Resilience of the Internet to Random Breakdowns

TLDR

Many large networks, including the Internet, exhibit a scale‑free power‑law connectivity distribution. The study investigates how such networks withstand random node removals. Using percolation theory, the authors derive a general condition for the critical removal fraction p(c) that causes network disintegration. Analytical and numerical results show that for exponent α≤3 the percolation transition never occurs in infinite networks, and for the Internet’s α≈2.5 the critical fraction exceeds 0.99, indicating extreme robustness.

Abstract

A common property of many large networks, including the Internet, is that the connectivity of the various nodes follows a scale-free power-law distribution, P(k) = ck(-alpha). We study the stability of such networks with respect to crashes, such as random removal of sites. Our approach, based on percolation theory, leads to a general condition for the critical fraction of nodes, p(c), that needs to be removed before the network disintegrates. We show analytically and numerically that for alpha</=3 the transition never takes place, unless the network is finite. In the special case of the physical structure of the Internet (alpha approximately 2.5), we find that it is impressively robust, with p(c)>0.99.