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CayleyGraph[group]

returns a Cayley graph representation of group.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Possible Issues  
Neat Examples  
See Also
Tech Notes
Related Guides
Related Demonstrations
History
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CayleyGraph

CayleyGraph[group]

returns a Cayley graph representation of group.

Details and Options

  • CayleyGraph[group] returns a graph object with head Graph.
  • A Cayley graph is both a description of a group and of the generators used to describe that group. The generators are those returned by the function GroupGenerators.
  • Group elements are represented as vertices, and generators are represented as directed edges. An edge from a group element g1 to an element g2 means that the product of g1 with the generator of the edge gives g2.
  • Vertices are numbered as ordered by GroupElements and GroupElementPosition. The identity element is always numbered 1.
  • Generators are represented by default using different colors, following the sequence of colors used by Plot with several curves.

Examples

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Basic Examples  (1)

This is the Cayley graph connecting the 24 elements of a permutation group defined by two generators, the first represented in blue and the second in green:

Scope  (3)

Cayley graph of the symmetric group of degree four defined by three transpositions:

Cayley graph of the symmetric group of degree four with the default generating set:

The identity permutation is removed from the list of generators:

Possible Issues  (1)

This is only a useful representation for small groups. For groups with a few hundred elements, the graph is generally already too complex:

Neat Examples  (1)

A point:

A line:

A square:

A cube:

A 4D cube:

A 5D cube:

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

Text

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

CMS

Wolfram Language. 2010. "CayleyGraph." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CayleyGraph.html.

APA

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

BibTeX

@misc{reference.wolfram_2025_cayleygraph, author="Wolfram Research", title="{CayleyGraph}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/CayleyGraph.html}", note=[Accessed: 04-February-2026]}

BibLaTeX

@online{reference.wolfram_2025_cayleygraph, organization={Wolfram Research}, title={CayleyGraph}, year={2010}, url={https://reference.wolfram.com/language/ref/CayleyGraph.html}, note=[Accessed: 04-February-2026]}