Breakdown of the Internet under Intentional Attack

TLDR

The study investigates how random networks tolerate intentional attacks that remove a fraction p of the most connected nodes. The authors analyze scale‑free networks with a power‑law connectivity distribution using percolation theory to determine the critical attack fraction p_c and the size of the largest cluster. The results show that scale‑free networks with exponent a ≤ 3, though robust to random failures, are vulnerable to intentional attacks, with the average distance in the largest cluster scaling as √M near criticality and disruptive effects appearing before the critical threshold.

Abstract

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.