

    +
    + +
    +
    + + + diff --git a/docs/reference/indirect_relations.html b/docs/reference/indirect_relations.html new file mode 100644 index 0000000..e66d6bf --- /dev/null +++ b/docs/reference/indirect_relations.html @@ -0,0 +1,272 @@ + + + + + + + + +Indirect relations in a network — indirect_relations • netrankr + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + +
    + +
    +
    +
    +

    Indirect relations in a network

    +
    + + +

    Derive indirect relations for a given network. +Observed relations, like presents or absence of a relation, are commonly not the center +of analysis, but are transformed in a new set of indirect relation like geodesic +distances among nodes. These transformations are usually an implicit step when centrality +indices are used. Making this step explicit gives more possibilities, for example +calculating partial centrality rankings with positional_dominance.

    + + + 
    indirect_relations(g, type = "geodesic", FUN = identity, ...)
    + +

    Arguments

    + + + + + + + + + + + + + + + + + + +
    g

    igraph object. The network for which relations should be derived.

    type

    String giving the relation to be calculated. See Details for options.

    FUN

    A function that allows the transformation of relations. See Details.

    ...

    Additional arguments passed to FUN.

    + +

    Value

    + +

    A matrix containing indirect relations in a network.

    + +

    Details

    + +

    The type parameter has the following options. + 'identity' returns the adjacency matrix of the network. + 'distances' returns geodesic distances between all pairs of nodes. + 'dependencies' returns dyadic dependencies +$$\delta(u,s) = \sum_{t \in V} \frac{\sigma(s,t|u)}{\sigma(s,t)}$$ +where \(\sigma(s,t|u)\) is the number of shortest paths from s to t that include u and +\(\sigma(s,t)\) is the total number of shortest (s,t)-paths. This relation is mostly used +for betweenness-like centrality indices. + 'walks' returns walk counts between pairs of nodes, usually they are +weighted decreasingly in their lengths or other properties which can be done by adding +a function in FUN. See transform_relations for options. + 'resistance' returns the resistance distance between all pairs of vertices.

    +

    The function FUN is used to further specify the indirect +relation. See transform_relations for predefined functions and additional help.

    + +

    See also

    + +

    aggregate_positions to build centrality indices, positional_dominance to derive dominance relations

    + + +

    Examples

    + 
    require(igraph)
+g <- graph.empty(n=11,directed = FALSE)
+g <- add_edges(g,c(1,11,2,4,3,5,3,11,4,8,5,9,5,11,6,7,6,8,
+                   6,10,6,11,7,9,7,10,7,11,8,9,8,10,9,10))
+#geodesic distances
+D <- indirect_relations(g,type = "geodesic")
+
+#dyadic dependencies
+D <- indirect_relations(g,type = "dependencies")
+
+#walks attenuated exponentially by there length
+W <- indirect_relations(g,type = "walks",FUN = walks_exp)
+
+#positional dominance of a transformed relation...
+D <- indirect_relations(g,type = "geodesic")
+
+#...under total heterogeneity
+positional_dominance(D, map = FALSE ,benefit = FALSE)
    #>       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11]
+#>  [1,]    0    0    1    0    1    1    1    0    0     0     1
+#>  [2,]    0    0    0    1    0    0    0    1    0     0     0
+#>  [3,]    0    0    0    0    1    0    0    0    0     0     1
+#>  [4,]    0    0    0    0    0    0    0    0    0     0     0
+#>  [5,]    0    0    0    0    0    0    0    0    0     0     0
+#>  [6,]    0    0    0    0    0    0    0    0    0     0     0
+#>  [7,]    0    0    0    0    0    0    0    0    0     0     0
+#>  [8,]    0    0    0    0    0    0    0    0    0     0     0
+#>  [9,]    0    0    0    0    0    0    0    0    0     0     0
+#> [10,]    0    0    0    0    0    0    0    0    0     0     0
+#> [11,]    0    0    0    0    0    0    0    0    0     0     0
    #...under total homogeneity
+positional_dominance(D, map = TRUE ,benefit = FALSE)
    #>       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11]
+#>  [1,]    0    0    1    1    1    1    1    1    1     1     1
+#>  [2,]    1    0    1    1    1    1    1    1    1     1     1
+#>  [3,]    0    0    0    0    1    1    1    1    1     1     1
+#>  [4,]    0    0    0    0    1    1    1    1    1     1     1
+#>  [5,]    0    0    0    0    0    1    1    1    1     0     1
+#>  [6,]    0    0    0    0    0    0    0    0    0     0     0
+#>  [7,]    0    0    0    0    0    1    0    1    1     0     1
+#>  [8,]    0    0    0    0    0    1    0    0    1     0     0
+#>  [9,]    0    0    0    0    0    1    0    1    0     0     0
+#> [10,]    0    0    0    0    0    1    0    1    1     0     0
+#> [11,]    0    0    0    0    0    0    0    0    0     0     0
    +
    + +
    + +
    +
    +

    Developed by David Schoch.

    +
    + +
    +

    Site built with pkgdown.

    +
    + +
    +
    + + + diff --git a/docs/reference/is_preserved.html b/docs/reference/is_preserved.html new file mode 100644 index 0000000..f15e702 --- /dev/null +++ b/docs/reference/is_preserved.html @@ -0,0 +1,211 @@ + + + + + + + + +Check preservation — is_preserved • netrankr + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + +
    + +
    +
    +
    +

    Check preservation

    +
    + + +

    Checks if a partial ranking is preserved in the ranking induced by scores.

    + + + 
    is_preserved(P, scores)
    + +

    Arguments

    + + + + + + + + + + +
    P

    A partial ranking as matrix object calculated with neighborhood_inclusion +or positional_dominance.

    scores

    Numeric vector containing the scores of a centrality index.

    + +

    Value

    + +

    Logical scaler whether scores preserves the relations in P.

    + +

    Details

    + +

    In order for a score vector to preserve a partial ranking, the following +condition must be fulfilled: +P[u,v]==1 & scores[i]<=scores[j].

    + + +

    Examples

    + 
    
+require(igraph)
+# standard measures of centrality preserve the neighborhood inclusion preorder
+g <- graph.empty(n=11,directed = FALSE)
+g <- add_edges(g,c(1,11,2,4,3,5,3,11,4,8,5,9,5,11,6,7,6,8,
+                   6,10,6,11,7,9,7,10,7,11,8,9,8,10,9,10))
+P<-neighborhood_inclusion(g)
+
+is_preserved(P,degree(g))
    #> [1] TRUE
    is_preserved(P,betweenness(g))
    #> [1] TRUE
    is_preserved(P,closeness(g))
    #> [1] TRUE
    +
    + +
    + +
    +
    +

    Developed by David Schoch.

    +
    + +
    +

    Site built with pkgdown.

    +
    + +
    +
    + + + diff --git a/docs/reference/majorization_gap.html b/docs/reference/majorization_gap.html new file mode 100644 index 0000000..273b2ad --- /dev/null +++ b/docs/reference/majorization_gap.html @@ -0,0 +1,222 @@ + + + + + + + + +Majorization gap — majorization_gap • netrankr + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + +
    + +
    +
    +
    +

    Majorization gap

    +
    + + +

    Calculates the (normalized) majorization gap of an undirected graph. +The majorization gap indicates how far the degree sequence of a graph is +from a degree sequence of a threshold_graph.

    + + + 
    majorization_gap(g, norm = TRUE)
    + +

    Arguments

    + + + + + + + + + + +
    g

    An igraph object

    norm

    True (Default) if the normalized majorization gap should be returned.

    + +

    Value

    + +

    Majorization gap of an undirected graph.

    + +

    Details

    + +

    The distance is measured by the number of reverse unit +transformations necessary to turn the degree sequence into a threshold sequence. +First, the corrected conjugated degree sequence d' is calculated from the degree sequence d as follows: +$$d'_k= |\{ i : i<k \land d_i\geq k-1 \} | + +| \{ i : i>k \land d_i\geq k \} |.$$ +the majorization gap is then defined as +$$1/2 \sum_{k=1}^n \max\{d'_k - d_k,0\}$$ +The higher the value, the further away is a graph to be a threshold graph.

    + +

    References

    + +

    Schoch, D., Valente, T. W. and Brandes, U., 2017. Correlations among centrality +indices and a class of uniquely ranked graphs. Social Networks 50, 46–54.

    +

    Arikati, S.R. and Peled, U.N., 1994. Degree sequences and majorization. +Linear Algebra and its Applications, 199, 179-211.

    + + +

    Examples

    + 
    require(igraph)
+g <- graph.star(5,'undirected')
+majorization_gap(g) #0 since star graphs are threshold graphs
    #> [1] 0
    
+g <- sample_gnp(100,0.15)
+majorization_gap(g,norm=TRUE) #fraction of reverse unit transformation
    #> [1] 0.7274
    majorization_gap(g,norm=FALSE) #number of reverse unit transformation
    #> [1] 547
    +
    + +
    + +
    +
    +

    Developed by David Schoch.

    +
    + +
    +

    Site built with pkgdown.

    +
    + +
    +
    + + + diff --git a/docs/reference/mcmc_rank_prob.html b/docs/reference/mcmc_rank_prob.html new file mode 100644 index 0000000..78c49f7 --- /dev/null +++ b/docs/reference/mcmc_rank_prob.html @@ -0,0 +1,231 @@ + + + + + + + + +Estimate rank probabilities with Markov Chains — mcmc_rank_prob • netrankr + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + +
    + +
    +
    +
    +

    Estimate rank probabilities with Markov Chains

    +
    + + +

    Performs a probabilistic rank analysis based on an almost uniform +sample of possible rankings that preserve a partial ranking.

    + + + 
    mcmc_rank_prob(P, rp = nrow(P)^3)
    + +

    Arguments

    + + + + + + + + + + +
    P

    P A partial ranking as matrix object calculated with neighborhood_inclusion +or positional_dominance.

    rp

    Integer indicating the number of samples to be drawn.

    + +

    Value

    + + + +
    expected.rank

    Estimated expected ranks of nodes

    +
    relative.rank

    Matrix containing estimated relative rank probabilities: +relative.rank[u,v] is the probability that u is ranked lower than v.

    + + +

    Details

    + +

    This function can be used instead of exact_rank_prob +if the number of elements in P is too large for an exact computation. As a rule of thumb, +the number of samples should be at least cubic in the number of elements in P. +See vignette("benchmarks",package="netrankr") for guidelines and benchmark results.

    + +

    References

    + +

    Bubley, R. and Dyer, M., 1999. Faster random generation of linear extensions. +Discrete Mathematics, 201(1):81-88

    + +

    See also

    + +

    exact_rank_prob, approx_rank_relative, approx_rank_expected

    + + +

    Examples

    + 
    # NOT RUN {
+data("florentine_m")
+P <- neighborhood_inclusion(florentine_m)
+res <- exact_rank_prob(P)
+mcmc <- mcmc_rank_prob(P,rp = vcount(g)^3)
+
+# mean absolute error (expected ranks)
+mean(abs(res$expected.rank-mcmc$expected.rank))
+# }
    +
    + +
    + +
    +
    +

    Developed by David Schoch.

    +
    + +
    +

    Site built with pkgdown.

    +
    + +
    +
    + + + diff --git a/docs/reference/neighborhood_inclusion.html b/docs/reference/neighborhood_inclusion.html new file mode 100644 index 0000000..2b53593 --- /dev/null +++ b/docs/reference/neighborhood_inclusion.html @@ -0,0 +1,231 @@ + + + + + + + + +Neighborhood-inclusion preorder — neighborhood_inclusion • netrankr + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + +
    + +
    +
    +
    +

    Neighborhood-inclusion preorder

    +
    + + +

    Calculates the neighborhood-inclusion preorder of an undirected graph.

    + + + 
    neighborhood_inclusion(g)
    + +

    Arguments

    + + + + + + +
    g

    An igraph object

    + +

    Value

    + +

    The neighborhood-inclusion preorder of g as matrix object. P[u,v]=1 if \(N(u)\subseteq N[v]\)

    + +

    Details

    + +

    Neighborhood-inclusion is defined as +$$N(u)\subseteq N[v]$$ +where \(N(u)\) is the neighborhood of \(u\) and \(N[v]=N(v)\cup \lbrace v\rbrace\) is the closed neighborhood of \(v\). +\(N(u) \subseteq N[v]\) implies that \(c(u) \leq c(v)\), +where \(c\) is an arbitrary centrality index. Neighborhood-inclusion is thus preserved in any centrality ranking.

    + +

    References

    + +

    Schoch, D. and Brandes, U., 2016. Re-conceptualizing centrality in social networks. +European Journal of Applied Mathematics 27(6), 971-985.

    +

    Brandes, U. Heine, M., Müller, J. and Ortmann, M., 2017. +Positional Dominance: Concepts and Algorithms. +Conference on Algorithms and Discrete Applied Mathematics, 60-71.

    + +

    See also

    + +

    positional_dominance, exact_rank_prob

    + + +

    Examples

    + 
    require(igraph)
+#the neighborhood inclusion preorder of a star graph is complete
+g <- graph.star(5,'undirected')
+P <- neighborhood_inclusion(g)
+comparable_pairs(P)
    #> [1] 1
    
+#the same holds for threshold graphs
+tg <- threshold_graph(50,0.1)
+P <- neighborhood_inclusion(tg)
+comparable_pairs(P)
    #> [1] 1
    
+#standard centrality indices preserve neighborhood-inclusion
+g <- graph.empty(n=11,directed = FALSE)
+g <- add_edges(g,c(1,11,2,4,3,5,3,11,4,8,5,9,5,11,6,7,6,8,
+                   6,10,6,11,7,9,7,10,7,11,8,9,8,10,9,10))
+P <- neighborhood_inclusion(g)
+
+is_preserved(P,degree(g))
    #> [1] TRUE
    is_preserved(P,closeness(g))
    #> [1] TRUE
    is_preserved(P,betweenness(g))
    #> [1] TRUE
    +
    + +
    + +
    +
    +

    Developed by David Schoch.

    +
    + +
    +

    Site built with pkgdown.

    +
    + +
    +
    + + + diff --git a/docs/reference/netrankr.html b/docs/reference/netrankr.html new file mode 100644 index 0000000..72bf5eb --- /dev/null +++ b/docs/reference/netrankr.html @@ -0,0 +1,197 @@ + + + + + + + + +netrankr: An R package to analyze partial rankings in networks — netrankr • netrankr + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + +
    + +
    +
    +
    +

    netrankr: An R package to analyze partial rankings in networks

    +
    + + +

    netrankr provides several functions to analyze partial rankings for network +centrality. The main focus lies on methods that do not rely on indices like degree, +betweenness or closeness.

    +

    The package follows the philosophy, that centrality +can be decomposed in a series of micro steps. Starting from a network, +indirect_relations can be derived which can either be aggregated into an index with +aggregate_positions, or alternatively turned into a partial ranking with positional_dominance. +The partial ranking can then be further analyzed with exact_rank_prob, to obtain +probabilistic centrality rankings.

    + + + +

    Details

    + +

    Some features of the package are:

      +

    • Working with the neighborhood inclusion preorder. This forms the bases +for any centrality analysis on undirected and unweighted graphs. +More details can be found in the dedicated vignette: +vignette("neighborhood_inclusion",package = "netrankr")

      • +

    • Constructing graphs with a unique centrality ranking. +This class of graphs, known as threshold graphs, can be used to benchmark +centrality indices, since they only allow for one ranking of the nodes. +For more details consult the vignette: vignette("threshold_graph",package = "netrankr")

      • +

    • Probabilistic centrality. Why apply a handful of indices and choosing +the one that fits best, when it is possible to analyze all centrality rankings at once? +The package includes several function to calculate rank probabilities of nodes +in a network. These include expected ranks and relative rank probabilities +(how likely is it that a node is more central than another?) +Consult vignette("probabilistic_cent",package = "netrankr") for more info.

      • +
    +

    The package provides several additional vignettes that explain the functionality +of netrankr and its conceptual ideas. See browseVignettes(package = 'netrankr') +or the online manual.

    + + +
    + +
    + +
    +
    +

    Developed by David Schoch.

    +
    + +
    +

    Site built with pkgdown.

    +
    + +
    +
    + + + diff --git a/docs/reference/plot_rank_intervals.html b/docs/reference/plot_rank_intervals.html new file mode 100644 index 0000000..3a2de57 --- /dev/null +++ b/docs/reference/plot_rank_intervals.html @@ -0,0 +1,232 @@ + + + + + + + + +Plot rank intervals — plot_rank_intervals • netrankr + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + +
    + +
    +
    +
    +

    Plot rank intervals

    +
    + + +

    Compute rank intervals (minimal and maximal possible rank) and visualize them with ggplot.

    + + + 
    plot_rank_intervals(P, names, cent.df, ties.method = "min")
    + +

    Arguments

    + + + + + + + + + + + + + + + + + + +
    P

    A partial ranking as matrix object calculated with neighborhood_inclusion +or positional_dominance.

    names

    String with potential names of nodes used in the plot (optional).

    cent.df

    A data frame containing centrality scores of indices (optional). See Details.

    ties.method

    String specifying how ties are treated in the base rank function.

    + +

    Value

    + +

    a ggplot object.

    + +

    Details

    + +

    If a data frame of centrality scores is added, the respective ranks of nodes are +shown in the intervals. Note that some points might fall outside of the +intervals depending how ties are treated.

    + +

    See also

    + +

    rank_intervals

    + + +

    Examples

    + 
    require(igraph)
+require(ggplot2)
+g <- graph.empty(n=11,directed = FALSE)
+g <- add_edges(g,c(1,11,2,4,3,5,3,11,4,8,5,9,5,11,6,7,6,8,
+                   6,10,6,11,7,9,7,10,7,11,8,9,8,10,9,10))
+P <- neighborhood_inclusion(g)
    # NOT RUN {
+plot_rank_intervals(P)
+# }
    
+#adding index based rankings
+cent_scores <- data.frame(
+  degree = degree(g),
+  betweenness = round(betweenness(g),4),
+  closeness = round(closeness(g),4),
+  eigenvector = round(eigen_centrality(g)$vector,4))
    # NOT RUN {
+plot_rank_intervals(P,cent.df=cent_scores)
+# }
    +
    + +
    + +
    +
    +

    Developed by David Schoch.

    +
    + +
    +

    Site built with pkgdown.

    +
    + +
    +
    + + + diff --git a/docs/reference/positional_dominance.html b/docs/reference/positional_dominance.html new file mode 100644 index 0000000..b2bc16d --- /dev/null +++ b/docs/reference/positional_dominance.html @@ -0,0 +1,246 @@ + + + + + + + + +Generalized Dominance in Graphs — positional_dominance • netrankr + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + +
    + +
    +
    +
    +

    Generalized Dominance in Graphs

    +
    + + +

    generalized dominance relations.

    + + + 
    positional_dominance(A, type = "one-mode", map = FALSE, benefit = TRUE)
    + +

    Arguments

    + + + + + + + + + + + + + + + + + + +
    A

    Matrix containing attributes or relations, for instance calculated by indirect_relations.

    type

    A string which is either 'one-mode' (Default) if A is a regular one-mode network +or 'two-mode' if A is a general data matrix.

    map

    Logical scalar, whether rows can be sorted or not (Default). See Details.

    benefit

    Logical scalar, whether the attributes or relations are benefit or cost variables.

    + +

    Value

    + +

    Dominance relations as matrix object. An entry [u,v] is 1 if u is dominated by v.

    + +

    Details

    + +

    Positional dominance is a generalization of neighborhood-inclusion for +arbitrary network data. In the default case, it checks for all pairs \(u,v\) if +\(A_{ut} \ge A_{vt}\) holds for all \(t\) if benefit = TRUE or +\(A_{ut} \le A_{vt}\) holds for all \(t\) if benefit = FALSE. +This form of dominance is referred to as dominance under total heterogeneity. +If map=TRUE, the rows of \(A\) are sorted decreasingly (benefit = TRUE) +or increasingly (benefit = FALSE) and then the dominance condition is checked. This second +form of dominance is referred to as dominance under total homogeneity, while the +first is called dominance under total heterogeneity.

    + +

    References

    + +

    Brandes, U., 2016. Network positions. Methodological Innovations 9, +2059799116630650.

    +

    Schoch, D. and Brandes, U., 2016. Re-conceptualizing centrality in social networks. +European Journal of Applied Mathematics 27(6), 971-985.

    + +

    See also

    + +

    neighborhood_inclusion, indirect_relations, exact_rank_prob

    + + +

    Examples

    + 
    require(igraph)
+
+g <- graph.empty(n=11,directed = FALSE)
+g <- add_edges(g,c(1,11,2,4,3,5,3,11,4,8,5,9,5,11,6,7,6,8,
+                   6,10,6,11,7,9,7,10,7,11,8,9,8,10,9,10))
+P<-neighborhood_inclusion(g)
+comparable_pairs(P)
    #> [1] 0.1636
    
+# positional dominance under total heterogeneity
+dist <- indirect_relations(g,type = "geodesic")
+D <- positional_dominance(dist,map = FALSE,benefit = FALSE)
+comparable_pairs(D)
    #> [1] 0.1636
    
+# positional dominance under total homogeneity
+D_map <- positional_dominance(dist,map = TRUE,benefit = FALSE)
+comparable_pairs(D_map) #more comparables than D
    #> [1] 0.8727
    
+
    +
    + +
    + +
    +
    +

    Developed by David Schoch.

    +
    + +
    +

    Site built with pkgdown.

    +
    + +
    +
    + + + diff --git a/docs/reference/rank_intervals.html b/docs/reference/rank_intervals.html new file mode 100644 index 0000000..8a2da96 --- /dev/null +++ b/docs/reference/rank_intervals.html @@ -0,0 +1,214 @@ + + + + + + + + +Rank interval of nodes — rank_intervals • netrankr + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + +
    + +
    +
    +
    +

    Rank interval of nodes

    +
    + + +

    Calculate the maximal and minimal rank possible for each node +in any ranking that is in accordance with the partial ranking P.

    + + + 
    rank_intervals(P)
    + +

    Arguments

    + + + + + + +
    P

    A partial ranking as matrix object calculated with neighborhood_inclusion +or positional_dominance.

    + +

    Value

    + +

    A data frame with the minimal, maximal rank of each node together +with the mid point of the two extrema.

    + +

    Details

    + +

    Note that the returned mid_point is not the same as the expected +rank, for instance computed with exact_rank_prob. +It is simply the average of min_rank and max_rank. For exact rank probabilities +use exact_rank_prob.

    + +

    See also

    + +

    plot_rank_intervals, exact_rank_prob

    + + +

    Examples

    + 
    P <- matrix(c(0,0,1,1,1,0,0,0,1,0,0,0,0,0,1,rep(0,10)),5,5,byrow=TRUE)
+rank_intervals(P)
    #>   min_rank max_rank mid_point
+#> 1        1        2       1.5
+#> 2        1        4       2.5
+#> 3        2        4       3.0
+#> 4        3        5       4.0
+#> 5        3        5       4.0
    +
    + +
    + +
    +
    +

    Developed by David Schoch.

    +
    + +
    +

    Site built with pkgdown.

    +
    + +
    +
    + + + diff --git a/docs/reference/spectral_gap.html b/docs/reference/spectral_gap.html new file mode 100644 index 0000000..a6edf4b --- /dev/null +++ b/docs/reference/spectral_gap.html @@ -0,0 +1,206 @@ + + + + + + + + +Spectral gap of a graph — spectral_gap • netrankr + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + +
    + +
    +
    +
    +

    Spectral gap of a graph

    +
    + + +

    The spectral (or eigen) gap of a graph is the absolute +difference between the biggest and second biggest eigenvalue +of the adjacency matrix. To compare spectral gaps across networks, the fraction can be used.

    + + + 
    spectral_gap(g, method = "frac")
    + +

    Arguments

    + + + + + + + + + + +
    g

    igraph object

    method

    A string, either "frac" or "abs"

    + +

    Value

    + +

    Numeric value

    + +

    Details

    + +

    The spectral gap is bounded between 0 and 1 if method="frac". The closer +the value to one, the bigger the gap.

    + + +

    Examples

    + 
    #The fractional spectral gap of a threshold graph is usually close to 1
+g <- threshold_graph(50,0.3)
+spectral_gap(g,method = "frac")
    #> [1] 0.8238
    
+
    +
    + +
    + +
    +
    +

    Developed by David Schoch.

    +
    + +
    +

    Site built with pkgdown.

    +
    + +
    +
    + + + diff --git a/docs/reference/threshold_graph.html b/docs/reference/threshold_graph.html new file mode 100644 index 0000000..76a0dde --- /dev/null +++ b/docs/reference/threshold_graph.html @@ -0,0 +1,231 @@ + + + + + + + + +Random threshold graphs — threshold_graph • netrankr + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + +
    + +
    +
    +
    +

    Random threshold graphs

    +
    + + +

    Constructs a random threshold graph. +A threshold graph is a graph where the neighborhood inclusion preorder is complete.

    + + + 
    threshold_graph(n, p)
    + +

    Arguments

    + + + + + + + + + + +
    n

    The number of vertices in the graph.

    p

    The probability of inserting dominating vertices. Equates approximately +to the density of the graph. See Details.

    + +

    Value

    + +

    A threshold graph as igraph object

    + +

    Details

    + +

    Threshold graphs can be constructed with a binary sequence. For each 0, an isolated +vertex is inserted and for each 1, a vertex is inserted that connects to all previously inserted +vertices. The probability of inserting a dominating vertice is controlled with parameter p. +An important property of threshold graphs is, that all centrality indices induce the same ranking.

    + +

    References

    + +

    Mahadev, N. and Peled, U. N. , 1995. Threshold graphs and related topics.

    +

    Schoch, D., Valente, T. W. and Brandes, U., 2017. Correlations among centrality +indices and a class of uniquely ranked graphs. Social Networks 50, 46–54.

    + +

    See also

    + +

    neighborhood_inclusion, positional_dominance

    + + +

    Examples

    + 
    require(igraph)
+g <- threshold_graph(10,0.3)
    # NOT RUN {
+plot(g)
+
+# star graphs and complete graphs are threshold graphs
+complete <- threshold_graph(10,1) #complete graph
+plot(complete)
+
+star <- threshold_graph(10,0) #star graph
+plot(star)
+# }
    
+# centrality scores are perfectly rank correlated
+cor(degree(g),closeness(g),method = "kendall")
    #> [1] 1
    +
    + +
    + +
    +
    +

    Developed by David Schoch.

    +
    + +
    +

    Site built with pkgdown.

    +
    + +
    +
    + + + diff --git a/docs/reference/transform_relations.html b/docs/reference/transform_relations.html new file mode 100644 index 0000000..e6cf94c --- /dev/null +++ b/docs/reference/transform_relations.html @@ -0,0 +1,242 @@ + + + + + + + + +Transform indirect relations — transform_relations • netrankr + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + +
    + +
    +
    +
    +

    Transform indirect relations

    +
    + + +

    Mostly wrapper functions that can be used in conjunction +with indirect_relations to fine tune indirect relations.

    + + + 
    dist_2pow(x)
+
+dist_inv(x)
+
+dist_dpow(x, alpha = 1)
+
+dist_powd(x, alpha = 0.5)
+
+dist_triang(x)
+
+walks_limit_prop(x)
+
+walks_exp(x, alpha = 1)
+
+walks_exp_even(x, alpha = 1)
+
+walks_exp_odd(x, alpha = 1)
+
+walks_attenuated(x, alpha = 1/max(x) * 0.99)
+
+walks_uptok(x, alpha = 1, k = 3)
    + +

    Arguments

    + + + + + + + + + + + + + + +
    x

    Matrix of relations.

    alpha

    Potential weighting factor.

    k

    For walk counts up to a certain length.

    + +

    Value

    + +

    Transformed relations as matrix

    + +

    Details

    + +

    The predefined functions follow the naming scheme relation_transformation. +Predefined functions walks_* are thus best used with type="walks" in +indirect_relations. Theoretically, however, any transformation can be used with any relation. +The results might, however, not be interpretable.

    +

    The following functions are implemented so far: + dist_2pow returns \(2^{-x}\) + dist_inv returns \(1/x\) + dist_dpow returns \(x^{-\alpha}\) where \(\alpha\) should be chosen greater than 0. + dist_powd returns \(\alpha^x\) where \(\alpha\) should be chosen between 0 and 1. + dist_triang returns \(\sum_t\frac{x_{st}}{x_{su}+x_{st}}\). This function is used for +a corrected betweenness version. + walks_limit_prop returns the limit proportion of walks between pairs of nodes. Calculating +rowSums of this relation will result in the principle eigenvector of the network. + walks_exp returns \(\sum_{k=0}^\infty \frac{A^k}{k!}\) + walks_exp_even returns \(\sum_{k=0}^\infty \frac{A^{2k}}{(2k)!}\) + walks_exp_odd returns \(\sum_{k=0}^\infty \frac{A^{2k+1}}{(2k+1)!}\) + walks_attenuated returns \(\sum_{k=0}^\infty \alpha^k A^k\) + walks_uptok returns \(\sum_{j=0}^k \alpha^j A^j\)

    +

    Walk based transformation are defined on the eigen decomposition of the +adjacency matrix using the fact that +$$f(A)=Xf(\Lambda)X^T.$$ +Care has to be taken when using user defined functions.

    + + +
    + +
    + +
    +
    +

    Developed by David Schoch.

    +
    + +
    +

    Site built with pkgdown.

    +
    + +
    +
    + + + diff --git a/docs/reference/transitive_reduction.html b/docs/reference/transitive_reduction.html new file mode 100644 index 0000000..c7737aa --- /dev/null +++ b/docs/reference/transitive_reduction.html @@ -0,0 +1,197 @@ + + + + + + + + +Transitive Reduction — transitive_reduction • netrankr + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + +
    + +
    +
    +
    +

    Transitive Reduction

    +
    + + +

    Calculates the transitive reduction of a partial ranking.

    + + + 
    transitive_reduction(P)
    + +

    Arguments

    + + + + + + +
    P

    A partial ranking as matrix object calculated with neighborhood_inclusion +or positional_dominance.

    + +

    Value

    + +

    transitive reduction of P

    + + +

    Examples

    + 
    require(igraph)
+
+g <- threshold_graph(100,0.1)
+P <- neighborhood_inclusion(g)
+sum(P)
    #> [1] 5834
    
+T <- transitive_reduction(P)
+sum(T)
    #> [1] 181
    +
    + +
    + +
    +
    +

    Developed by David Schoch.

    +
    + +
    +

    Site built with pkgdown.

    +
    + +
    +
    + + + diff --git a/index.Rmd b/index.Rmd new file mode 100644 index 0000000..ac0f6e6 --- /dev/null +++ b/index.Rmd @@ -0,0 +1,202 @@ +--- +title: "netrankr: Centrality (almost) without Indices" +author: "" +output: github_document +always_allow_html: yes +--- + +```{r setup, include=FALSE} +knitr::opts_chunk$set( + echo = TRUE, + comment = "#>", + fig.path = "index-", + fig.width = 6, + fig.align = 'center', + out.width = "70%") +``` + +# Overview + +The literature is flooded with centrality indices and new ones are introduced +on a regular basis. Although there exist several theoretical and empirical guidelines +on when to use certain indices, there still exists plenty of ambiguity in the concept +of network centrality. To date, network centrality is nothing more than applying indices +to a network: + +```{r old,echo=FALSE} +DiagrammeR::DiagrammeR('graph LR + A[network]==>B{centrality
    indices} + style A fill:#fff,stroke:#000, stroke-width:2px + style B fill:#fff,stroke:#000, stroke-width:2px + ', height = 200 +) +``` + +The only degree of freedom is the choice of index. + +The `netrankr` package is based on the idea that centrality is more than a +conglomeration of indices. Decomposing them in a series of microsteps offers +the posibility to gradually add ideas about centrality, without succumbing to +trial-and-error approaches. Further, it allows for alternative assessment methods +which can be more general than the index-driven approach: + +```{r new,echo=FALSE} +DiagrammeR::DiagrammeR('graph LR + A[network]==>B{indirect relation} + B ==>P[position] + P==>C[aggregate position] + C==>D[centrality index] + P==>E{positional
    dominance} + E==>F[partial centrality] + E==>G[probabilistic centrality] + style A fill:#fff,stroke:#000, stroke-width:2px + style B fill:#fff,stroke:#000, stroke-width:2px + style C fill:#fff,stroke:#000, stroke-width:2px + style D fill:#fff,stroke:#000, stroke-width:2px + style E fill:#fff,stroke:#000, stroke-width:2px + style F fill:#fff,stroke:#000, stroke-width:2px + style G fill:#fff,stroke:#000, stroke-width:2px + style P fill:#EEC900,stroke:#000, stroke-width:3px +', height = 300 +) +``` + +The new approach is centered around the concept of *positions*, which are defined as +the relations and potential attributes of a node in a network. The aggregation +of the relations leads to the definition of indices. However, positions can also +be compared via *positional dominance*, leading to partial centrality rankings and +the option to calculate probabilistic centrality rankings. + +For a more detailed theoretical background, consult the [Literature](#literature) +at the end of this page. + +________________________________________________________________________________ + +## Installation + +To install from CRAN: [not released yet] + + + + + +To install the developer version from github: +```{r install_git, eval=FALSE} +require(devtools) +install_github("schochastics/netrankr") +``` + +________________________________________________________________________________ + +## Simple Example + +This example briefly explains some of the functionality of the package and the +difference to an index driven approach. For a more realistic application see +the [use case](articles/use_case.html) example. + +We work with the following small graph. +```{r example_graph, warning=FALSE,message=FALSE} +library(igraph) +library(netrankr) + +g <- graph.empty(n = 11,directed = FALSE) +g <- add_edges(g,c(1,11,2,4,3,5,3,11,4,8,5,9,5,11,6,7,6,8, + 6,10,6,11,7,9,7,10,7,11,8,9,8,10,9,10)) +``` + +```{r dbces_neutral, echo=FALSE} +knitr::include_graphics("dbces-neutral.png") +``` + +Say we are interested in the most central node of the graph and simply compute some +standard centrality scores with the `igraph` package. Defining centrality indices +in the `netrankr` package is explained [here](articles/centrality_indices.html). +```{r cent,warning=FALSE} +cent_scores <- data.frame( + degree = degree(g), + betweenness = round(betweenness(g),4), + closeness = round(closeness(g),4), + eigenvector = round(eigen_centrality(g)$vector,4), + subgraph = round(subgraph_centrality(g),4)) + +# What are the most central nodes for each index? +apply(cent_scores,2,which.max) +``` +```{r dbces_color, echo=FALSE} +knitr::include_graphics("dbces-color.png") +``` + +As you can see, each index assigns the highest value to a different vertex. + +A more general assessment starts by calculating the neighborhood inclusion preorder. +```{r ex_ni} +P <- neighborhood_inclusion(g) +P +``` +If `P[u,v]=1`, then $N(u) \subseteq N[v]$ which implies that +$c(u) \leq c(v)$ for all centrality indices $c$! + +Neighborhood-inclusion defines a partial ranking on the set of nodes. Each ranking +that is in accordance with this partial ranking yields a proper centrality ranking. +Each of these ranking can thus potentially be the outcome of a centrality index. + +Using rank intervals, we can examine the minimal and maximal possible rank of each node. +The bigger the intervals are, the more freedom exists for indices to rank nodes differently. +```{r partial} +plot_rank_intervals(P,names = 1:11,cent.df = cent_scores,ties.method="average") +``` + +The potential ranks of nodes are not uniformly distributed in the intervals. To get +the exact probabilities, the function `exact_rank_prob()` can be used. +```{r ex_p} +res <- exact_rank_prob(P) +str(res) +``` +`lin.ext` is the number of possible rankings. For the graph `g` we could therefore come up with +`r format(res$lin.ext,big.mark = ",")` indices that would rank the nodes differently. + +`rank.prob` contains the probabilities for each node to occupy a certain rank. +For instance, the probability for each node to be the most central one is as follows. +```{r most_central} +round(res$rank.prob[ ,11],2) +``` + +`relative.rank` contains the relative rank probabilities. An entry `relative.rank[u,v]` +indicates how likely it is that `v` is more central than `u`. +```{r rel_rank} +# How likely is it, that 6 is more central than 3? +round(res$relative.rank[3,6],2) +``` + +`expected.ranks` contains the expected centrality ranks for all nodes. They are +derived on the basis of `rank.prob`. +```{r exp_rank} +round(res$expected.rank,2) +``` +The higher the value, the more central a node is expected to be. + +**Note**: The set of rankings grows exponentially in the number of nodes and the exact +calculation becomes infeasible quite quickly and approximations need to be used. +Check the [benchmark results](articles/benchmarks.html) for guidelines. + +________________________________________________________________________________ + +## Theoretical Background {#literature} + +`netrankr` is based on a series of papers that appeared in recent years. If you +want to learn more about the theoretical background of the package, +consult the following literature: + +> Brandes, Ulrik. (2016). Network Positions. +*Methodological Innovations*, **9**, 2059799116630650. +([link](http://dx.doi.org/10.1177/2059799116630650)) + +> Schoch, David & Brandes, Ulrik. (2016). Re-conceptualizing centrality in social networks. +*European Journal of Appplied Mathematics*, **27**(6), 971–985. +([link](https://doi.org/10.1017/S0956792516000401)) + +> Schoch, David & Valente, Thomas W., & Brandes, Ulrik. (2017). Correlations among centrality indices +and a class of uniquely ranked graphs. *Social Networks*, **50**, 46-54.([link](http://doi.org/10.1016/j.socnet.2017.03.010)) + + + \ No newline at end of file diff --git a/index.md b/index.md new file mode 100644 index 0000000..9d51c15 --- /dev/null +++ b/index.md @@ -0,0 +1,156 @@ + + + +netrankr: Centrality (almost) without Indices +--------------------------------------------- + +The literature is flooded with [centrality indices](https://en.wikipedia.org/wiki/Centrality) and new ones are still introduced on a regular basis. Just take a look at the [periodic table](http://schochastics.net/sna/periodic.html) of network centrality to get an overview of the variety of indices. Although there exist several theoretical and empirical guidelines on when to use certain indices, there still exists plenty of ambiguity in the concept of network centrality. + +The `netrankr` package introduces alternative and complementary methods to the index-driven assessment of centrality. See the + +From + + + +to + +Simple Example +-------------- + +This example briefly explains some of the functionality of the package and the difference to an index driven approach. For a more realistic application see the [use case](use_case.html) example. + +We work with the following small graph. + +``` r +library(igraph) +library(netrankr) + +g <- graph.empty(n = 11,directed = FALSE) +g <- add_edges(g,c(1,11,2,4,3,5,3,11,4,8,5,9,5,11,6,7,6,8, + 6,10,6,11,7,9,7,10,7,11,8,9,8,10,9,10)) +``` + + + +Say we are interested in the most central node of the graph and simply compute some standard centrality scores with the `igraph` package. + +``` r +cent_scores <- data.frame( + degree = degree(g), + betweenness = round(betweenness(g),4), + closeness = round(closeness(g),4), + eigenvector = round(eigen_centrality(g)$vector,4), + subgraph = round(subgraph_centrality(g),4)) +``` + + #> Warning in eigen_centrality(g): '.Random.seed' is not an integer vector but + #> of type 'NULL', so ignored + +``` r +# What are the most central nodes for each index? +apply(cent_scores,2,which.max) +``` + + #> degree betweenness closeness eigenvector subgraph + #> 11 8 6 7 10 + + + +As you can see, each index assigns the highest value to a different vertex. + +Calculate the neighborhood inclusion preorder. + +``` r +P <- neighborhood_inclusion(g) +P +``` + + #> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] + #> [1,] 0 0 1 0 1 1 1 0 0 0 1 + #> [2,] 0 0 0 1 0 0 0 1 0 0 0 + #> [3,] 0 0 0 0 1 0 0 0 0 0 1 + #> [4,] 0 0 0 0 0 0 0 0 0 0 0 + #> [5,] 0 0 0 0 0 0 0 0 0 0 0 + #> [6,] 0 0 0 0 0 0 0 0 0 0 0 + #> [7,] 0 0 0 0 0 0 0 0 0 0 0 + #> [8,] 0 0 0 0 0 0 0 0 0 0 0 + #> [9,] 0 0 0 0 0 0 0 0 0 0 0 + #> [10,] 0 0 0 0 0 0 0 0 0 0 0 + #> [11,] 0 0 0 0 0 0 0 0 0 0 0 + +If `P[u,v]=1`, then *N*(*u*)⊆*N*\[*v*\] which implies that *c*(*u*)≤*c*(*v*) for all centrality indices *c*! + +Neighborhood-inclusion defines a partial ranking on the set of nodes. Each ranking that is in accordance with this partial ranking yields a proper centrality ranking. Each of these ranking can thus potentially be the outcome of a centrality index. + +The function `exact_rank_prob()` can be used to calculate all these ranking and produce probabilistic centrality rankings. + +``` r +res <- exact_rank_prob(P) +str(res) +``` + + #> List of 7 + #> $ lin.ext : num 739200 + #> $ names : chr [1:11] "1" "2" "3" "4" ... + #> $ mse : int [1:11] 1 2 3 4 5 6 7 8 9 10 ... + #> $ rank.prob : num [1:11, 1:11] 0.545 0.273 0 0 0 ... + #> $ relative.rank: num [1:11, 1:11] 0 0.3333 0 0.0476 0 ... + #> $ expected.rank: num [1:11] 1.71 3 4.29 7.5 8.14 ... + #> $ rank.spread : num [1:11] 0.958 1.897 1.725 2.54 2.16 ... + +`lin.ext` is the number of possible rankings. For the graph `g` we could therefore come up with 739,200 indices that would rank the nodes differently. + +`rank.prob` contains the probabilities for each node to occupy a certain rank. For instance, the probability for each node to be the most central one is as follows. + +``` r +round(res$rank.prob[ ,11],2) +``` + + #> [1] 0.00 0.00 0.00 0.14 0.16 0.11 0.11 0.14 0.09 0.09 0.16 + +`relative.rank` contains the relative rank probabilities. An entry `relative.rank[u,v]` indicates how likely it is that `v` is more central than `u`. + +``` r +# How likely is it, that 6 is more central than 3? +round(res$relative.rank[3,6],2) +``` + + #> [1] 0.75 + +`expected.ranks` contains the expected centrality ranks for all nodes. They are derived on the basis of `rank.prob`. + +``` r +round(res$expected.rank,2) +``` + + #> [1] 1.71 3.00 4.29 7.50 8.14 6.86 6.86 7.50 6.00 6.00 8.14 + +The higher the value, the more central a node is expected to be. + +**Note**: The set of rankings grows exponentially in the number of nodes and the exact calculation becomes infeasible quite quickly and approximations need to be used. +Check the vignettes for help and further package functionality. + +Installation +------------ + +To install from CRAN: \[not yet published\] + +To install the developer version from github: + +``` r +require(devtools) +install_github("schochastics/netrankr") +``` + +Theoretical Background +---------------------- + +`netrankr` is based on a series of papers that appeared in recent years. If you want to learn more about the theoretical background of the package, consult the following literature: + +> Brandes, Ulrik. (2016). Network Positions. *Methodological Innovations*, **9**, 2059799116630650. ([link](http://dx.doi.org/10.1177/2059799116630650)) + +> Schoch, David & Brandes, Ulrik. (2016). Re-conceptualizing centrality in social networks. *European Journal of Appplied Mathematics*, **27**(6), 971–985. ([link](https://doi.org/10.1017/S0956792516000401)) + +> Schoch, David & Valente, Thomas W., & Brandes, Ulrik. (2017). Correlations among centrality indices and a class of uniquely ranked graphs. *Social Networks*, **50**, 46-54.([link](http://doi.org/10.1016/j.socnet.2017.03.010)) + +> Schoch, David. (2017). Centrality without Indices: Partial Rankings and Rank Probabilities in Networks. *under review* diff --git a/inst/CITATION b/inst/CITATION index 2d91e04..91945d2 100644 --- a/inst/CITATION +++ b/inst/CITATION @@ -4,6 +4,7 @@ citEntry(entry = "Manual", title = "netrankr: An R package to analyze partial rankings in networks", author = personList(as.person("David Schoch")), year = "2017", + url = "https://schochastics.github.io/netrankr", textVersion = paste("David Schoch (2017).",