Hi! I'm one of the authors.

There certainly are many interesting parallels here. I often think about this from the perspective of systems biology, in Uri Alon's tradition. There are a range of graphs in biology with excitation and inhibitory edges -- transcription networks, protein networks, networks of biological neurons -- and one can study recurring motifs that turn up in these networks and try to learn from them.

It wouldn't be surprising if some lessons from that work may also transfer to artificial neural networks, although there are some technical things to consider.