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Optimization of robustness of complex networks

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  • G. Paul
  • T. Tanizawa
  • S. Havlin
  • H. Stanley

Abstract

Networks with a given degree distribution may be very resilient to one type of failure or attack but not to another. The goal of this work is to determine network design guidelines which maximize the robustness of networks to both random failure and intentional attack while keeping the cost of the network (which we take to be the average number of links per node) constant. We find optimal parameters for: (i) scale free networks having degree distributions with a single power-law regime, (ii) networks having degree distributions with two power-law regimes, and (iii) networks described by degree distributions containing two peaks. Of these various kinds of distributions we find that the optimal network design is one in which all but one of the nodes have the same degree, k 1 (close to the average number of links per node), and one node is of very large degree, $k_2 \sim N^{2/3}$ , where N is the number of nodes in the network. Copyright Springer-Verlag Berlin/Heidelberg 2004

Suggested Citation

  • G. Paul & T. Tanizawa & S. Havlin & H. Stanley, 2004. "Optimization of robustness of complex networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 38(2), pages 187-191, March.
    • Handle: RePEc:spr:eurphb:v:38:y:2004:i:2:p:187-191
    DOI: 10.1140/epjb/e2004-00112-3
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    1. Dorogovtsev, S.N. & Mendes, J.F.F., 2003. "Evolution of Networks: From Biological Nets to the Internet and WWW," OUP Catalogue, Oxford University Press, number 9780198515906.
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    2. 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.
    3. Deng, Ye & Wu, Jun & Tan, Yue-jin, 2016. "Optimal attack strategy of complex networks based on tabu search," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 74-81.
    4. B. G. Tóth, 2021. "The effect of attacks on the railway network of Hungary," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(2), pages 567-587, June.
    5. Yu, Yang & Deng, Ye & Tan, Suo-Yi & Wu, Jun, 2018. "Efficient disintegration strategy in directed networks based on tabu search," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 435-442.
    6. Xia Cao & Chuanyun Li & Wei Chen & Jinqiu Li & Chaoran Lin, 2020. "Research on the invulnerability and optimization of the technical cooperation innovation network based on the patent perspective—A case study of new energy vehicles," PLOS ONE, Public Library of Science, vol. 15(9), pages 1-19, September.
    7. Peng, Guan-sheng & Wu, Jun, 2016. "Optimal network topology for structural robustness based on natural connectivity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 212-220.
    8. Vitor H. P. Louzada & Fabio Daolio & Hans J. Herrmann & Marco Tomassini, "undated". "Smart rewiring for network robustness," Working Papers ETH-RC-14-004, ETH Zurich, Chair of Systems Design.
    9. Ren, Baoan & Zhang, Yu & Chen, Jing & Shen, Lincheng, 2019. "Efficient network disruption under imperfect information: The sharpening effect of network reconstruction with no prior knowledge," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 196-207.
    10. Chen, Sai & Ding, Yueting & Zhang, Yanfang & Zhang, Ming & Nie, Rui, 2022. "Study on the robustness of China's oil import network," Energy, Elsevier, vol. 239(PB).
    11. Beygelzimer, Alina & Grinstein, Geoffrey & Linsker, Ralph & Rish, Irina, 2005. "Improving network robustness by edge modification," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 357(3), pages 593-612.
    12. Feng, Zhidan & Song, Huimin & Qi, Xingqin, 2024. "A novel algorithm for the generalized network dismantling problem based on dynamic programming," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    13. Yan, Xin & Li, Chunlin & Zhang, Ling & Hu, Yaogai, 2016. "A new method optimizing the subgraph centrality of large networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 373-387.
    14. Yang, Zhirou & Liu, Jing, 2018. "A memetic algorithm for determining the nodal attacks with minimum cost on complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 1041-1053.
    15. Wu, Jian-Jun & Gao, Zi-You & Sun, Hui-jun, 2008. "Optimal traffic networks topology: A complex networks perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(4), pages 1025-1032.
    16. 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).
    17. Ichinose, Genki & Tsuchiya, Tomohiro & Watanabe, Shunsuke, 2021. "Robustness of football passing networks against continuous node and link removals," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    18. Das, Sai Saranga & Raman, Karthik, 2022. "Effect of dormant spare capacity on the attack tolerance of complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 598(C).
    19. 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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