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GraphPower
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GraphPower

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GraphPower[g,n]

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

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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)Summary of the most common use cases

Graph power of cycle graphs:

In[1]:=1
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https://wolfram.com/xid/0j450zq2-b1kkxi
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0j450zq2-b3rg0e
Out[2]=2

Scope  (5)Survey of the scope of standard use cases

GraphPower works with undirected graphs:

In[1]:=1
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https://wolfram.com/xid/0j450zq2-jkrcuo
Out[1]=1

Directed graphs:

In[1]:=1
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https://wolfram.com/xid/0j450zq2-bltp69
Out[1]=1

Multigraphs:

In[1]:=1
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https://wolfram.com/xid/0j450zq2-iog63o
Out[1]=1

Mixed graphs:

In[1]:=1
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https://wolfram.com/xid/0j450zq2-czvddh
Out[1]=1

Use rules to specify the graph:

In[1]:=1
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https://wolfram.com/xid/0j450zq2-bndh30
Out[1]=1

Properties & Relations  (2)Properties of the function, and connections to other functions

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

In[1]:=1
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https://wolfram.com/xid/0j450zq2-oavpvp
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0j450zq2-ilq46b
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0j450zq2-dl8tsi
Out[3]=3

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

In[1]:=1
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https://wolfram.com/xid/0j450zq2-d2je4k
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0j450zq2-ey2x2k
In[3]:=3
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https://wolfram.com/xid/0j450zq2-gvg4na
Out[3]=3
Wolfram Research (2010), GraphPower, Wolfram Language function, https://reference.wolfram.com/language/ref/GraphPower.html (updated 2015).
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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).

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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.

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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

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

BibTeX

@misc{reference.wolfram_2025_graphpower, author="Wolfram Research", title="{GraphPower}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/GraphPower.html}", note=[Accessed: 06-May-2025 ]}

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@misc{reference.wolfram_2025_graphpower, author="Wolfram Research", title="{GraphPower}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/GraphPower.html}", note=[Accessed: 06-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_graphpower, organization={Wolfram Research}, title={GraphPower}, year={2015}, url={https://reference.wolfram.com/language/ref/GraphPower.html}, note=[Accessed: 06-May-2025 ]}

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@online{reference.wolfram_2025_graphpower, organization={Wolfram Research}, title={GraphPower}, year={2015}, url={https://reference.wolfram.com/language/ref/GraphPower.html}, note=[Accessed: 06-May-2025 ]}