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Returns the maximum cardinality matching of the bipartite graph \(G\).

Parameters:G (NetworkX graph) – Undirected bipartite graph
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


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


[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://dx.doi.org/10.1137/0202019>.