IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v161y2022ics096007792200474x.html
   My bibliography  Save this article

A betweenness structural entropy of complex networks

Author

Listed:
  • Zhang, Qi
  • Li, Meizhu

Abstract

The structural entropy of the complex networks quantifies the static network's topological structure complexity. The definition of structural entropy is based on the Shannon information entropy and the structural components of each node. The traditional structural entropy of the complex networks is based on the degree distribution of nodes in the network. However, the degree-structural entropy is not always effective, especially when the topology structure change is under the same degree distribution. The isotopic networks with the same node's degree distribution but different structural complexity show that the definition of the structural entropy needs to base on different structural components. In this work, we propose the betweenness structural entropy of complex networks to quantify the structural complexity of static networks. Simultaneously, several processes of network growth with different seed networks under different growth rules are built in this work. These processes offer a series of networks that can be used to check how the structural entropy of the networks changes in network growth, both the degree and betweenness structural entropy. We find that the betweenness structural entropy is always smaller than the degree structural entropy of the same network. We also defined the structural entropy ratio to quantify the relative difference between the betweenness structural entropy and the degree structural entropy. Surprisingly, we find that the difference between the networks' structural entropies (degree and betweenness structural entropy) gives a new measurement to quantify the network's structure stability. This finding inspired us that the difference in different structural entropy can be used as a new structural complexity measurement for the networks: the structural entropy ratio. When the structural entropy ratio for a network is big, the network's topology structure is not stable.

Suggested Citation

  • Zhang, Qi & Li, Meizhu, 2022. "A betweenness structural entropy of complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:chsofr:v:161:y:2022:i:c:s096007792200474x
    DOI: 10.1016/j.chaos.2022.112264
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007792200474X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.112264?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. Christian von Mering & Roland Krause & Berend Snel & Michael Cornell & Stephen G. Oliver & Stanley Fields & Peer Bork, 2002. "Comparative assessment of large-scale data sets of protein–protein interactions," Nature, Nature, vol. 417(6887), pages 399-403, May.
    2. Dror Kenett & Shlomo Havlin, 2015. "Network science: a useful tool in economics and finance," Mind & Society: Cognitive Studies in Economics and Social Sciences, Springer;Fondazione Rosselli, vol. 14(2), pages 155-167, November.
    3. Elad Schneidman & Michael J. Berry & Ronen Segev & William Bialek, 2006. "Weak pairwise correlations imply strongly correlated network states in a neural population," Nature, Nature, vol. 440(7087), pages 1007-1012, April.
    4. 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.
    5. Zareie, Ahmad & Sheikhahmadi, Amir & Fatemi, Adel, 2017. "Influential nodes ranking in complex networks: An entropy-based approach," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 485-494.
    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. Zhao, Tong & Li, Zhen & Deng, Yong, 2023. "Information fractal dimension of Random Permutation Set," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Huifang Liu & Xiaoyi Shi & Pengwei Yuan & Xiaoqing Dong, 2022. "Study on the Evolution of Multiple Network Resilience of Urban Agglomerations in the Yellow River Basin," Sustainability, MDPI, vol. 14(18), pages 1-24, September.

    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. Wang, Xiaojie & Slamu, Wushour & Guo, Wenqiang & Wang, Sixiu & Ren, Yan, 2022. "A novel semi local measure of identifying influential nodes in complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    2. Lipovetsky, Stan, 2018. "Quantum paradigm of probability amplitude and complex utility in entangled discrete choice modeling," Journal of choice modelling, Elsevier, vol. 27(C), pages 62-73.
    3. Mark L Ioffe & Michael J Berry II, 2017. "The structured ‘low temperature’ phase of the retinal population code," PLOS Computational Biology, Public Library of Science, vol. 13(10), pages 1-31, October.
    4. Katarína Bod’ová & Enikő Szép & Nicholas H Barton, 2021. "Dynamic maximum entropy provides accurate approximation of structured population dynamics," PLOS Computational Biology, Public Library of Science, vol. 17(12), pages 1-22, December.
    5. MohammadReza Zahedian & Mahsa Bagherikalhor & Andrey Trufanov & G. Reza Jafari, 2022. "Financial Crisis in the Framework of Non-zero Temperature Balance Theory," Papers 2202.03198, arXiv.org.
    6. Shekhtman, Louis M. & Danziger, Michael M. & Havlin, Shlomo, 2016. "Recent advances on failure and recovery in networks of networks," Chaos, Solitons & Fractals, Elsevier, vol. 90(C), pages 28-36.
    7. X. Zhang & L. D. Valdez & H. E. Stanley & L. A. Braunstein, 2019. "Modeling Risk Contagion in the Venture Capital Market: A Multilayer Network Approach," Complexity, Hindawi, vol. 2019, pages 1-11, December.
    8. Gaëlle Desbordes & Jianzhong Jin & Chong Weng & Nicholas A Lesica & Garrett B Stanley & Jose-Manuel Alonso, 2008. "Timing Precision in Population Coding of Natural Scenes in the Early Visual System," PLOS Biology, Public Library of Science, vol. 6(12), pages 1-11, December.
    9. Yasser Roudi & Sheila Nirenberg & Peter E Latham, 2009. "Pairwise Maximum Entropy Models for Studying Large Biological Systems: When They Can Work and When They Can't," PLOS Computational Biology, Public Library of Science, vol. 5(5), pages 1-18, May.
    10. Maulana, Ardian & Situngkir, Hokky, 2015. "Korelasi Bebas-skala dalam Studi Geo-politik Pemilihan [Scale-free correlation within Geopolitics of Election Studies]," MPRA Paper 66351, University Library of Munich, Germany.
    11. 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).
    12. Mingshuo Nie & Dongming Chen & Dongqi Wang, 2022. "Graph Embedding Method Based on Biased Walking for Link Prediction," Mathematics, MDPI, vol. 10(20), pages 1-13, October.
    13. Hideaki Shimazaki & Shun-ichi Amari & Emery N Brown & Sonja Grün, 2012. "State-Space Analysis of Time-Varying Higher-Order Spike Correlation for Multiple Neural Spike Train Data," PLOS Computational Biology, Public Library of Science, vol. 8(3), pages 1-27, March.
    14. Zareie, Ahmad & Sheikhahmadi, Amir, 2019. "EHC: Extended H-index Centrality measure for identification of users’ spreading influence in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 141-155.
    15. Timothy R Lezon & Ivet Bahar, 2010. "Using Entropy Maximization to Understand the Determinants of Structural Dynamics beyond Native Contact Topology," PLOS Computational Biology, Public Library of Science, vol. 6(6), pages 1-12, June.
    16. Xiaoyuan Liu & Hayato Ushijima-Mwesigwa & Avradip Mandal & Sarvagya Upadhyay & Ilya Safro & Arnab Roy, 2022. "Leveraging special-purpose hardware for local search heuristics," Computational Optimization and Applications, Springer, vol. 82(1), pages 1-29, May.
    17. Sacha Jennifer van Albada & Moritz Helias & Markus Diesmann, 2015. "Scalability of Asynchronous Networks Is Limited by One-to-One Mapping between Effective Connectivity and Correlations," PLOS Computational Biology, Public Library of Science, vol. 11(9), pages 1-37, September.
    18. Sahar Gelfman & Quanli Wang & Yi-Fan Lu & Diana Hall & Christopher D Bostick & Ryan Dhindsa & Matt Halvorsen & K Melodi McSweeney & Ellese Cotterill & Tom Edinburgh & Michael A Beaumont & Wayne N Fran, 2018. "meaRtools: An R package for the analysis of neuronal networks recorded on microelectrode arrays," PLOS Computational Biology, Public Library of Science, vol. 14(10), pages 1-20, October.
    19. Jason S Prentice & Olivier Marre & Mark L Ioffe & Adrianna R Loback & Gašper Tkačik & Michael J Berry II, 2016. "Error-Robust Modes of the Retinal Population Code," PLOS Computational Biology, Public Library of Science, vol. 12(11), pages 1-32, November.
    20. 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).

    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:161:y:2022:i:c:s096007792200474x. 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.