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Note

This documents the development version of NetworkX. Documentation for the current release can be found here.

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networkx.algorithms.graph_hashing.weisfeiler_lehman_graph_hash

weisfeiler_lehman_graph_hash(G, edge_attr=None, node_attr=None, iterations=3, digest_size=16)[source]

Return Weisfeiler Lehman (WL) graph hash.

The function iteratively aggregates and hashes neighbourhoods of each node. After each node’s neighbors are hashed to obtain updated node labels, a hashed histogram of resulting labels is returned as the final hash.

Hashes are identical for isomorphic graphs and strong guarantees that non-isomorphic graphs will get different hashes. See [1] for details.

Note: Similarity between hashes does not imply similarity between graphs.

If no node or edge attributes are provided, the degree of each node is used as its initial label. Otherwise, node and/or edge labels are used to compute the hash.

Parameters

  • G (graph) – The graph to be hashed. Can have node and/or edge attributes. Can also have no attributes.

  • edge_attr (string) – The key in edge attribute dictionary to be used for hashing. If None, edge labels are ignored.

  • node_attr (string) – The key in node attribute dictionary to be used for hashing. If None, and no edge_attr given, use degree of node as label.

  • iterations (int) – Number of neighbor aggregations to perform. Should be larger for larger graphs.

  • digest_size (int) – Size of blake2b hash digest to use for hashing node labels.

Returns

h – Hexadecimal string corresponding to hash of the input graph.

Return type

string

Examples

Two graphs with edge attributes that are isomorphic, except for differences in the edge labels.

>>> G1 = nx.Graph()
>>> G1.add_edges_from(
...     [
...         (1, 2, {"label": "A"}),
...         (2, 3, {"label": "A"}),
...         (3, 1, {"label": "A"}),
...         (1, 4, {"label": "B"}),
...     ]
... )
>>> G2 = nx.Graph()
>>> G2.add_edges_from(
...     [
...         (5, 6, {"label": "B"}),
...         (6, 7, {"label": "A"}),
...         (7, 5, {"label": "A"}),
...         (7, 8, {"label": "A"}),
...     ]
... )

Omitting the edge_attr option, results in identical hashes.

>>> weisfeiler_lehman_graph_hash(G1)
'0db442538bb6dc81d675bd94e6ebb7ca'
>>> weisfeiler_lehman_graph_hash(G2)
'0db442538bb6dc81d675bd94e6ebb7ca'

With edge labels, the graphs are no longer assigned the same hash digest.

>>> weisfeiler_lehman_graph_hash(G1, edge_attr="label")
'408c18537e67d3e56eb7dc92c72cb79e'
>>> weisfeiler_lehman_graph_hash(G2, edge_attr="label")
'f9e9cb01c6d2f3b17f83ffeaa24e5986'

References

1

Shervashidze, Nino, Pascal Schweitzer, Erik Jan Van Leeuwen, Kurt Mehlhorn, and Karsten M. Borgwardt. Weisfeiler Lehman Graph Kernels. Journal of Machine Learning Research. 2011. http://www.jmlr.org/papers/volume12/shervashidze11a/shervashidze11a.pdf