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Mathematical Problems in Engineering
Volume 2017, Article ID 8217361, 14 pages
Research Article

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

1School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China
2School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798
3School of Information Science and Technology, Donghua University, Shanghai 201620, China

Correspondence should be addressed to Zhongtuan Zheng; moc.361@gnehznautgnohz

Received 23 March 2017; Accepted 14 May 2017; Published 17 August 2017

Academic Editor: Huanqing Wang

Copyright © 2017 Zhongtuan Zheng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.