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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Long Li & Weigang Sun & Guixiang Wang & Guanghui Xu, 2014. "Mean first-passage time on a family of small-world treelike networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 25(03), pages 1-10.
    • Handle: RePEc:wsi:ijmpcx:v:25:y:2014:i:03:n:s0129183113500976
    DOI: 10.1142/S0129183113500976
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