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Random walks on real metro systems

Author

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  • Yueying Zhu

    (IMMM, UMR CNRS 6283, Université du Maine, 72085 Le Mans, France†Complexity Science Center & Institute of Particle Physics, Central China Normal University, Wuhan 430079, P. R. China)

  • Longfeng Zhao

    (#x2020;Complexity Science Center & Institute of Particle Physics, Central China Normal University, Wuhan 430079, P. R. China)

  • Wei Li

    (#x2020;Complexity Science Center & Institute of Particle Physics, Central China Normal University, Wuhan 430079, P. R. China‡Max-Planck Institute for Mathematics in the Sciences, Inselst. 22, 04103, Germany)

  • Qiuping A. Wang

    (IMMM, UMR CNRS 6283, Université du Maine, 72085 Le Mans, France)

  • Xu Cai

    (#x2020;Complexity Science Center & Institute of Particle Physics, Central China Normal University, Wuhan 430079, P. R. China)

Abstract

In this paper, we investigate the random walks on metro systems in 28 cities from worldwide via the Laplacian spectrum to realize the trapping process on real systems. The average trapping time is a primary description to response the trapping process. Firstly, we calculate the mean trapping time to each target station and to each entire system, respectively. Moreover, we also compare the average trapping time with the strength (the weighted degree) and average shortest path length for each station, separately. It is noted that the average trapping time has a close inverse relation with the station’s strength but rough positive correlation with the average shortest path length. And we also catch the information that the mean trapping time to each metro system approximately positively correlates with the system’s size. Finally, the trapping process on weighted and unweighted metro systems is compared to each other for better understanding the influence of weights on trapping process on metro networks. Numerical results show that the weights have no significant impact on the trapping performance on metro networks.

Suggested Citation

  • Yueying Zhu & Longfeng Zhao & Wei Li & Qiuping A. Wang & Xu Cai, 2016. "Random walks on real metro systems," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 27(10), pages 1-11, October.
    • Handle: RePEc:wsi:ijmpcx:v:27:y:2016:i:10:n:s0129183116501229
    DOI: 10.1142/S0129183116501229
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