Modulus of families of walks on graphs
  We introduce the notion of modulus of families of walks on graphs. We show how Beurling's famous criterion for extremality, that was formulated in the continuous case, can be interpreted on graphs as an instance of the Karush-Kuhn-Tucker conditions. We then develop an algorithm to numerically compute modulus using Beurling's criterion as our guide. 
Nathan Albin, Pietro Poggi-Corradini, Faryad Darabi Sahneh, Max   Goering
math.CO math.CV