wgsdZddlZddlmZddlmZddlm Z dgZ e de dejd d d Zy) z"Functions related to graph covers.N)hopcroft_karp_matching)min_edge_cover)not_implemented_forrdirected multigraphbipartite_min_edge_cover)namecf|jdk(r tS|t}t||S)aReturns 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. Parameters ---------- 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, :func:`~networkx.algorithms.bipartite.matching.hopcroft_karp_matching` will be used. Other possibilities include :func:`~networkx.algorithms.bipartite.matching.eppstein_matching`, Returns ------- set A set of the edges in a minimum edge cover of the graph, given as pairs of nodes. It contains both the edges `(u, v)` and `(v, u)` for given nodes `u` and `v` among the edges of minimum edge cover. Notes ----- 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 ``matching_algorithm``. r)matching_algorithm)ordersetr_min_edge_cover)Gr s k/home/mcse/projects/flask/flask-venv/lib/python3.12/site-packages/networkx/algorithms/bipartite/covering.pyrr s3T wwyA~u !3 11C DD)N) __doc__networkxnx&networkx.algorithms.bipartite.matchingrnetworkx.algorithms.coveringrrnetworkx.utilsr__all__ _dispatchablerrrsZ(IJ.  Z \"12+E3#!+Er