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Entropy optimization of scale-free networks’ robustness to random failures

Author

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  • Wang, Bing
  • Tang, Huanwen
  • Guo, Chonghui
  • Xiu, Zhilong

Abstract

Many networks are characterized by highly heterogeneous distributions of links which are called scale-free networks, and the degree distributions follow p(k)∼ck-α. We study the robustness of scale-free networks to random failures from the character of their heterogeneity. Entropy of the degree distribution can be an average measure of a network's heterogeneity. Optimization of scale-free networks’ robustness to random failures with average connectivity constant is equivalent to maximizing the entropy of the degree distribution. By examining the relationship of the entropy of the degree distribution, scaling exponent and the minimal connectivity, we get the optimal design of scale-free networks to random failures. We conclude that the entropy of the degree distribution is an effective measure of network's resilience to random failures.

Suggested Citation

  • Wang, Bing & Tang, Huanwen & Guo, Chonghui & Xiu, Zhilong, 2006. "Entropy optimization of scale-free networks’ robustness to random failures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 591-596.
    • Handle: RePEc:eee:phsmap:v:363:y:2006:i:2:p:591-596
    DOI: 10.1016/j.physa.2005.08.025
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    Cited by:

    1. Billio, Monica & Casarin, Roberto & Costola, Michele & Pasqualini, Andrea, 2016. "An entropy-based early warning indicator for systemic risk," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 45(C), pages 42-59.
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    3. Zhen Chen & Jun Zhang & Wen-Bo Du & Oriol Lordan & Jiangjun Tang, 2015. "Optimal Allocation of Node Capacity in Cascade-Robustness Networks," PLOS ONE, Public Library of Science, vol. 10(10), pages 1-12, October.
    4. Hu, Ping & Mei, Ting, 2018. "Ranking influential nodes in complex networks with structural holes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 624-631.
    5. 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.
    6. Lin, Li & Guo, Xin-Yu, 2019. "Identifying fragility for the stock market: Perspective from the portfolio overlaps network," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 62(C), pages 132-151.
    7. Dong, Gaogao & Tian, Lixin & Du, Ruijin & Fu, Min & Stanley, H. Eugene, 2014. "Analysis of percolation behaviors of clustered networks with partial support–dependence relations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 370-378.
    8. Liu, Jiming & Shi, Benyun, 2012. "Towards understanding the robustness of energy distribution networks based on macroscopic and microscopic evaluations," Energy Policy, Elsevier, vol. 49(C), pages 318-327.
    9. Umut Yılmaz Çetinkaya & Erkan Erdil, 2016. "Cohesion and Competition of Europe: Innovation Policy from the Perspective of Networks and Entropy," Foresight-Russia Форсайт, CyberLeninka;Федеральное государственное автономное образовательное учреждение высшего образования «Национальный исследовательский университет «Высшая школа экономики», vol. 10(4 (eng)), pages 7-24.
    10. Ou, Ruiqiu & Yang, Jianmei, 2012. "On structural properties of scale-free networks with finite size," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 887-894.
    11. Umut Yilmaz Cetinkaya & Erkan Erdil, 2015. "Cohesion and Competition of Europe: Policy Suggestions from The Perspective of Network and Entropy," STPS Working Papers 1505, STPS - Science and Technology Policy Studies Center, Middle East Technical University, revised Dec 2015.
    12. 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).
    13. Belkoura, Seddik & Cook, Andrew & Peña, José Maria & Zanin, Massimiliano, 2016. "On the multi-dimensionality and sampling of air transport networks," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 94(C), pages 95-109.
    14. Zanin, Massimiliano, 2014. "Network analysis reveals patterns behind air safety events," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 201-206.
    15. Milena Oehlers & Benjamin Fabian, 2021. "Graph Metrics for Network Robustness—A Survey," Mathematics, MDPI, vol. 9(8), pages 1-48, April.
    16. Zanin, Massimiliano, 2015. "Can we neglect the multi-layer structure of functional networks?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 430(C), pages 184-192.
    17. Vodák, Rostislav & Bíl, Michal & Sedoník, Jiří, 2015. "Network robustness and random processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 368-382.

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