Important: The networks package has been deprecated.  Use the superseding command GraphTheory[AllPairsDistance] instead.

This procedure is an implementation of Floyd's allpairs shortest path algorithm.

The result,  T, is a table of distances between any two vertices. Thus  is the shortest distance from u to v.

The optional extra parameter (eg. parents) is used to supply a name for a table of ancestors.  Thus  is the ancestor of v in the shortest path tree rooted at u.

Edge weights are assumed to be lengths or distances. Undirected edges are assumed to be bidirectional.

Edge weights must be non-negative.

This routine is normally loaded via the command with(networks) but may also be referenced using the full name networks[allpairs](...).