The main use of nauty is to determine if two graphs are isomorphic. We can demonstrate it for two given graphs with the method areIsomorphic.
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Further, a list of graphs can be reduced to only graphs that are non-isomorphic with the method removeIsomorphs. Here we create a list of 120 different labellings of the 5-cycle and use nauty to verify they are indeed all the same.
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The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/NautyGraphs.m2:809:0.