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.

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.

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'