Resilience of the Internet to random breakdowns

Details Resilience of the Internet to random breakdowns Resilience of the Internet to random breakdowns

2000-07-04

arxiv.org/abs/cond-mat/0007048v2

Phys. Rev. Lett 85, 4626 (2000)

Physics

Condensed Matter

Disordered Systems and Neural Networks

latex, 3 pages, 1 figure (eps), explanations added, Phys. Rev. Lett., in press

Scientific paper

10.1103/PhysRevLett.85.4626

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, p_c, 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 p_c is approximately 0.99.

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