Open Access

Attack induced cascading breakdown in complex networks

  • Liang Zhao1,
  • Kwangho Park2,
  • Ying-Cheng Lai2 and
  • Thiago Henrique Cupertino1
Journal of the Brazilian Computer Society13:BF03192546


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 capacity. 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.


complex networks scale-free networks power grids computer networks degree distribution cascading breakdown