Random walk and first passage time on a weighted hierarchical network

Feng Zhu (), Meifeng Dai, Yujuan Dong and Jie Liu
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Feng Zhu: Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu, 212013, P. R. China
Meifeng Dai: Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu, 212013, P. R. China
Yujuan Dong: Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu, 212013, P. R. China
Jie Liu: Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu, 212013, P. R. China

International Journal of Modern Physics C (IJMPC), 2014, vol. 25, issue 09, 1-10

Abstract: This paper reports a weighted hierarchical network generated on the basis of self-similarity, in which each edge is assigned a different weight in the same scale. We studied two substantial properties of random walk: the first-passage time (FPT) between a hub node and a peripheral node and the FPT from a peripheral node to a local hub node over the network. Meanwhile, an analytical expression of the average sending time (AST) is deduced, which reflects the average value of FPT from a hub node to any other node. Our result shows that the AST from a hub node to any other node is related to the scale factor and the number of modules. We found that the AST grows sublinearly, linearly and superlinearly respectively with the network order, depending on the range of the scale factor. Our work may shed some light on revealing the diffusion process in hierarchical networks.

Keywords: Weighted hierarchical network; biased random walk; first-passage time; average sending time; 11.25.Hf; 123.1K (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (3)

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DOI: 10.1142/S0129183114500375

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