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Source code for networkx.algorithms.approximation.matching

# -*- coding: utf-8 -*-
Graph Matching

Given a graph G = (V,E), a matching M in G is a set of pairwise non-adjacent
edges; that is, no two edges share a common vertex.

#   Copyright (C) 2011-2012 by
#   Nicholas Mancuso <nick.mancuso@gmail.com>
#   All rights reserved.
#   BSD license.
import networkx as nx
__all__ = ["min_maximal_matching"]
__author__ = """Nicholas Mancuso (nick.mancuso@gmail.com)"""

[docs]def min_maximal_matching(G): r"""Returns the minimum maximal matching of G. That is, out of all maximal matchings of the graph G, the smallest is returned. Parameters ---------- G : NetworkX graph Undirected graph Returns ------- min_maximal_matching : set Returns a set of edges such that no two edges share a common endpoint and every edge not in the set shares some common endpoint in the set. Cardinality will be 2*OPT in the worst case. Notes ----- The algorithm computes an approximate solution fo the minimum maximal cardinality matching problem. The solution is no more than 2 * OPT in size. Runtime is `O(|E|)`. References ---------- .. [1] Vazirani, Vijay Approximation Algorithms (2001) """ return nx.maximal_matching(G)