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Symmetry-based structure entropy of complex networks

Author

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  • Xiao, Yang-Hua
  • Wu, Wen-Tao
  • Wang, Hui
  • Xiong, Momiao
  • Wang, Wei

Abstract

Precisely quantifying the heterogeneity or disorder of network systems is important and desired in studies of behaviors and functions of network systems. Although various degree-based entropies have been available to measure the heterogeneity of real networks, heterogeneity implicated in the structures of networks can not be precisely quantified yet. Hence, we propose a new structure entropy based on automorphism partition. Analysis of extreme cases shows that entropy based on automorphism partition can quantify the structural heterogeneity of networks more precisely than degree-based entropies. We also summarized symmetry and heterogeneity statistics of many real networks, finding that real networks are more heterogeneous in the view of automorphism partition than what have been depicted under the measurement of degree-based entropies; and that structural heterogeneity is strongly negatively correlated to symmetry of real networks.

Suggested Citation

  • Xiao, Yang-Hua & Wu, Wen-Tao & Wang, Hui & Xiong, Momiao & Wang, Wei, 2008. "Symmetry-based structure entropy of complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(11), pages 2611-2619.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:11:p:2611-2619
    DOI: 10.1016/j.physa.2008.01.027
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    Citations

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    Cited by:

    1. Singh, Priti & Chakraborty, Abhishek & Manoj, B.S., 2017. "Link Influence Entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 701-713.
    2. Ruiz Palazuelos, Sofía, 2021. "Network Perception in Network Games," MPRA Paper 115212, University Library of Munich, Germany, revised 21 Jun 0022.
    3. Zhu, Jia & Wei, Daijun, 2021. "Analysis of stock market based on visibility graph and structure entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 576(C).
    4. Asif, Muhammad & Inam, Azhar & Adamowski, Jan & Shoaib, Muhammad & Tariq, Hisham & Ahmad, Shakil & Alizadeh, Mohammad Reza & Nazeer, Aftab, 2023. "Development of methods for the simplification of complex group built causal loop diagrams: A case study of the Rechna doab," Ecological Modelling, Elsevier, vol. 476(C).
    5. Maiorino, Enrico & Livi, Lorenzo & Giuliani, Alessandro & Sadeghian, Alireza & Rizzi, Antonello, 2015. "Multifractal characterization of protein contact networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 302-313.
    6. Deng, ZhengHong & Xu, Jiwei & Song, Qun & Hu, Bin & Wu, Tao & Huang, Panfei, 2020. "Robustness of multi-agent formation based on natural connectivity," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    7. Zheng, Wen & Guan, Xin, 2020. "Measurement of DNSE based on the Linear Growth and Preferential Attachment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    8. Wang, Fei & Zheng, Xia-zhong & Li, Nan & Shen, Xuesong, 2019. "Systemic vulnerability assessment of urban water distribution networks considering failure scenario uncertainty," International Journal of Critical Infrastructure Protection, Elsevier, vol. 26(C).

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