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networks

 allpairs
 all-pairs shortest paths in a graph

 Calling Sequence allpairs(G) allpairs(G, v)

Parameters

 G - graph or network v - name used to return a table of parents

Description

 • 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 ${T}_{u,v}$ 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 ${\mathrm{parents}}_{u,v}$ 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](...).

Examples

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

 > $\mathrm{with}\left(\mathrm{networks}\right):$
 > $G≔\mathrm{petersen}\left(\right):$
 > $T≔\mathrm{allpairs}\left(G,p\right):$
 > $T\left[1,3\right]$
 ${2}$ (1)
 > $p\left[1,3\right]$
 ${2}$ (2)