IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v132y2020ics0960077919305478.html
   My bibliography  Save this article

A box-covering Tsallis information dimension and non-extensive property of complex networks

Author

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

Abstract

In this article, a box-covering Tsallis information dimension is introduced, and the physical interpretation of this new dimension has been assigned. Moreover, based on the introduced parameter q→, a characterization of non-extensive networks is stated, allowing the classification according to super-extensive (q→≺1), sub-extensive (q→≻1) or extensive (q→=1). The experimental results on both synthetic and real complex networks shed light on the type of interaction of the boxes. The results support the conjecture that the box-covering Tsallis information dimension is a suitable and flexible measure of information of real complex networks that exhibit a rich structural diversity.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:132:y:2020:i:c:s0960077919305478
    DOI: 10.1016/j.chaos.2019.109590
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077919305478
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2019.109590?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wen, Tao & Jiang, Wen, 2018. "An information dimension of weighted complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 501(C), pages 388-399.
    2. 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.
    3. 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.
    4. Chaoming Song & Shlomo Havlin & Hernán A. Makse, 2005. "Self-similarity of complex networks," Nature, Nature, vol. 433(7024), pages 392-395, January.
    5. Zhang, Qi & Luo, Chuanhai & Li, Meizhu & Deng, Yong & Mahadevan, Sankaran, 2015. "Tsallis information dimension of complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 707-717.
    6. 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.
    7. Mark D Humphries & Kevin Gurney, 2008. "Network ‘Small-World-Ness’: A Quantitative Method for Determining Canonical Network Equivalence," PLOS ONE, Public Library of Science, vol. 3(4), pages 1-10, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Li, Hanwen & Shang, Qiuyan & Deng, Yong, 2021. "A generalized gravity model for influential spreaders identification in complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    2. Zhou, Qianli & Deng, Yong, 2023. "Generating Sierpinski gasket from matrix calculus in Dempster–Shafer theory," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    3. Lei, Mingli, 2022. "Information dimension based on Deng entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    4. 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).
    5. 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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lei, Mingli, 2022. "Information dimension based on Deng entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    2. 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).
    3. 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.
    4. Li, Meizhu & Zhang, Qi & Deng, Yong, 2018. "Evidential identification of influential nodes in network of networks," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 283-296.
    5. Wen, Tao & Jiang, Wen, 2019. "Identifying influential nodes based on fuzzy local dimension in complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 332-342.
    6. Pavón-Domínguez, Pablo & Moreno-Pulido, Soledad, 2022. "Sandbox fixed-mass algorithm for multifractal unweighted complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    7. Huang, Yubo & Dong, Hongli & Zhang, Weidong & Lu, Junguo, 2019. "Stability analysis of nonlinear oscillator networks based on the mechanism of cascading failures," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 5-15.
    8. Feng, Shiyuan & Weng, Tongfeng & Chen, Xiaolu & Ren, Zhuoming & Su, Chang & Li, Chunzi, 2024. "Scaling law of diffusion processes on fractal networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 640(C).
    9. Pavón-Domínguez, Pablo & Moreno-Pulido, Soledad, 2020. "A Fixed-Mass multifractal approach for unweighted complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    10. de Sá, Luiz Alberto Pereira & Zielinski, Kallil M.C. & Rodrigues, Érick Oliveira & Backes, André R. & Florindo, João B. & Casanova, Dalcimar, 2022. "A novel approach to estimated Boulingand-Minkowski fractal dimension from complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    11. Nie, Chun-Xiao & Song, Fu-Tie, 2018. "Analyzing the stock market based on the structure of kNN network," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 148-159.
    12. 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.
    13. 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.
    14. Andrea Avena-Koenigsberger & Xiaoran Yan & Artemy Kolchinsky & Martijn P van den Heuvel & Patric Hagmann & Olaf Sporns, 2019. "A spectrum of routing strategies for brain networks," PLOS Computational Biology, Public Library of Science, vol. 15(3), pages 1-24, March.
    15. 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.
    16. Ikeda, Nobutoshi, 2020. "Fractal networks induced by movements of random walkers on a tree graph," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    17. Mark D Humphries & Javier A Caballero & Mat Evans & Silvia Maggi & Abhinav Singh, 2021. "Spectral estimation for detecting low-dimensional structure in networks using arbitrary null models," PLOS ONE, Public Library of Science, vol. 16(7), pages 1-22, July.
    18. Sun, Bingbin & Yao, Jialing & Xi, Lifeng, 2019. "Eigentime identities of fractal sailboat networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 338-349.
    19. Lu, Qing-Chang & Xu, Peng-Cheng & Zhao, Xiangmo & Zhang, Lei & Li, Xiaoling & Cui, Xin, 2022. "Measuring network interdependency between dependent networks: A supply-demand-based approach," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    20. Lambiotte, R. & Panzarasa, P., 2009. "Communities, knowledge creation, and information diffusion," Journal of Informetrics, Elsevier, vol. 3(3), pages 180-190.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:132:y:2020:i:c:s0960077919305478. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.