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-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, pc, 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 pc>0.99.
Physical Review Letters
- Pub Date:
- November 2000
- Condensed Matter - Disordered Systems and Neural Networks
- latex, 3 pages, 1 figure (eps), explanations added, Phys. Rev. Lett., in press