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Fractality of multiple colored substitution networks

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  • Li, Ziyu
  • Yao, Jialing
  • Wang, Qin

Abstract

For multiple colored initial graphs, we can construct evolving self-similar networks by substitution rules. In this paper, we obtain the fractality of our substitution networks through the estimates on the cardinality of the minimal covering of boxes.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:525:y:2019:i:c:p:402-408
    DOI: 10.1016/j.physa.2019.03.079
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    References listed on IDEAS

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    1. Barabási, Albert-László & Albert, Réka & Jeong, Hawoong, 2000. "Scale-free characteristics of random networks: the topology of the world-wide web," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 281(1), pages 69-77.
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    3. Li, Ziyu & Yu, Zhouyu & Xi, Lifeng, 2018. "Scale-free effect of substitution networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 1449-1455.
    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. Barabási, Albert-László & Albert, Réka & Jeong, Hawoong, 1999. "Mean-field theory for scale-free random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 272(1), pages 173-187.
    6. 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:

    1. Hu, Zhongren & Wu, Bo, 2023. "The average shortest distance of three colored substitution networks," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).

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