Nauty in Macaulay2

TL;DR

The paper introduces the Nauty package for Macaulay2, enabling graph isomorphism testing and graph family generation using nauty's algorithms, thus enhancing computational graph analysis within algebraic geometry software.

Contribution

It provides the first integration of nauty's graph algorithms into Macaulay2, facilitating advanced graph analysis in algebraic geometry workflows.

Findings

Efficient graph isomorphism testing within Macaulay2.

Generation of restricted graph families using nauty.

Enhanced computational tools for graph analysis in algebraic geometry.

Abstract

We introduce a new Macaulay2 package, Nauty, which gives access to powerful methods on graphs provided by the software nauty by Brendan McKay. The primary motivation for accessing nauty is to determine if two graphs are isomorphic. We also implement methods to generate families of graphs restricted in various ways using tools provided with the software nauty.