Eur. Phys. J. B (2013) 86: 156
https://doi.org/10.1140/epjb/e2013-30905-x

Regular Article

Expanded Koch networks: structure and trapping time of random walks

¹ Department of Mathematics, Shanghai University, Shanghai 200444, P.R. China
² College of Territorial Resources and Tourism, Anhui Normal University, Wuhu 241002, Anhui, P.R. China

^a e-mail: zhanghongjuan@shu.edu.cn

Received: 6 October 2012
Received in final form: 11 December 2012
Published online: 15 April 2013

Abstract

Based on the Koch network constructed using Koch fractals, we proposed a class of expanded Koch networks in this paper. The original triangle is replaced by r-polygon, and each node generates m sub r-polygons by every step, which makes the Koch network more general. We studied the structure and properties of the networks. The exact analytical result of the degree distribution, clustering coefficient and average path length were obtained. When parameters m and r satisfy some certain conditions, the networks follow a power-law distribution and have a small average path length. Finally, we introduced the random walk on the network. Our discussions focused on the trapping problem, particularly the calculation and derivation of mean first passage time (MFPT) and global mean first passage time (GMFPT). In addition, we also gave the relationship between the above results and the network size.