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The trapping problem and the average shortest weighted path of the weighted pseudofractal scale-free networks

Author

Listed:
  • Meifeng Dai

    (Institute of Applied System Analysis, Jiangsu University, Zhenjiang 212013, P. R. China)

  • Changxi Dai

    (Institute of Applied System Analysis, Jiangsu University, Zhenjiang 212013, P. R. China)

  • Huiling Wu

    (#x2020;Junior College, Zhejiang Wanli University, Ningbo, Zhejiang 315100, P. R. China)

  • Xianbin Wu

    (#x2020;Junior College, Zhejiang Wanli University, Ningbo, Zhejiang 315100, P. R. China)

  • Wenjing Feng

    (Institute of Applied System Analysis, Jiangsu University, Zhenjiang 212013, P. R. China)

  • Weiyi Su

    (#x2021;Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China)

Abstract

In this paper, we study the trapping time in the weighted pseudofractal scale-free networks (WPSFNs) and the average shortest weighted path in the modified weighted pseudofractal scale-free networks (MWPSFNs) with the weight factor r. At first, for exceptional case with the trap fixed at a hub node for weight-dependent walk, we derive the exact analytic formulas of the trapping time through the structure of WPSFNs. The obtained rigorous solution shows that the trapping time approximately grows as a power-law function of the number of network nodes with the exponent represented by ln2+4r2+rln3. Then, we deduce the scaling expression of the average shortest weighted path through the iterative process of the construction of MWPSFNs. The obtained rigorous solution shows that the scalings of average shortest weighted path with network size obey three laws along with the range of the weight factor. We provide a theoretical study of the trapping time for weight-dependent walk and the average shortest weighted path in a wide range of deterministic weighted networks.

Suggested Citation

  • Meifeng Dai & Changxi Dai & Huiling Wu & Xianbin Wu & Wenjing Feng & Weiyi Su, 2019. "The trapping problem and the average shortest weighted path of the weighted pseudofractal scale-free networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 30(01), pages 1-17, January.
    • Handle: RePEc:wsi:ijmpcx:v:30:y:2019:i:01:n:s0129183119500104
    DOI: 10.1142/S0129183119500104
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    Citations

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    Cited by:

    1. Dai, Lingfei & Dai, Meifeng & Huang, Yu & Li, Yin & Shen, Junjie & Chi, Huijia & Su, Weiyi, 2020. "Searching efficiency of multiple walkers on the weighted networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    2. Hu, Zhongren & Wu, Bo, 2023. "The average shortest distance of three colored substitution networks," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).

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