The Minimum Spanning Tree of a weighted graph is a set of edges of minimum total weight which form a spanning tree of the graph. When a graph is unweighted, any spanning tree is a minimum spanning tree. A minimum spanning tree (MST) or minimum weight spanning tree is then a spanning tree with weight less than or equal to the weight of every other spanning tree. More generally, any undirected graph has a minimum spanning forest, which is a union of minimum spanning trees for its connected components.
Fig: The minimum spanning tree of a planar graph. Each edge is labeled with its weight, which here is roughly proportional to its length.
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