Resilience of the Internet to Random Breakdowns
Abstract
A common property of many large networks, including the Internet, is that the connectivity of the various nodes follows a scalefree powerlaw distribution, P\(k\) = ck^{α}. 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 α<=3 the transition never takes place, unless the network is finite. In the special case of the physical structure of the Internet \(α~2.5\), we find that it is impressively robust, with p_{c}>0.99.
 Publication:

Physical Review Letters
 Pub Date:
 November 2000
 DOI:
 10.1103/PhysRevLett.85.4626
 arXiv:
 arXiv:condmat/0007048
 Bibcode:
 2000PhRvL..85.4626C
 Keywords:

 Condensed Matter  Disordered Systems and Neural Networks
 EPrint:
 latex, 3 pages, 1 figure (eps), explanations added, Phys. Rev. Lett., in press