Note

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

# networkx.algorithms.isomorphism.is_isomorphic¶

is_isomorphic(G1, G2, node_match=None, edge_match=None)[source]

Returns True if the graphs G1 and G2 are isomorphic and False otherwise.

Parameters
• G1, G2 (graphs) – The two graphs G1 and G2 must be the same type.

• node_match (callable) – A function that returns True if node n1 in G1 and n2 in G2 should be considered equal during the isomorphism test. If node_match is not specified then node attributes are not considered.

The function will be called like

node_match(G1.nodes[n1], G2.nodes[n2]).

That is, the function will receive the node attribute dictionaries for n1 and n2 as inputs.

• edge_match (callable) – A function that returns True if the edge attribute dictionary for the pair of nodes (u1, v1) in G1 and (u2, v2) in G2 should be considered equal during the isomorphism test. If edge_match is not specified then edge attributes are not considered.

The function will be called like

edge_match(G1[u1][v1], G2[u2][v2]).

That is, the function will receive the edge attribute dictionaries of the edges under consideration.

Notes

Uses the vf2 algorithm 1.

Examples

>>> import networkx.algorithms.isomorphism as iso


For digraphs G1 and G2, using ‘weight’ edge attribute (default: 1)

>>> G1 = nx.DiGraph()
>>> G2 = nx.DiGraph()
>>> nx.add_path(G1, [1, 2, 3, 4], weight=1)
>>> nx.add_path(G2, [10, 20, 30, 40], weight=2)
>>> em = iso.numerical_edge_match("weight", 1)
>>> nx.is_isomorphic(G1, G2)  # no weights considered
True
>>> nx.is_isomorphic(G1, G2, edge_match=em)  # match weights
False


For multidigraphs G1 and G2, using ‘fill’ node attribute (default: ‘’)

>>> G1 = nx.MultiDiGraph()
>>> G2 = nx.MultiDiGraph()
>>> G2.add_nodes_from([10, 20, 30, 40], fill="red")
>>> nx.add_path(G1, [1, 2, 3, 4], weight=3, linewidth=2.5)
>>> nx.add_path(G2, [10, 20, 30, 40], weight=3)
>>> nm = iso.categorical_node_match("fill", "red")
>>> nx.is_isomorphic(G1, G2, node_match=nm)
True


For multidigraphs G1 and G2, using ‘weight’ edge attribute (default: 7)

>>> G1.add_edge(1, 2, weight=7)
1
1
>>> em = iso.numerical_multiedge_match("weight", 7, rtol=1e-6)
>>> nx.is_isomorphic(G1, G2, edge_match=em)
True


For multigraphs G1 and G2, using ‘weight’ and ‘linewidth’ edge attributes with default values 7 and 2.5. Also using ‘fill’ node attribute with default value ‘red’.

>>> em = iso.numerical_multiedge_match(["weight", "linewidth"], [7, 2.5])
>>> nm = iso.categorical_node_match("fill", "red")
>>> nx.is_isomorphic(G1, G2, edge_match=em, node_match=nm)
True


References

1

L. P. Cordella, P. Foggia, C. Sansone, M. Vento, “An Improved Algorithm for Matching Large Graphs”, 3rd IAPR-TC15 Workshop on Graph-based Representations in Pattern Recognition, Cuen, pp. 149-159, 2001. http://amalfi.dis.unina.it/graph/db/papers/vf-algorithm.pdf