Mean First-passage Time on a Network through Edge Iteration

Abstract

In this paper, we study mean first-passage time (MFPT) for random walks on a network through edge iteration. The feature of this kind of network is that every existing edge gives birth to finite nodes at each step. According to the network structures, we obtain the analytical expression for MFPT, which shows that the MFPT grows as a power-law function with the number of nodes in the large limit of network order. In addition, the scaling exponent of MFPT is same for the initial state of the networks with three or four nodes.