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Scale-free and small-world properties of Sierpinski networks

Author

Listed:
  • Wang, Songjing
  • Xi, Lifeng
  • Xu, Hui
  • Wang, Lihong

Abstract

In this paper, we construct the evolving networks from Sierpinski carpet, using the encoding approach in fractal geometry. We consider the small similar copies of unit square as nodes of network, where two nodes are neighbors if and only if their corresponding copies have common surface. For our networks, we check their scale-free and small-world effect by the self-similar structures, the exponent of power-law on degree distribution is log38 which is the Hausdorff dimension of the carpet.

Suggested Citation

  • Wang, Songjing & Xi, Lifeng & Xu, Hui & Wang, Lihong, 2017. "Scale-free and small-world properties of Sierpinski networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 690-700.
    • Handle: RePEc:eee:phsmap:v:465:y:2017:i:c:p:690-700
    DOI: 10.1016/j.physa.2016.08.069
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    References listed on IDEAS

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    1. Chen, Jin & Le, Anbo & Wang, Qin & Xi, Lifeng, 2016. "A small-world and scale-free network generated by Sierpinski Pentagon," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 449(C), pages 126-135.
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    4. Chaoming Song & Shlomo Havlin & Hernán A. Makse, 2005. "Self-similarity of complex networks," Nature, Nature, vol. 433(7024), pages 392-395, January.
    5. Zhongzhi Zhang & Shuigeng Zhou & Zhan Su & Tao Zou & Jihong Guan, 2008. "Random Sierpinski network with scale-free small-world and modular structure," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 65(1), pages 141-147, September.
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    Cited by:

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