Network resilience against intelligent attacks constrained by the degree-dependent node removal cost

We study the resilience of complex networks against attacks in which nodes are targeted intelligently, but where disabling a node has a cost to the attacker which depends on its degree. Attackers have to meet these costs with limited resources, which constrains their actions. A network's integrity is quantified in terms of the efficacy of the process that it supports. We calculate how the optimal attack strategy and the most attack-resistant network degree statistics depend on the node removal cost function and the attack resources. The resilience of networks against intelligent attacks is found to depend strongly on the node removal cost function faced by the attacker. In particular, if node removal costs increase sufficiently fast with the node degree, power law networks are found to be more resilient than Poissonian ones, even against optimized intelligent attacks. For cost functions increasing quadratically in the node degrees, intelligent attackers cannot damage the network more than random damages would.