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graph_data_storage.md

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Graph Data

For each graph, the associated data are:

  • x: node signals/features, of size (N, C)
  • edge_index: edge indexes, of size (2, E)
  • y (for node classification): node labels, of size (N,), each element an integer in [0, num_class)
  • edge_attr (optional): edge attributes/features, of size (E, D)
  • edge_y (for edge classification): edge labels, of size (E,), each element an integer in [0, num_class)
  • any others

where

  • N: number of nodes
  • E: number of edges
  • C: dimension of node features
  • D: dimension of edge features
  • num_class: number of labels (this is 2 for chord data based on whether a node is "evil")

Storage Format

The graph data is stored in HDF5 files.

The Python library to handle HDF5 data io is h5py (basic) and deepdish (higher level).

The HDF5 file works like dictionaries of NumPy arrays. Here are how the graph data is structured in storage.

Collection of graphs

\ (file root)
├── '0' (graph id)
│   ├── 'x'
│   ├── 'edge_index'
│   ├── 'y'
│   ├── 'edge_attr'
│   ├── 'edge_y'
│   ├── ... (any other data)
│   └── attrs (metadata attributes for the current graph)
|       ├── 'num_nodes'
|       ├── 'num_edges'
|       ├── 'num_evils'
|       ├── 'num_evil_edges'
│       └── ... (any other attributes, such as 'is_directed', 'contains_self_loops', etc.)
├── ...
├── '800'
│   ├── 'x'
│   ├── 'edge_index'
│   ├── 'y'
│   ├── 'edge_attr'
│   ├── 'edge_y'
│   ├── ... (any other data)
│   └── attrs
|       ├── 'num_nodes'
|       ├── 'num_edges'
|       ├── 'num_evils'
|       ├── 'num_evil_edges'
│       └── ... (any other attributes, such as 'is_directed', 'contains_self_loops', etc.)
├── ...
└── attrs (metadata attributes for the whole graph data set)
    ├── 'num_graphs'
    ├── 'num_nodes_avg'
    ├── 'num_edges_avg'
    ├── 'num_evils_avg'
    ├── 'is_directed'
    ├── 'contains_self_loops'
    └── ... (any other attributes, such as 'contains_multi_edges', etc.)

Note:

  • The root level is an h5py.File object, and then the h5py.Groups under it are different graphs.
  • The top level keys are graph ids (keys need to be str), and each graph contains different h5py.Datasets such as x and edge_index.
  • Each graph can have some attributes aside to describe the graph, such as "num_nodes" and "num_edges" in the graph.
  • The root level file could also have some attributes to describe some statistics of the graph dataset, such as "num_graphs" in the dataset.

Write and Read

For writing graph data, check code in this directory.

For reading graph data, one can do:

import h5py
with h5py.File('filename', 'r') as f:
    e = f['0']['edge_index'][()]             # take out the edge indexes from the first graph with id '0'
    num_nodes = f['0'].attrs['num_nodes']    # access the statistics stored in attributes of the first graph with id '0'
    num_graphs = f.attrs['num_graphs']       # access the statistics stored in attributes of the dataset file

Or using deepdish:

import deepdish as dd
graphs = dd.io.load('filename')        # this will return a dictionary, with each graph as a sub-dictionary, and
                                       # attributes are key-item pairs in the dictionaries as well

deepdish also allows partial loading of the data based on data path and slice indexes.

Time Series Graph Data (Dynamic Graph)

Data can be stored in the same way, except that there should be extra attributes with relevant information, such as the size of time window based on which the graph labels are generated, number of different time series and their lengths, etc.