In coming across a post related to this question's topic, posting in Theoretical Computer Science might be the right place. In combinatorial maps (1,2,3), are generalized map involutions captured by Graph Neural Networks?
Generalized maps (gmap) can be defined by the data structure: M = (D, $\sigma$, $\alpha$) where $\alpha$ is a permutation that gives the other dart connected on the same edge , i.e., the neighboring dart/s (see 2).
Involutions can be properties of nodes. This is ideal for local structure aggregation in GNNs and GCNs. However, in conversation with others, there are suggestions that the GNN handles involutions information (such as the face a triangle forms in planar graphs). Is that right?