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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
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Properties & Relations  
See Also
Related Guides
History
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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:

Wolfram Language code: Table[CycleGraph[n], {n, 4, 6}]
Wolfram Language code: GraphPower[#, 2]& /@ %

Scope  (5)

GraphPower works with undirected graphs:

Wolfram Language code: GraphPower[[image], 2]

Directed graphs:

Wolfram Language code: GraphPower[[image], 2]

Multigraphs:

Wolfram Language code: GraphPower[[image], 2]

Mixed graphs:

Wolfram Language code: GraphPower[[image], 2]

Use rules to specify the graph:

Wolfram Language code: GraphPower[{1 -> 2, 2 -> 3, 3 -> 1, 3 -> 4}, 2]

Properties & Relations  (2)

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

Wolfram Language code: CycleGraph[7]
Wolfram Language code: GraphPower[%, GraphDiameter[%]]
Wolfram Language code: CompleteGraphQ[%]

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

Wolfram Language code: g = CycleGraph[7]
Wolfram Language code: m = AdjacencyMatrix[g];
Wolfram Language code: {GraphPower[g, 3], SimpleGraph[AdjacencyGraph[Clip[m + m.m + m.m.m]]]}
Wolfram Research (2010), GraphPower, Wolfram Language function, https://reference.wolfram.com/language/ref/GraphPower.html (updated 2015).

Text

Wolfram Research (2010), GraphPower, Wolfram Language function, https://reference.wolfram.com/language/ref/GraphPower.html (updated 2015).

CMS

Wolfram Language. 2010. "GraphPower." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/GraphPower.html.

APA

Wolfram Language. (2010). GraphPower. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GraphPower.html

BibTeX

@misc{reference.wolfram_2026_graphpower, author="Wolfram Research", title="{GraphPower}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/GraphPower.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_graphpower, organization={Wolfram Research}, title={GraphPower}, year={2015}, url={https://reference.wolfram.com/language/ref/GraphPower.html}, note=[Accessed: 13-June-2026]}