# Are generalized map involutions captured by GNN?

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?

• Please edit your question to define your terms, make it self-contained, and show your work so far. I suggest you define what is a 'generalized map involution', and what it means for it to be 'captured' by a GNN. I don't know what you mean by your last paragraph ('the face info is already handled' etc.). What does this have to do with theoretical computer science? See our help center, especially the part beginning "You should only post questions you're actually seriously..." – D.W. Dec 17 '20 at 9:01