networkx.algorithms.bipartite.matching.hopcroft_karp_matching

hopcroft_karp_matching(G, top_nodes=None)[source]

Returns the maximum cardinality matching of the bipartite graph G.

Parameters
  • G (NetworkX graph) – Undirected bipartite graph

  • top_nodes (container) – Container with all nodes in one bipartite node set. If not supplied it will be computed. But if more than one solution exists an exception will be raised.

Returns

matches – The matching is returned as a dictionary, matches, such that matches[v] == w if node v is matched to node w. Unmatched nodes do not occur as a key in mate.

Return type

dictionary

Raises

AmbiguousSolution – Raised if the input bipartite graph is disconnected and no container with all nodes in one bipartite set is provided. When determining the nodes in each bipartite set more than one valid solution is possible if the input graph is disconnected.

Notes

This function is implemented with the Hopcroft–Karp matching algorithm for bipartite graphs.

See bipartite documentation for further details on how bipartite graphs are handled in NetworkX.

References

1

John E. Hopcroft and Richard M. Karp. “An n^{5 / 2} Algorithm for Maximum Matchings in Bipartite Graphs” In: SIAM Journal of Computing 2.4 (1973), pp. 225–231. <https://doi.org/10.1137/0202019>.