Optimization of Network Robustness to Random Breakdowns

Gerald Paul; Sameet Sreenivasan; Shlomo Havlin; H. Eugene Stanley

doi:10.1016/j.physa.2006.02.044

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arXiv · cond-mat/0507249

Optimization of Network Robustness to Random Breakdowns

Gerald Paul·Sameet Sreenivasan·Shlomo Havlin·H. Eugene Stanley

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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 $\kav$. We find that the network design that maximizes $f_c$, the fraction of nodes that are randomly removed before global connectivity is lost, consists of $q=[(\kav-1)/\sqrt\kav]\sqrt N$ high degree nodes (``hubs'') of degree $\sqrt{\kav N}$ and $N-q$ nodes of degree 1. Also, we show that $1-f_c$ approaches 0 as $1/\sqrt N$--faster than any other network configuration including scale-free networks. We offer a simple heuristic argument to explain our results.

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Gerald Paul, Sameet Sreenivasan, Shlomo Havlin, H. Eugene Stanley. 2005-07-11. Optimization of Network Robustness to Random Breakdowns. https://doi.org/10.1016/j.physa.2006.02.044

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