2000/07/31 by Reuven Cohen, Keren Erez, Daniel ben-Avraham +1 · 1 citation
Physics and Astronomy · #cond-mat.dis-nn
paper · pdf · doi:10.1103/physrevlett.85.4626
published as Phys. Rev. Lett 85, 4626 (2000) · latex, 3 pages, 1 figure (eps), explanations added, Phys. Rev. Lett., in press
arxiv created 2000/10/19 · arxiv updated 2009/11/30
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-a. 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, pc, that need to be removed before the network disintegrates. We show that for a<=3 the transition never takes place, unless the network is finite. In the special case of the Internet (a=2.5), we find that it is impressively robust, where pc is approximately 0.99.