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Fractality and scale-free effect of a class of self-similar networks

Author

Listed:
  • Xi, Lifeng
  • Wang, Lihong
  • Wang, Songjing
  • Yu, Zhouyu
  • Wang, Qin

Abstract

In this paper, given an initial directed graph as a self-similar pattern and fix two nodes in the pattern, we can iterate the graph by replacing any directed edge with the initial graph of pattern and identifying the fixed nodes of pattern with the endpoints of directed edge. Using the iteration again and again, we obtain a family of growing self-similar networks. Modify these networks to be undirected ones, we obtain growing self-similar undirected networks. We obtain the fractality of our self-similar networks and find out the scale-free effect in terms of the matrix related to two fixed nodes in the initial graph.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:478:y:2017:i:c:p:31-40
    DOI: 10.1016/j.physa.2017.02.049
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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. Gallos, Lazaros K. & Song, Chaoming & Makse, Hernán A., 2007. "A review of fractality and self-similarity in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(2), pages 686-691.
    3. Chaoming Song & Shlomo Havlin & Hernán A. Makse, 2005. "Self-similarity of complex networks," Nature, Nature, vol. 433(7024), pages 392-395, January.
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    Cited by:

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    2. Yao, Jialing & Sun, Bingbin & Xi, lifeng, 2019. "Fractality of evolving self-similar networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 211-216.
    3. 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).
    4. Yang, Jinjin & Wang, Songjing & Xi, Lifeng & Ye, Yongchao, 2018. "Average geodesic distance of skeleton networks of Sierpinski tetrahedron," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 269-277.
    5. Li, Ziyu & Yao, Jialing & Wang, Qin, 2019. "Fractality of multiple colored substitution networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 402-408.

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