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Network robustness to targeted attacks. The interplay of expansibility and degree distribution

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  • E. Estrada

Abstract

We study the property of certain complex networks of being both sparse and highly connected, which is known as “good expansion” (GE). A network has GE properties if every subset S of nodes (up to 50% of the nodes) has a neighborhood that is larger than some “expansion factor” φ multiplied by the number of nodes in S. Using a graph spectral method we introduce here a new parameter measuring the good expansion character of a network. By means of this parameter we are able to classify 51 real-world complex networks — technological, biological, informational, biological and social — as GENs or non-GENs. Combining GE properties and node degree distribution (DD) we classify these complex networks in four different groups, which have different resilience to intentional attacks against their nodes. The simultaneous existence of GE properties and uniform degree distribution contribute significantly to the robustness in complex networks. These features appear solely in 14% of the 51 real-world networks studied here. At the other extreme we find that ∼40% of all networks are very vulnerable to targeted attacks. They lack GE properties, display skewed DD — exponential or power-law — and their topologies are changed more dramatically by targeted attacks directed at bottlenecks than by the removal of network hubs. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

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  • E. Estrada, 2006. "Network robustness to targeted attacks. The interplay of expansibility and degree distribution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 52(4), pages 563-574, August.
    • Handle: RePEc:spr:eurphb:v:52:y:2006:i:4:p:563-574
    DOI: 10.1140/epjb/e2006-00330-7
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    Citations

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    Cited by:

    1. Wen, Xiangxi & Tu, Congliang & Wu, Minggong, 2018. "Node importance evaluation in aviation network based on “No Return” node deletion method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 546-559.
    2. Duan, Boping & Liu, Jing & Zhou, Mingxing & Ma, Liangliang, 2016. "A comparative analysis of network robustness against different link attacks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 448(C), pages 144-153.
    3. Sohn, Insoo, 2019. "A robust complex network generation method based on neural networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 593-601.
    4. Pietro DeLellis & Anna DiMeglio & Franco Garofalo & Francesco Lo Iudice, 2017. "The evolving cobweb of relations among partially rational investors," PLOS ONE, Public Library of Science, vol. 12(2), pages 1-21, February.
    5. Estrada, Ernesto, 2007. "Graphs (networks) with golden spectral ratio," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1168-1182.
    6. Antonio Candelieri & Bruno G. Galuzzi & Ilaria Giordani & Francesco Archetti, 2019. "Vulnerability of public transportation networks against directed attacks and cascading failures," Public Transport, Springer, vol. 11(1), pages 27-49, June.
    7. LaRocca, Sarah & Guikema, Seth D., 2015. "Characterizing and predicting the robustness of power-law networks," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 157-166.
    8. Ma, Xiangyu & Zhou, Huijie & Li, Zhiyi, 2021. "On the resilience of modern power systems: A complex network perspective," Renewable and Sustainable Energy Reviews, Elsevier, vol. 152(C).
    9. 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.
    10. Heng Ye & Zhiping Li & Guangyue Li & Yiran Liu, 2022. "Topology Analysis of Natural Gas Pipeline Networks Based on Complex Network Theory," Energies, MDPI, vol. 15(11), pages 1-20, May.

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