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Canonical graph

Posted 3 years ago
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Hello

I'm wanting to find out what the definition of canonical graph labelling is for the canonicalgraph function in mathematica. Any ideas where I can get that information? All I can see in the description is that it puts the graph in a canonical form, but no indication on what that form is e.g. Maximising or minimising sequences from the adjacency matrix etc.

Cheers

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Graph canonization is a NP-hard computational problem. A discussion of canonical graphs is given, for example, in

http://www.math.unl.edu/~aradcliffe1/Papers/Canonical.pdf

For the intended application, it does not matter. What is important is that g1 and g2 are isomorphic if and only if CanonicalGraph[g1] === CanonicalGraph[g2].

There are many different ways to define (and compute) a canonical form with this property. All of them are complicated. For example, the Bliss library (which you can access in Mathematica through IGraph/M) provides multiple such forms.

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