Breakdown of the internet under intentional attack.

By R. Cohen, Keren Erez, Daniel ben-Avraham, Shlomo Havlin. Physical Review Letters, 2000

1,317 citations recorded by the source corpus.

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.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/79ebadceb03ebab290bfa88e19fc7cd19ca47386

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Citations in the corpus

Statistical mechanics of complex networks (2001, background): “The theoretical framework of Cohen et al. (2000) can also be extended to the case of intentional attack on a scale-free network with degree distribution (136) (Cohen et al., 2001).”
Networks formed from interdependent networks (2011, background): “The percolation approach was also proved to be extremely useful in addressing other scenarios, such as efficient attacks or immunization 6,7,54,55 , and for obtaining optimal paths 56 aswellasfordesigningrobustnetworks 53 .”
Emergence of network features from multiplexity (2012, neutral): “The results are shown in Fig.”
Catastrophic cascade of failures in interdependent networks (2009, background): “pology of their network like, Internet, airport connections, and power grids [7]. Recently, special emphasis has been focused on the robustness of such systems to random failures or malicious attacks [8, 9, 10, 11, 12, 13, 14]. Most of these works have been focused on single, isolated networks where”
Network resilience (2020, background): “While performing a critical role in the networks, rich-club nodes are also the targets of intentional attacks [607].”
With Great Training Comes Great Vulnerability: Practical Attacks against Transfer Learning (2018, background): “increasing the impact of targeted attacks on network hubs [21], supernodes in overlay networks [54], and the impact of software vulnerabilities in popular libraries [71, 22].”
Vital nodes identification in complex networks (2016, methodology): “Heuristic algorithms The most straightforward method is to directly pick up the top-k nodes subject to some certain centrality measures, such as degree and betweenness [22, 23, 13].”
Statistical physics of vaccination (2016, background): “and the degree distribution of the resulting network becomes [275, 290]”