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)∼k−γ) 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)∼kα, where α varies from −∞ (most harmless attack) to +∞ (most harmful “intentional” attack). We show that the critical fraction pc needed to disintegrate the network increases monotonically when α is decreased and study how at pc the topology of the diluted network depends on the attack strategy.