ABSTRACT
After a failure or attack the structure of a complex network changes due to node removal. Here, we show that the degree distribution of the distorted network, under any node disturbances, can be easily computed through a simple formula. Based on this expression, we derive a general condition for the stability of noncorrelated finite complex networks under any arbitrary attack. We apply this formalism to derive an expression for the percolation threshold f_{c} under a general attack of the form f_{k} approximately k;{gamma} , where f_{k} stands for the probability of a node of degree k of being removed during the attack. We show that f_{c} of a finite network of size N exhibits an additive correction which scales as N;{-1} with respect to the classical result for infinite networks.
