William Harter explored a similar concept in Representations of Multidimensional Symmetries in Networks. In this article, the author also considers inductance and capacitance. You need these other functions if you want to have interesting time-dynamic behavior. It's also nice to consider analog multipliers such as MPY634 in this circuit diagram, which I built and tested successfully 5-10 yrs ago.

Thanks Sander. I guess there are two competing things going on, adding paths to give the electrons more choices and making the paths longer for the electrons. Does anyone know how this calculation matches up with a physics-style sum of paths calculation? Is it a one-liner to count the number of paths (say without loops)?

Thanks Brad. I guess I was thinking of interesting time dynamic behavior as being something other than a linear second order ODE. Is that right?