min_edge_cover(G, matching_algorithm=None)
The smallest edge cover can be found in polynomial time by finding a maximum matching and extending it greedily so that all nodes are covered.
An edge cover of a graph is a set of edges such that every node of the graph is incident to at least one edge of the set. A minimum edge cover is an edge covering of smallest cardinality.
Due to its implementation, the worst-case running time of this algorithm is bounded by the worst-case running time of the function matching_algorithm
.
An undirected bipartite graph.
A function that returns a maximum cardinality matching in a given bipartite graph. The function must take one input, the graph G
, and return a dictionary mapping each node to its mate. If not specified, ~networkx.algorithms.bipartite.matching.hopcroft_karp_matching
will be used. Other possibilities include ~networkx.algorithms.bipartite.matching.eppstein_matching
,
A set of the edges in a minimum edge cover of the graph, given as pairs of nodes. It contains both the edges :None:None:`(u, v)` and :None:None:`(v, u)` for given nodes :None:None:`u` and :None:None:`v` among the edges of minimum edge cover.
Returns a set of edges which constitutes the minimum edge cover of the graph.
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