Source-linked AI summary
Breakdown of the Internet under intentional attack
Reuven Cohen, Keren Erez, Daniel ben-Avraham, Shlomo Havlin
TL;DR
The paper examines how scale-free networks withstand targeted removal of their highest-connectivity sites. Using analytical and numerical percolation theory, it finds strong sensitivity to sabotage, including for networks resilient to random removal, and sharply increased distances near criticality.
Problem
The paper asks how intentional removal of the most connected sites affects scale-free network stability, beyond known resilience to random site removal.
Source: p. 1Method
The authors use analytical and numerical percolation theory to calculate the disruption threshold, remaining spanning-cluster size, and distances within that cluster.
Source: pp. 1–2Results
Scale-free networks are highly sensitive to sabotage for all α, including α < 3, while near criticality spanning-cluster distances grow as sqrt(M) rather than log_k M.
Source: pp. 1, 3Takeaways & Limitations
Intentional attack can make communication inefficient before the spanning cluster is completely disrupted.
Source: pp. 1, 3The analysis assumes a truncated power-law connectivity distribution P(k) = ck^-α with minimum connectivity m and finite-network cutoff K.
Source: p. 1
Abstract
from arXiv · showhide
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 of P(k)~k^(-a) (where k is the site connectivity), 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 a<=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 sqrt(M), rather than as log_k M, as expected for random networks away from criticality. Thus, the disruptive effects of intentional attack become relevant even before the critical threshold is reached.