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# networkx.algorithms.approximation.treewidth.treewidth_min_fill_in¶

treewidth_min_fill_in(G)[source]

Returns a treewidth decomposition using the Minimum Fill-in heuristic.

The heuristic chooses a node from the graph, where the number of edges added turning the neighbourhood of the chosen node into clique is as small as possible.

Parameters: G (NetworkX graph) Treewidth decomposition – 2-tuple with treewidth and the corresponding decomposed tree. (int, Graph) tuple