Random walks on non-homogenous weighted Koch networks

Abstract

In this paper, we introduce new models of non-homogenous weighted Koch networks on real traffic systems depending on the three scaling factors r1,r2,r3∈(0,1). Inspired by the definition of the average weighted shortest path (AWSP), we define the average weighted receiving time (AWRT). Assuming that the walker, at each step, starting from its current node, moves uniformly to any of its neighbors, we show that in large network, the AWRT grows as power-law function of the network order with the exponent, represented by θ(r1,r2,r3)=log4(1+r1+r2+r3). Moreover, the AWSP, in the infinite network order limit, only depends on the sum of scaling factors r1,r2,r3.