Returns the minimum vertex cover corresponding to the given maximum matching of the bipartite graph \(G\).
- G (NetworkX graph) – Undirected bipartite graph
- matching (dictionary) – A dictionary whose keys are vertices in \(G\) and whose values are the
distinct neighbors comprising the maximum matching for \(G\), as returned
by, for example,
maximum_matching(). The dictionary must represent the maximum matching.
vertex_cover – The minimum vertex cover in \(G\).
This function is implemented using the procedure guaranteed by Konig’s theorem, which proves an equivalence between a maximum matching and a minimum vertex cover in bipartite graphs.
Since a minimum vertex cover is the complement of a maximum independent set for any graph, one can compute the maximum independent set of a bipartite graph this way:
>>> import networkx as nx >>> G = nx.complete_bipartite_graph(2, 3) >>> matching = nx.bipartite.maximum_matching(G) >>> vertex_cover = nx.bipartite.to_vertex_cover(G, matching) >>> independent_set = set(G) - vertex_cover >>> print(list(independent_set)) [2, 3, 4]