godshorse, you may use the "shortestPaths" method of this graph class of mine: http://sourceforge.net/projects/pynetwork/
(It uses the same Dijkstra code by Eppstein). (Once you have all distances from a node to the other ones, it's not too much difficult to find the tree you talk about). Also see the Minimum spanning tree: http://en.wikipedia.org/wiki/Minimum_spanning_tree Bye, bearophile -- http://mail.python.org/mailman/listinfo/python-list
