Graph isomorphism problem for labeled graphs In the case of unlabeled graphs, the graph isomorphism problem can be tackled by a number of algorithms which perform very well in practice. That is, although the worst case running time is exponential, one usually has a polynomial running time.

I was hoping that the situation is similar in the case of labeled graphs. However, I have a really hard time to find any reference which proposes an "practically efficient" algorithm.

Remark: Here, we require that the isomorphism preserves the labels. That is, an isomorphism between two finite automata/process algebra terms would imply that the automata/terms are essentially "equal up to renaming of the nodes".

The only reference I found was the one in Wikipedia that states the the isomorphism problem of labeled graphs can be polynomially reduced to that of ordinary graphs. The underlying paper, however, is more about complexity theory than practical algorithms.

I am missing something, or is it really the case that the there are no efficient "heuristical" algorithms to decide whether two labeled graphs are isomorphic?

Any hint or reference would be great.
You might be interested in this paper:

Aidan Hogan:
Skolemising Blank Nodes while Preserving Isomorphism. 
WWW 2015: 430-440

It has an algorithm (based on Nauty) for testing the isomorphism of RDF graphs, which are essentially directed labelled graphs that may contain fixed labels. The algorithm takes labels into account to narrow the search space.

If you can represent your input labelled graph as an RDF graph, you could try use the associated software package "blabel" to test isomorphism.