Modified localized attack on complex network

Since a shell structure contains a wealth of information, it is not only very important for understanding the transport properties of the network, but also essential to identify influential spreaders in complex networks. Nodes within each shell can be classified into two categories: protected nodes and unprotected nodes. In this paper, we propose a generalization of the localized attack, modified localized attack, which means that when a randomly chosen node (root node) is under attack, protected nodes will not be removed, but unprotected nodes in the nearest shells will fail. We numerically and analytically study the system robustness under this attack by taking an Erdos-Renyi (ER) network, a regular random (RR) network and a scale-free (SF) network as examples. Moreover, a fraction of nodes belonging to giant component S and a critical threshold qc, where S approaches to zero, are given. The result implies that increasing connection density has been found to be useful to significantly improve network robustness. Copyright (C) EPLA, 2016