The European Physical Journal B

, Volume 84, Issue 2, pp 331–338 | Cite as

Role of fractal dimension in random walks on scale-free networks

  • Zhongzhi ZhangEmail author
  • Yihang Yang
  • Shuyang Gao
Regular Article Interdisciplinary Physics


Fractal dimension is central to understanding dynamical processes occurring on networks; however, the relation between fractal dimension and random walks on fractal scale-free networks has been rarely addressed, despite the fact that such networks are ubiquitous in real-life world. In this paper, we study the trapping problem on two families of networks. The first is deterministic, often called (x,y)-flowers; the other is random, which is a combination of (1,3)-flower and (2,4)-flower and thus called hybrid networks. The two network families display rich behavior as observed in various real systems, as well as some unique topological properties not shared by other networks. We derive analytically the average trapping time for random walks on both the (x,y)-flowers and the hybrid networks with an immobile trap positioned at an initial node, i.e., a hub node with the highest degree in the networks. Based on these analytical formulae, we show how the average trapping time scales with the network size. Comparing the obtained results, we further uncover that fractal dimension plays a decisive role in the behavior of average trapping time on fractal scale-free networks, i.e., the average trapping time decreases with an increasing fractal dimension.


Fractal Dimension Network Size Degree Distribution Initial Node Network Family 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.School of Computer ScienceFudan UniversityShanghaiP.R. China
  2. 2.Shanghai Key Lab of Intelligent Information ProcessingFudan UniversityShanghaiP.R. China

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