The nauty and traces software package is able to calculate automorphism groups of vertex colored graphs. The accompanying manual also describes (in section 14) how to obtain automorphism groups of edge colored graphs by mapping the problem to an equivalent one over vertex colored graphs.
My question is whether there exists a similar approach for the same problem over totally colored graphs. One possible solution might be to compute the automorphism groups for variants of such a graph with vertex-/edge-only coloring first and to then compute their intersection but I believe that this might be computationally expensive and would also require a base and strong generating set for both these groups which are internally generated by nauty but not actually accessible via its C-interface (at least that is my impression after reading the manual).
Can anyone give me a suggestion as to what would be the most efficient approach from a practical standpoint?