gives a canonical form of the graph g.


uses rules vw to specify the graph.


  • 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.
  • CanonicalGraph[g] returns a graph with vertices 1, 2, that is isomorphic to g.
  • Isomorphic graphs have the same canonical graph.


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:

Introduced in 2014
Updated in 2015