Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, random minimal spanning tree, or random MST, is a model (actually two related models) for a random spanning tree of a graph (see also minimal spanning tree). It might be compared against the uniform spanning tree, a different model for a random tree which has been researched much more extensively. For additional types of random tree, see random tree. Let G be a finite connected graph. To define the random MST on G, make G into a weighted graph by choosing weights randomly, uniformly between 0 and 1 independently for each edge. Now pick the MST from this weighted graph i.e. the spanning tree with the lowest total weight. Almost surely, there would be only one i.e. there would be not be two distinct spanning trees with identical total weight. This tree (denote it by T) is also a spanning tree for the unweighted graph G. This is the random MST.

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