Non-uniform random spanning trees on weighted graphs

We study random walks on undirected graphs with weighted edges. Our main result shows that any spanning tree defined by the edges corresponding to a first visit of a vertex, appears with a probability proportional to its weight, which is the product of the weight of its edges. This provides an algorithm for generating non uniform random spanning trees in a weighted graph. The technique used here is based on linear equations over regular expressions and finite automata theory. (C) 1999 Elsevier Science B.V. All rights reserved.