Attack Induced Cascading Breakdown in Complex Networks

The possibility that a complex network can be brought down by attack on a single or very few nodes through the process of cascading failures is of significant concern. In this paper, we investigate cascading failures in complex networks and uncover a phase-transition phenomenon in terms of the key parameter characterizing the node capac-ity. For parameter value below the phase-transition point, cascading failures can cause the network to disintegrate almost entirely. Then we show how to design networks of finite capacity that are safe against cascading breakdown. Our theory yields estimates for the maximally achievable network integrity via controlled removal of a small set of low-degree nodes