Returns a set of edges which constitutes the minimum edge cover of the graph.
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.
G (NetworkX graph) – An undirected bipartite graph.
matching_algorithm (function) – 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,
hopcroft_karp_matching()will be used. Other possibilities include
A set of the edges in a minimum edge cover of the graph, given as pairs of nodes. It contains both the edges
(v, u)for given nodes
vamong the edges of minimum edge cover.
- Return type
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