ALLSPATH - solve the All Pairs Shortest Path problem
Rapidly returns the shortest node-to-node distance along the edges of a graph, for all nodes in the graph.
USAGE: B = allspath(A)
A = input distance matrix between nodes
B = shortest path distance matrix between all nodes
(1) For a graph with n nodes, A is an n-by-n distance matrix giving the distances between adjacent nodes. Since the distance from point i to point j is the same as the distance from point j to point i, A must be a symmetric matrix
(2) The distance from a node to itself can either be entered as zero or infinity. (Either will produce a correct result.) This means that the diagonal elements of the matrix A must all be either zero or infinity.
(3) The distance between nodes that are not adjacent to each other must be entered as either zero or infinity. (Either will produce a correct result.) This means that the (i,j) and (j,i) elements of A, where i and j are non-adjacent nodes, must all be either zero or infinity.
(4) If the input graph is not "connected," meaning that some nodes cannot be reached from other nodes no matter how many edges are traversed, then the distances between nodes that cannot be connected will be returned as infinite.
(5) Distances between a node and itself are returned as zero.
(6) This function codifies an original algorithm created by the author.
(7) No warranties; use at your own risk.
(8) Written by Michael Kleder, October 2005.