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Asymptotic formula on average path length in a hierarchical scale-free network with fractal structure

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  • Zhang, Qian
  • Xue, Yumei
  • Wang, Daohua
  • Niu, Min

Abstract

In this paper, we study a hierarchical scale-free network with special fractal structure. We study the average path length and associate the average path length with the symbol length. Then using a recursive method, we obtain the asymptotic formula for average path length of our networks.

Suggested Citation

  • Zhang, Qian & Xue, Yumei & Wang, Daohua & Niu, Min, 2019. "Asymptotic formula on average path length in a hierarchical scale-free network with fractal structure," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 196-201.
    • Handle: RePEc:eee:chsofr:v:122:y:2019:i:c:p:196-201
    DOI: 10.1016/j.chaos.2019.03.021
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    References listed on IDEAS

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    1. Komjáthy, Júlia & Simon, Károly, 2011. "Generating hierarchial scale-free graphs from fractals," Chaos, Solitons & Fractals, Elsevier, vol. 44(8), pages 651-666.
    2. Z.-Z. Zhang & S.-G. Zhou & T. Zou, 2007. "Self-similarity, small-world, scale-free scaling, disassortativity, and robustness in hierarchical lattices," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 56(3), pages 259-271, April.
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    Cited by:

    1. Lu, Ying & Xu, Jiajun & Xi, Lifeng, 2023. "Fractal version of hyper-Wiener index," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    2. Huang, Yuke & Zhang, Hanxiong & Zeng, Cheng & Xue, Yumei, 2020. "Scale-free and small-world properties of a multiple-hub network with fractal structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).

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