Tolerance of scale-free networks: from friendly to intentional attack strategies

We study the tolerance of a scale-free network (having a connectivity distribution P(k) similar to k(-gamma)) under systematic variation of the attack strategy. In an attack, the probability that a given node is destroyed, depends on the number of its links k via W(k) similar to k(proportional to), where alpha varies from -infinity (most harmless attack) to +infinity (most harmful "intentional" attack). We show that the critical fraction p, needed to disintegrate the network increases monotonically when alpha is decreased and study how at p, the topology of the diluted network depends on the attack strategy. (C) 2004 Published by Elsevier B.V.