GraphPower

GraphPower[g,n]

gives the graph-n^(th) power of the graph g.

GraphPower[{vw,},]

uses rules vw to specify the graph g.

Details and Options

  • The graph-n^(th) power has the same vertices, and vertex vi is adjacent to vertex vj only if there is a path of at most length n from vi to vj.
  • GraphPower works with undirected graphs, directed graphs, multigraphs, and mixed graphs.

Examples

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Basic Examples  (1)

Graph power of cycle graphs:

Scope  (5)

GraphPower works with undirected graphs:

Directed graphs:

Multigraphs:

Mixed graphs:

Use rules to specify the graph:

Properties & Relations  (2)

Raising a connected graph to the power of its graph diameter gives a complete graph:

Graph-^(th) powers can be obtained by the sum of the first powers of the adjacency matrix:

Introduced in 2010
 (8.0)
 |
Updated in 2014
 (10.0)
2015
 (10.3)