Random Walk on Undirected Networks Based on the Neighbor Nodes Degree Distribution

Abstract

In this paper, we introduce a new random walk on undirected networks, which transition probabilities depend on the degree distribution of neighbor nodes. We have derived an analytical expression for MFPT between two nodes, and obtained an explicit solution to the average MFPT in the network with at any node. Further we provided a low bound for GMFPT by Cauthy's inequality, and the lower bound is sharp and can be attained in complete graph.