weisfeiler_lehman_graph_hash

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

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.

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, default=None

The key in edge attribute dictionary to be used for hashing. If None, edge labels are ignored.

node_attr: string, default=None

The key in node attribute dictionary to be used for hashing. If None, and no edge_attr given, use the degrees of the nodes as labels.

iterations: int, default=3

Number of neighbor aggregations to perform. Should be larger for larger graphs.

digest_size: int, default=16

Size (in bits) of blake2b hash digest to use for hashing node labels.

Returns

hstring

Hexadecimal string corresponding to hash of the input graph.

See also

weisfeiler_lehman_subgraph_hashes

Notes

To return the WL hashes of each subgraph of a graph, use weisfeiler_lehman_subgraph_hashes

Similarity between hashes does not imply similarity between graphs.

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

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.

>>> nx.weisfeiler_lehman_graph_hash(G1)
'7bc4dde9a09d0b94c5097b219891d81a'
>>> nx.weisfeiler_lehman_graph_hash(G2)
'7bc4dde9a09d0b94c5097b219891d81a'

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

>>> nx.weisfeiler_lehman_graph_hash(G1, edge_attr="label")
'c653d85538bcf041d88c011f4f905f10'
>>> nx.weisfeiler_lehman_graph_hash(G2, edge_attr="label")
'3dcd84af1ca855d0eff3c978d88e7ec7'