Caroline Melles and I have written a preprint that collects numerous examples of harmonic quotient morphisms , where is a quotient graph obtained from some subgroup . The examples are for graphs having a small number of vertices (no more than 12). For the most part, we also focused on regular graphs with small degree (no more than 5). They were all computed using SageMath and a module of special purpose Python functions I’ve written (available on request). I’ve not counted, but the number of examples is relatively large, maybe over one hundred.
I’ll post it to the math arxiv at some point but if you are interested now, here’s a copy: click here for pdf.