Anomalous behavior of trapping on a fractal scale-free network

¹  School of Computer Science, Fudan University - Shanghai 200433, China
²  Shanghai Key Lab of Intelligent Information Processing, Fudan University - Shanghai 200433, China
³  Department of Computer Science and Technology, Tongji University - 4800 Cao'an Road, Shanghai 201804, China

Corresponding authors: zhangzz@fudan.edu.cn sgzhou@fudan.edu.cn jhguan@tongji.edu.cn

Received: 29 April 2009
Accepted: 16 September 2009

Abstract

It is known that the heterogeneity of scale-free networks helps enhancing the efficiency of trapping processes performed on them. In this paper, we show that transport efficiency is much lower in a fractal scale-free network than in non-fractal networks. To this end, we examine a simple random walk with a fixed trap at a given position on a fractal scale-free network. We calculate analytically the mean first-passage time (MFPT) as a measure of the efficiency for the trapping process, and obtain a closed-form expression for MFPT, which agrees with direct numerical calculations. We find that, in the limit of a large network order V, the MFPT behaves superlinearly as with an exponent much larger than 1, which is in sharp contrast to the scaling with , previously obtained for non-fractal scale-free networks. Our results indicate that the degree distribution of scale-free networks is not sufficient to characterize trapping processes taking place on them. Since various real-world networks are simultaneously scale-free and fractal, our results may shed light on the understanding of trapping processes running on real-life systems.