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Weighted Fractal Networks

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  • Carletti, Timoteo
  • Righi, Simone

Abstract

In this paper we define a new class of weighted complex networks sharing several properties with fractal sets, and whose topology can be completely analytically characterized in terms of the involved parameters and of the fractal dimension. General networks with fractal or hierarchical structures can be set in the proposed framework that moreover could be used to provide some answers to the widespread emergence of fractal structures in nature.

Suggested Citation

  • Carletti, Timoteo & Righi, Simone, 2010. "Weighted Fractal Networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(10), pages 2134-2142.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:10:p:2134-2142
    DOI: 10.1016/j.physa.2010.01.019
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    References listed on IDEAS

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    Cited by:

    1. Le, Anbo & Gao, Fei & Xi, Lifeng & Yin, Shuhua, 2015. "Complex networks modeled on the Sierpinski gasket," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 646-657.
    2. Sun, Lina & Huang, Ning & Li, Ruiying & Bai, Yanan, 2019. "A new fractal reliability model for networks with node fractal growth and no-loop," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 699-707.
    3. Huang, Da-Wen & Yu, Zu-Guo & Anh, Vo, 2017. "Multifractal analysis and topological properties of a new family of weighted Koch networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 695-705.
    4. Blagus, Neli & Šubelj, Lovro & Bajec, Marko, 2012. "Self-similar scaling of density in complex real-world networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(8), pages 2794-2802.
    5. Wei, Bo & Deng, Yong, 2019. "A cluster-growing dimension of complex networks: From the view of node closeness centrality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 80-87.
    6. Ye, Dandan & Dai, Meifeng & Sun, Yu & Su, Weiyi, 2017. "Average weighted receiving time on the non-homogeneous double-weighted fractal networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 390-402.
    7. Zong, Yue & Dai, Meifeng & Wang, Xiaoqian & He, Jiaojiao & Zou, Jiahui & Su, Weiyi, 2018. "Network coherence and eigentime identity on a family of weighted fractal networks," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 184-194.
    8. 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.
    9. Dai, Meifeng & Wang, Xiaoqian & Sun, Yanqiu & Sun, Yu & Su, Weiyi, 2017. "Eigentime identities for random walks on a family of treelike networks and polymer networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 132-140.
    10. Sun, Yu & Dai, Meifeng & Xi, Lifeng, 2014. "Scaling of average weighted shortest path and average receiving time on weighted hierarchical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 110-118.
    11. Wuyue (Phoebe) Shangguan & Alvin Chung Man Leung & Ashish Agarwal & Prabhudev Konana & Xi Chen, 2022. "Developing a Composite Measure to Represent Information Flows in Networks: Evidence from a Stock Market," Information Systems Research, INFORMS, vol. 33(2), pages 413-428, June.
    12. 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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