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Scale-free and small-world properties of a multiple-hub network with fractal structure

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  • Huang, Yuke
  • Zhang, Hanxiong
  • Zeng, Cheng
  • Xue, Yumei

Abstract

In this paper, we introduce a new kind of multiple-hub network with fractal structure. We aim to present a study on some properties of this network, such as the box dimension of the adjacency matrix, degree distribution, average clustering coefficient and average path length, which show the scale-free and small-world effects of this network.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:558:y:2020:i:c:s0378437120305227
    DOI: 10.1016/j.physa.2020.125001
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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. 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.
    3. Xi, Lifeng & Wang, Lihong & Wang, Songjing & Yu, Zhouyu & Wang, Qin, 2017. "Fractality and scale-free effect of a class of self-similar networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 478(C), pages 31-40.
    4. Chaoming Song & Shlomo Havlin & Hernán A. Makse, 2005. "Self-similarity of complex networks," Nature, Nature, vol. 433(7024), pages 392-395, January.
    5. Chen, Jin & Dai, Meifeng & Wen, Zhixiong & Xi, Lifeng, 2014. "Trapping on modular scale-free and small-world networks with multiple hubs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 542-552.
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    Cited by:

    1. Wang, Shuliang & Guo, Zhaoyang & Huang, Xiaodi & Zhang, Jianhua, 2024. "A three-stage model of quantifying and analyzing power network resilience based on network theory," Reliability Engineering and System Safety, Elsevier, vol. 241(C).

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