CanonicalGraph

gives a canonical form of the graph g.

CanonicalGraph[{vw,}]

uses rules vw to specify the graph.

Details and Options

• CanonicalGraph is also known as canonical graph labeling or canonical form of a graph.
• CanonicalGraph is often used to compare and match a graph to a large collection of graphs.
• returns a graph with vertices 1, 2, that is isomorphic to g.
• Isomorphic graphs have the same canonical graph.
• A Method option can be given. Possible Method settings include:
•  "Bliss" Bliss canonicalization "Nauty" Nauty canonicaliization

Examples

open allclose all

Basic Examples(1)

Find a canonical graph of the Pappus graph:

These two graphs are isomorphic:

Scope(4)

CanonicalGraph works with undirected graphs:

Directed graphs:

Use rules to specify the graph:

CanonicalGraph works with large graphs:

Applications(1)

Find if two graphs are isomorphic:

The graphs are isomorphic if they have the same canonical graph:

Properties & Relations(3)

A graph and its canonical graph are isomorphic:

Isomorphic graphs have the same canonical graph:

Use FindGraphIsomorphism to find a canonical ordering of vertices of a graph:

Wolfram Research (2014), CanonicalGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/CanonicalGraph.html (updated 2021).

Text

Wolfram Research (2014), CanonicalGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/CanonicalGraph.html (updated 2021).

CMS

Wolfram Language. 2014. "CanonicalGraph." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2021. https://reference.wolfram.com/language/ref/CanonicalGraph.html.

APA

Wolfram Language. (2014). CanonicalGraph. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CanonicalGraph.html

BibTeX

@misc{reference.wolfram_2022_canonicalgraph, author="Wolfram Research", title="{CanonicalGraph}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/CanonicalGraph.html}", note=[Accessed: 01-June-2023 ]}

BibLaTeX

@online{reference.wolfram_2022_canonicalgraph, organization={Wolfram Research}, title={CanonicalGraph}, year={2021}, url={https://reference.wolfram.com/language/ref/CanonicalGraph.html}, note=[Accessed: 01-June-2023 ]}