Mean first-passage time on a family of small-world treelike networks

Long Li, Weigang Sun (), Guixiang Wang and Guanghui Xu
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Long Li: Institute of Operational Research and Cybernetics, Hangzhou Dianzi University, Hangzhou 310018, P. R. China
Weigang Sun: Institute of Applied Mathematics and Engineering Computations, Hangzhou Dianzi University, Hangzhou 310018, P. R. China
Guixiang Wang: Institute of Operational Research and Cybernetics, Hangzhou Dianzi University, Hangzhou 310018, P. R. China
Guanghui Xu: School of Science, Zhejiang A & F University, Hangzhou 311300, P. R. China

International Journal of Modern Physics C (IJMPC), 2014, vol. 25, issue 03, 1-10

Abstract: In this paper, we obtain exact scalings of mean first-passage time (MFPT) of random walks on a family of small-world treelike networks formed by two parameters, which includes three kinds. First, we determine the MFPT for a trapping problem with an immobile trap located at the initial node, which is defined as the average of the first-passage times (FPTs) to the trap node over all possible starting nodes, and it scales linearly with network sizeNin large networks. We then analytically obtain the partial MFPT (PMFPT) which is the mean of FPTs from the trap node to all other nodes and show that it increases withNasNlnN. Finally we establish the global MFPT (GMFPT), which is the average of FPTs over all pairs of nodes. It also grows withNasNlnNin the large limit ofN. For these three kinds of random walks, we all obtain the analytical expressions of the MFPT and they all increase with network parameters. In addition, our method for calculating the MFPT is based on the self-similar structure of the considered networks and avoids the calculations of the Laplacian spectra.

Keywords: Complex networks; mean first-passage time; random walks; 89.75.Fb; 89.75.Hc; 05.40.Fb (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1142/S0129183113500976

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