# maximal_matching#

maximal_matching(G)[source]#

Find a maximal matching in the graph.

A matching is a subset of edges in which no node occurs more than once. A maximal matching cannot add more edges and still be a matching.

Parameters:
GNetworkX graph

Undirected graph

Returns:
matchingset

A maximal matching of the graph.

Notes

The algorithm greedily selects a maximal matching M of the graph G (i.e. no superset of M exists). It runs in $$O(|E|)$$ time.

Examples

>>> G = nx.Graph([(1, 2), (1, 3), (2, 3), (2, 4), (3, 5), (4, 5)])
>>> sorted(nx.maximal_matching(G))
[(1, 2), (3, 5)]