2000/10/31 by Reuven Cohen, Keren Erez, Daniel ben‐Avraham +2 · 8 citations
Mathematics · Physics and Astronomy · #Cluster (spacecraft) #Combinatorics #Complex Network Analysis Techniques #Computer network #Computer science #Criticality #Focus (optics) #Fraction (chemistry) #Graph #Mathematics #Nuclear physics #Opinion Dynamics and Social Influence #Percolation (cognitive psychology) #Percolation theory #Physics #Random graph #Statistical physics #Stochastic processes and statistical mechanics #Topology (electrical circuits) #cond-mat.dis-nn
paper · pdf · doi:10.1103/physrevlett.86.3682
published as Phys. Rev. Lett 86, 3682 (2001) · Latex, 4 pages, 3 eps figures
arxiv created 2001/03/29 · openalex publication_date 2001/04/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the tolerance of random networks to intentional attack, whereby a fraction p of the most connected sites is removed. We focus on scale-free networks, having connectivity distribution P(k) approximately k(-alpha), and use percolation theory to study analytically and numerically the critical fraction p(c) needed for the disintegration of the network, as well as the size of the largest connected cluster. We find that even networks with alpha < or = 3, known to be resilient to random removal of sites, are sensitive to intentional attack. We also argue that, near criticality, the average distance between sites in the spanning (largest) cluster scales with its mass, M, as square root of [M], rather than as log (k)M, as expected for random networks away from criticality.