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Given a labelled graph G = (V, E, L), L is function that maps vertices to labels. I want find subsets S ⊆ V such that the mappings of vertices in S in all the automorphisms (should satisfy edge and label constraints) lie in the same set S. I am not sure if these constraints are enough to call S as an orbit of the graph G.
Are there any commonly used algorithms to compute these subsets ?
It looks like the nauty algorithm for the graph isomorphism problem can also be used to compute the orbits in vertex colored graphs( or labeled graphs).
Nauty
Official Nauty website