Generalized entropy for random walks in regular networks and graphs as a super diffusion

Abstract

In this paper, the entropy of the stochastic processes created by the movement of a walker in a graph is investigated. The Shannon-Khinchin entropy has four axioms that ignore one of them can make the generalized entropy. Here, we investigate the number of different finite paths asymptotically, for determining a generalized entropy. Then, we will study the regular infinite networks and graphs with finite nodes, with two different types of motion.