WHAT IS IT?
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This exploratory model is based off of:
- Wilensky, U. (2005).  NetLogo Preferential Attachment model.  http://ccl.northwestern.edu/netlogo/models/PreferentialAttachment

Wilensky's model produces the initial network.
Future Forward Institute added the functionality to decay the network.

In some networks, a few "hubs" have lots of connections, while everybody else only has a few.  This model shows one way such networks can arise.

This model generates these networks by a process of "preferential attachment", in which new network members prefer to make a connection to the more popular existing members.

This model then decays the network by a process of "random removal" of nodes along with their links.

HOW IT WORKS
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The model starts with two nodes connected by an edge.

At each step, a new node is added.  A new node picks an existing node to connect to randomly, but with some bias.  More specifically, a node's chance of being selected is directly proportional to the number of connections it already has, or its "degree." This is the mechanism which is called "preferential attachment."

The decay function removes nodes at random from the network, including all of the links associated with that node. This demonstrates how quickly large sections of the network can collapse.

HOW TO USE IT
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Pressing the GO ONCE button adds one new node.  To continuously add nodes, press GO.
Pressing the DECAY ONCE button removes one node and its links.  To continuously decay
the network , press DECAY.


The LAYOUT? switch controls whether or not the layout procedure is run.  This procedure attempts to move the nodes around to make the structure of the network easier to see.

The PLOT? switch turns off the plots which speeds up the model.

The RESIZE-NODES button will make all of the nodes take on a size representative of their degree distribution.  If you press it again the nodes will return to equal size.

If you want the model to run faster, you can turn off the LAYOUT? and PLOT? switches and/or freeze the view (using the on/off button in the control strip over the view). The LAYOUT? switch has the greatest effect on the speed of the model.

If you have LAYOUT? switched off, and then want the network to have a more appealing layout, press the REDO-LAYOUT button which will run the layout-step procedure until you press the button again. You can press REDO-LAYOUT at any time even if you had LAYOUT? switched on and it will try to make the network easier to see.


THINGS TO NOTICE
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The networks that result from running this model are often called "scale-free" or "power law" networks. These are networks in which the distribution of the number of connections of each node is not a normal distribution -- instead it follows what is a called a power law distribution.  Power law distributions are different from normal distributions in that they do not have a peak at the average, and they are more likely to contain extreme values (see Barabasi 2002 for a further description of the frequency and significance of scale-free networks).  Barabasi originally described this mechanism for creating networks, but there are other mechanisms of creating scale-free networks and so the networks created by the mechanism implemented in this model are referred to as Barabasi scale-free networks.

You can see the degree distribution of the network in this model by looking at the plots. The top plot is a histogram of the degree of each node.  The bottom plot shows the same data, but both axes are on a logarithmic scale.  When degree distribution follows a power law, it appears as a straight line on the log-log plot.  One simple way to think about power laws is that if there is one node with a degree distribution of 1000, then there will be ten nodes with a degree distribution of 100, and 100 nodes with a degree distribution of 10.

When you decay this network by random removal of nodes with their links, most of the nodes removed are likely to have few links.  Consequently, the network suffers little decay.  Removal of nodes with high-degree, i.e. 'hubs', will cause more decay to the network.  Eventually the network suffers enough decay that large numbers of nodes become isolated from each other.

This is a non-linear effect, not a trend, and is unpredictable.

The graph of the 'Giant Component' shows how quickly total collapse can occur.


NETWORK LAYOUT
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There are many ways to graphically display networks.  This model uses a common "spring" method where the movement of a node at each time step is the net result of "spring" forces that pulls connected nodes together and repulsion forces that push all the nodes away from each other.  This code is in the layout-step procedure. You can force this code to execute any time by pressing the REDO LAYOUT button, and pressing it again when you are happy with the layout.


RELATED MODELS
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See other models in the Networks section of the Models Library, such as Giant Component.

See also Network Example, in the Code Examples section.


CREDITS AND REFERENCES
----------------------
This model is based on:
Albert-Laszlo Barabasi. Linked: The New Science of Networks, Perseus Publishing, Cambridge, Massachusetts, pages 79-92.

For a more technical treatment, see:
Albert-Laszlo Barabasi & Reka Albert. Emergence of Scaling in Random Networks, Science, Vol 286, Issue 5439, 15 October 1999, pages 509-512.

Barabasi's webpage has additional information at: http://www.nd.edu/~alb/

The layout algorithm is based on the Fruchterman-Reingold layout algorithm.  More information about this algorithm can be obtained at: http://citeseer.ist.psu.edu/fruchterman91graph.html.

For a model similar to the one described in the first extension, please consult:
W. Brian Arthur, "Urban Systems and Historical Path-Dependence", Chapt. 4 in Urban systems and Infrastructure, J. Ausubel and R. Herman (eds.), National Academy of Sciences, Washington, D.C., 1988.


HOW TO CITE
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If you mention this model in an academic publication, Future Forward Institute asks that you include these citations for the model itself and for the NetLogo software:
Future Forward Institute
https://github.com/paulbhartzog/Network-Growth-and-Decay

If you mention this model in an academic publication, Wilensky asks that you include these citations for the model itself and for the NetLogo software:
- Wilensky, U. (2005).  NetLogo Preferential Attachment model.  http://ccl.northwestern.edu/netlogo/models/PreferentialAttachment.  Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.
- Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.
In other publications, please use:
- Copyright 2005 Uri Wilensky. All rights reserved. See http://ccl.northwestern.edu/netlogo/models/PreferentialAttachment for terms of use.


COPYRIGHT NOTICE
----------------
Creative Commons BY-SA 2011 Future Forward Institute. Some rights reserved.
This work is licensed under a Creative Commons Attribution-Share Alike 3.0 Unported License.

Url Wilensky's original code Copyright 2005 Uri Wilensky. All rights reserved.

Permission to use, modify or redistribute this model is hereby granted, provided that both of the following requirements are followed:
a) these copyright notices are included.
b) Url Wilensky's original code may not be redistributed for profit without permission from Uri Wilensky. Contact Uri Wilensky for appropriate licenses for redistribution for profit.