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networks

  

allpairs

  

all-pairs shortest paths in a graph

 

Calling Sequence

Parameters

Description

Examples

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 Tu,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 parentsu,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.

withnetworks:

Gpetersen:

TallpairsG,p:

T1,3

2

(1)

p1,3

2

(2)

See Also

GraphTheory

GraphTheory[AllPairsDistance]

networks(deprecated)[shortpathtree]

networks(deprecated)[spantree]

with

 


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