Small Synthetic Datasets

polygraph.datasets.PlanarGraphDataset

Bases: SplitGraphDataset

Planar graph dataset proposed by Martinkus et al. [1].

Each graph consists of 64 nodes and is connected and planar.

First 3 graphs

Dataset statistics:

Metric Train Val Test
# of Graphs 128 32 40
Min # of Nodes 64 64 64
Max # of Nodes 64 64 64
Avg # of Nodes 64.00 64.00 64.00
Min # of Edges 173 174 174
Max # of Edges 181 181 181
Avg # of Edges 177.83 177.75 177.93
Edge/Node Ratio 2.78 2.78 2.78
Is Undirected True True True
References

[1] Martinkus, K., Loukas, A., Perraudin, N., & Wattenhofer, R. (2022). SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generators. In Proceedings of the 39th International Conference on Machine Learning (ICML).

is_valid(graph)

Check whether graph is connnected and planar.

Parameters:
  • graph (Graph) –

    NetworkX graph to check.
Returns:
  • bool( bool ) –

    True if the graph is connected and planar, False otherwise.

polygraph.datasets.SBMGraphDataset

Bases: SplitGraphDataset

SBM graph dataset proposed by Martinkus et al. [1].

The graphs are sampled from stochastic block models with random parameters.

  • The number of communities is sampled uniformly at random from 2-5 (inclusive).
  • The number of nodes per community is sampled uniformly at random from 20-40 (inclusive).
  • The intra-community edge probability is set at 0.3.
  • The inter-community edge probability is set at 0.005.

First 3 graphs

Dataset statistics:

Metric Train Val Test
# of Graphs 128 32 40
Min # of Nodes 44 49 54
Max # of Nodes 187 162 174
Avg # of Nodes 105.99 91.28 107.85
Min # of Edges 129 183 210
Max # of Edges 1129 857 972
Avg # of Edges 512.51 425.19 521.88
Edge/Node Ratio 4.84 4.66 4.84
Is Undirected True True True
References

[1] Martinkus, K., Loukas, A., Perraudin, N., & Wattenhofer, R. (2022). SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generators. In Proceedings of the 39th International Conference on Machine Learning (ICML).

is_valid(graph)

Check if a graph is a valid SBM graph.

polygraph.datasets.LobsterGraphDataset

Bases: SplitGraphDataset

Dataset of lobster graphs proposed by Liao et al. [1].

A lobster graph is a tree which has a backbone path such that each node in the tree is at most two hops away from this backbone.

First 3 graphs

Dataset statistics:

Metric Train Val Test
# of Graphs 60 20 20
Min # of Nodes 10 11 14
Max # of Nodes 98 98 84
Avg # of Nodes 53.67 56.30 50.80
Min # of Edges 9 10 13
Max # of Edges 97 97 83
Avg # of Edges 52.67 55.30 49.80
Edge/Node Ratio 0.98 0.98 0.98
Is Undirected True True True
Warning

In the original dataset [1], the validation set was a subset of the training set. Here, we use disjoint splits.

References

[1] Liao, R., Li, Y., Song, Y., Wang, S., Hamilton, W., Duvenaud, D., Urtasun, R., & Zemel, R. (2019). Efficient Graph Generation with Graph Recurrent Attention Networks. In Advances in Neural Information Processing Systems (NeurIPS).

is_valid(graph)

Check if a graph is a valid lobster graph.