Dismantling complex networks based on the principal eigenvalue of the adjacency matrix

Abstract

The connectivity of complex networks is usually determined by a small fraction of key nodes. Earlier works successfully identify an influential single node, yet have some problems for the case of multiple ones. In this paper, based on the matrix spectral theory, we propose the collective influence of multiple nodes. An interesting finding is that some traditionally influential nodes have strong internal coupling interactions that reduce their collective influence. We then propose a greedy algorithm to dismantle complex networks by optimizing the collective influence of multiple nodes. Experimental results show that our proposed method outperforms the state of the art methods in terms of the principal eigenvalue and the giant component of the remaining networks.