Mean first passage time of random walks on deterministic recursive trees

Abstract

On the basis of recursive trees, we propose a new kind of deterministic recursive trees (DRT) with a feature that the initial state of recursive trees is a lattice with an arbitrary number of nodes. In the subsequent evolving step, existing nodes create finite nodes. We obtain analytical formulae for degree distribution and average path length. We also study mean first passage time (MFPT) between two nodes over all pairs, which is used to measure the efficiency of random walks in a network. In addition, we derive an exact formula for the MFPT by using the relationship between random walks and resistance distance in a electronic network.