IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v516y2019icp529-542.html
   My bibliography  Save this article

A new information dimension of complex network based on Rényi entropy

Author

Listed:
  • Duan, Shuyu
  • Wen, Tao
  • Jiang, Wen

Abstract

With the development of high technology and artificial intelligence, it evolves into an open issue to calculate the dimension of the complex network. In this paper, a new dimension — Rényi dimension, combined with Rényi entropy and information dimension is proposed. A modified box-covering algorithm is introduced to calculate the minimum number and the length of the boxes needed to cover the whole network. Additionally, the self weight factor (SWF) and the positive weight factor (PWF) are defined to illustrate the change of the dimension value based on the perspective of both topology structure and dynamic property. The concept of attractors is proposed to illuminate the physical meaning of the weighted parameter in the formula of Rényi entropy — α, PWF and SWF. Finally, to demonstrate the efficiency of our method, it is applied to calculate the dimension of Sierpinski weighted fractal network, BA networks and many real-world networks. The results show that attractors exist in the network researched and α can access the attractiveness of attractors as a criterion. The SWF quantifies the total attractiveness of attractors. The comparison results with Tsallis dimension indicate the stability of the Rényi dimension.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:516:y:2019:i:c:p:529-542
    DOI: 10.1016/j.physa.2018.10.045
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437118313931
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2018.10.045?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. Réka Albert & Hawoong Jeong & Albert-László Barabási, 1999. "Diameter of the World-Wide Web," Nature, Nature, vol. 401(6749), pages 130-131, September.
    2. 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.
    3. 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.
    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. Deng, Xinyang & Jiang, Wen & Wang, Zhen, 2019. "Zero-sum polymatrix games with link uncertainty: A Dempster-Shafer theory solution," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 101-112.
    7. Yandong Xiao & Marco Tulio Angulo & Jonathan Friedman & Matthew K. Waldor & Scott T. Weiss & Yang-Yu Liu, 2017. "Mapping the ecological networks of microbial communities," Nature Communications, Nature, vol. 8(1), pages 1-12, December.
    8. Fei, Liguo & Zhang, Qi & Deng, Yong, 2018. "Identifying influential nodes in complex networks based on the inverse-square law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 1044-1059.
    9. Yin, Likang & Deng, Yong, 2018. "Toward uncertainty of weighted networks: An entropy-based model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 176-186.
    10. Liu, Jie & Li, Yunpeng & Ruan, Zichan & Fu, Guangyuan & Chen, Xiaowu & Sadiq, Rehan & Deng, Yong, 2015. "A new method to construct co-author networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 29-39.
    11. Bandyopadhyay, Abhirup & Kar, Samarjit, 2018. "Coevolution of cooperation and network structure in social dilemmas in evolutionary dynamic complex network," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 710-730.
    12. Wang, Jiaoe & Mo, Huihui & Wang, Fahui & Jin, Fengjun, 2011. "Exploring the network structure and nodal centrality of China’s air transport network: A complex network approach," Journal of Transport Geography, Elsevier, vol. 19(4), pages 712-721.
    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. Lei, Mingli, 2022. "Information dimension based on Deng entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    2. 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.
    3. 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).
    4. 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).

    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. 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.
    2. 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.
    3. 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.
    4. 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).
    5. Ikeda, Nobutoshi, 2019. "Growth model for fractal scale-free networks generated by a random walk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 424-434.
    6. Chung-Yuan Huang & Chuen-Tsai Sun & Hsun-Cheng Lin, 2005. "Influence of Local Information on Social Simulations in Small-World Network Models," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 8(4), pages 1-8.
    7. 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.
    8. Laurienti, Paul J. & Joyce, Karen E. & Telesford, Qawi K. & Burdette, Jonathan H. & Hayasaka, Satoru, 2011. "Universal fractal scaling of self-organized networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3608-3613.
    9. Chen, Qinghua & Shi, Dinghua, 2004. "The modeling of scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(1), pages 240-248.
    10. Zhang, Zhongzhi & Rong, Lili & Comellas, Francesc, 2006. "High-dimensional random Apollonian networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 610-618.
    11. Xu, Hedong & Tian, Cunzhi & Ye, Wenxing & Fan, Suohai, 2018. "Effects of investors’ power correlations in the power-based game on networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 424-432.
    12. Rendón de la Torre, Stephanie & Kalda, Jaan & Kitt, Robert & Engelbrecht, Jüri, 2016. "On the topologic structure of economic complex networks: Empirical evidence from large scale payment network of Estonia," Chaos, Solitons & Fractals, Elsevier, vol. 90(C), pages 18-27.
    13. Kashin Sugishita & Yasuo Asakura, 2021. "Vulnerability studies in the fields of transportation and complex networks: a citation network analysis," Public Transport, Springer, vol. 13(1), pages 1-34, March.
    14. Zheng, Xiaolong & Zeng, Daniel & Li, Huiqian & Wang, Feiyue, 2008. "Analyzing open-source software systems as complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(24), pages 6190-6200.
    15. Matthew O. Jackson & Brian W. Rogers, 2005. "Search in the Formation of Large Networks: How Random are Socially Generated Networks?," Game Theory and Information 0503005, University Library of Munich, Germany.
    16. Pandey, Pradumn Kumar & Adhikari, Bibhas, 2015. "Context dependent preferential attachment model for complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 499-508.
    17. Ikeda, N., 2007. "Network formed by traces of random walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(2), pages 701-713.
    18. Çavuşoğlu, Abdullah & Türker, İlker, 2013. "Scientific collaboration network of Turkey," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 9-18.
    19. Rodrigo Huerta-Quintanilla & Efrain Canto-Lugo & Dolores Viga-de Alva, 2013. "Modeling Social Network Topologies in Elementary Schools," PLOS ONE, Public Library of Science, vol. 8(2), pages 1-9, February.
    20. Shen, Yi & Pei, Wenjiang & Wang, Kai & Li, Tao & Wang, Shaoping, 2008. "Recursive filtration method for detecting community structure in networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(26), pages 6663-6670.

    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:phsmap:v:516:y:2019:i:c:p:529-542. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.