Optimization of network robustness to random breakdowns

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

Research output: Contribution to journalArticlepeer-review

38 Scopus citations


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) / sqrt(〈) k 〉] sqrt(N) high degree nodes ("hubs") of degree sqrt(〈 k 〉 N) and N - q nodes of degree 1. Also, we show that 1 - fc 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.

Original languageEnglish
Pages (from-to)854-862
Number of pages9
JournalPhysica A: Statistical Mechanics and its Applications
Issue number2
StatePublished - 15 Oct 2006


  • Network robustness
  • Random breakdown


Dive into the research topics of 'Optimization of network robustness to random breakdowns'. Together they form a unique fingerprint.

Cite this