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Two-parameter fractional Tsallis information dimensions of complex networks

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  • Ramirez-Arellano, Aldo
  • Hernández-Simón, Luis Manuel
  • Bory-Reyes, Juan

Abstract

A two-parameter (namely, α→ and β→) fractional Tsallis information dimensions of complex networks based on q−logarithm is introduced. The meanings assigned to such parameters are the quantification of the interaction among the elements (nodes) that are part of the same sub-system (sub-network) and the interaction among the sub-systems (sub-networks), respectively. Also, the index of interaction ι – formulated based on the α→ and β→– captures the networks’ complex topology.

Suggested Citation

  • Ramirez-Arellano, Aldo & Hernández-Simón, Luis Manuel & Bory-Reyes, Juan, 2021. "Two-parameter fractional Tsallis information dimensions of complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    • Handle: RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921004677
    DOI: 10.1016/j.chaos.2021.111113
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    References listed on IDEAS

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    1. Chaoming Song & Shlomo Havlin & Hernán A. Makse, 2005. "Self-similarity of complex networks," Nature, Nature, vol. 433(7024), pages 392-395, January.
    2. Ramirez-Arellano, Aldo & Bermúdez-Gómez, Salvador & Hernández-Simón, Luis Manuel & Bory-Reyes, Juan, 2019. "D-summable fractal dimensions of complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 210-214.
    3. Ramirez-Arellano, Aldo & Hernández-Simón, Luis Manuel & Bory-Reyes, Juan, 2020. "A box-covering Tsallis information dimension and non-extensive property of complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    4. Lavagno, A & Swamy, P.Narayana, 2002. "q-Deformed structures and nonextensive statistics: a comparative study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 305(1), pages 310-315.
    5. G. Kaniadakis, 2009. "Maximum entropy principle and power-law tailed distributions," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 70(1), pages 3-13, July.
    6. Qi Zhang & Meizhu Li & Yong Deng, 2016. "A new structure entropy of complex networks based on nonextensive statistical mechanics," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 27(10), pages 1-12, October.
    7. Duan, Shuyu & Wen, Tao & Jiang, Wen, 2019. "A new information dimension of complex network based on Rényi entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 529-542.
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    Cited by:

    1. Lei, Mingli & Cheong, Kang Hao, 2022. "Node influence ranking in complex networks: A local structure entropy approach," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    2. Ortiz-Vilchis, Pilar & Lei, Mingli & Ramirez-Arellano, Aldo, 2024. "Reformulation of Deng information dimension of complex networks based on a sigmoid asymptote," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).

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