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Optimization of network robustness to random breakdowns

Author

Listed:
  • Paul, Gerald
  • Sreenivasan, Sameet
  • Havlin, Shlomo
  • Eugene Stanley, H.

Abstract

We study network configurations that provide optimal robustness to random breakdowns for networks with a given number of nodes N and a given cost—which we take as the average number of connections per node 〈k〉. We find that the network design that maximizes fc, the fraction of nodes that are randomly removed before global connectivity is lost, consists of q=[(〈k〉-1)/〈k〉]N high degree nodes (“hubs”) of degree 〈k〉N and N-q nodes of degree 1. Also, we show that 1-fc approaches 0 as 1/N—faster than any other network configuration including scale-free networks. We offer a simple heuristic argument to explain our results.

Suggested Citation

  • Paul, Gerald & Sreenivasan, Sameet & Havlin, Shlomo & Eugene Stanley, H., 2006. "Optimization of network robustness to random breakdowns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 854-862.
    • Handle: RePEc:eee:phsmap:v:370:y:2006:i:2:p:854-862
    DOI: 10.1016/j.physa.2006.02.044
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    Citations

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    Cited by:

    1. Sun, Shiwen & Li, Ruiqi & Wang, Li & Xia, Chengyi, 2015. "Reduced synchronizability of dynamical scale-free networks with onion-like topologies," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 249-256.
    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. Kyu-Min Lee & Jae-Suk Yang & Gunn Kim & Jaesung Lee & Kwang-Il Goh & In-mook Kim, 2010. "Impact of the topology of global macroeconomic network on the spreading of economic crises," Papers 1011.4336, arXiv.org, revised Apr 2011.
    4. Kyu-Min Lee & Jae-Suk Yang & Gunn Kim & Jaesung Lee & Kwang-Il Goh & In-mook Kim, 2011. "Impact of the Topology of Global Macroeconomic Network on the Spreading of Economic Crises," PLOS ONE, Public Library of Science, vol. 6(3), pages 1-11, March.
    5. 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.

    More about this item

    Keywords

    Network robustness; Random breakdown;

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