Mean First Passage Time of Preferential Random Walks on Complex Networks with Applications

Abstract

This paper investigates, both theoretically and numerically, preferential random walks (PRW) on weighted complex networks. By using two different analytical methods, two exact expressions are derived for the mean first passage time (MFPT) between two nodes. On one hand, the MFPT is got explicitly in terms of the eigenvalues and eigenvectors of a matrix associated with the transition matrix of PRW. On the other hand, the center-product-degree (CPD) is introduced as one measure of node strength and it plays a main role in determining the scaling of the MFPT for the PRW. Comparative studies are also performed on PRW and simple random walks (SRW). Numerical simulations of random walks on paradigmatic network models confirm analytical predictions and deepen discussions in different aspects. The work may provide a comprehensive approach for exploring random walks on complex networks, especially biased random walks, which may also help to better understand and tackle some practical problems such as search and routing on networks.