# CanonicalGraph

gives a canonical form of the graph g.

CanonicalGraph[{vw,}]

uses rules vw to specify the graph.

# Details • 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.

# 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: