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Generating hierarchial scale-free graphs from fractals

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  • Komjáthy, Júlia
  • Simon, Károly

Abstract

Motivated by the hierarchial network model of E. Ravasz, A.-L. Barabási, and T. Vicsek, we introduce deterministic scale-free networks derived from a graph directed self-similar fractal Λ. With rigorous mathematical results we verify that our model captures some of the most important features of many real networks: the scale-free and the high clustering properties. We also prove that the diameter is the logarithm of the size of the system. We point out a connection between the power law exponent of the degree distribution and some intrinsic geometric measure theoretical properties of the underlying fractal. Using our (deterministic) fractal Λ we generate random graph sequence sharing similar properties.

Suggested Citation

  • Komjáthy, Júlia & Simon, Károly, 2011. "Generating hierarchial scale-free graphs from fractals," Chaos, Solitons & Fractals, Elsevier, vol. 44(8), pages 651-666.
    • Handle: RePEc:eee:chsofr:v:44:y:2011:i:8:p:651-666
    DOI: 10.1016/j.chaos.2011.05.012
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    References listed on IDEAS

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    1. Barabási, Albert-László & Ravasz, Erzsébet & Vicsek, Tamás, 2001. "Deterministic scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(3), pages 559-564.
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    Cited by:

    1. Wang, Daohua & Zeng, Cheng & Zhao, Zixuan & Wu, Zhiqiang & Xue, Yumei, 2023. "Kirchhoff index of a class of polygon networks," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    2. Zeng, Cheng & Xue, Yumei & Huang, Yuke, 2021. "Fractal networks with Sturmian structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
    3. Rasul Kochkarov, 2021. "Research of NP-Complete Problems in the Class of Prefractal Graphs," Mathematics, MDPI, vol. 9(21), pages 1-20, October.
    4. 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.
    5. Rasul Kochkarov & Azret Kochkarov, 2022. "Introduction to the Class of Prefractal Graphs," Mathematics, MDPI, vol. 10(14), pages 1-17, July.
    6. 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.
    7. Feng, Qunqiang & Li, Xing & Hu, Zhishui, 2023. "Asymptotic degree distribution in a homogeneous evolving network model," Statistics & Probability Letters, Elsevier, vol. 193(C).
    8. 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).
    9. Dai, Meifeng & Shao, Shuxiang & Su, Weiyi & Xi, Lifeng & Sun, Yanqiu, 2017. "The modified box dimension and average weighted receiving time of the weighted hierarchical graph," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 475(C), pages 46-58.

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