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# -*- 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.
http://en.wikipedia.org/wiki/Matching_(graph_theory)
"""
# 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)"""
def min_maximal_matching(graph):
"""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.
Parameters
----------
graph : 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.
References
----------
.. [1] Vazirani, Vijay Approximation Algorithms (2001)
"""
return nx.maximal_matching(graph)
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