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- max_weight_matching(G, maxcardinality=False)¶
Compute a maximum-weighted matching of G.
A matching is a subset of edges in which no node occurs more than once. The cardinality of a matching is the number of matched edges. The weight of a matching is the sum of the weights of its edges.
G : NetworkX graph
maxcardinality: bool, optional
If maxcardinality is True, compute the maximum-cardinality matching with maximum weight among all maximum-cardinality matchings.
mate : dictionary
The matching is returned as a dictionary, mate, such that mate[v] == w if node v is matched to node w. Unmatched nodes do not occur as a key in mate.
If G has edges with ‘weight’ attribute the edge data are used as weight values else the weights are assumed to be 1.
This function takes time O(number_of_nodes ** 3).
If all edge weights are integers, the algorithm uses only integer computations. If floating point weights are used, the algorithm could return a slightly suboptimal matching due to numeric precision errors.
This method is based on the “blossom” method for finding augmenting paths and the “primal-dual” method for finding a matching of maximum weight, both methods invented by Jack Edmonds [R268].
[R268] (1, 2) “Efficient Algorithms for Finding Maximum Matching in Graphs”, Zvi Galil, ACM Computing Surveys, 1986.