Vulnerability of complex networks under multiple node-based attacks

We investigate the vulnerability of complex networks under different node-based attacks. The networks considered include scale-free network (SF), WS small-world network model, ER network and two real-world networks (autonomous system network and Italy power grid). The attacks are induced by removing the nodes in the descending order of the four kinds of weights defined in this paper. By measuring the relative size of the giant component and the average efficiency, the simulations demonstrate that, the kshell index-based attack can more effectively break the connectivity and the functionality of SF network and also is more harmful in reducing the efficiency of ER network. WS network shows more sensitive under the degree-based attack. Interestingly, the degree-based attack can more effectively break the connectivity and reduce the efficiency of the two real-world networks, which is similar to WS small-world network. The findings highlight the identification of key nodes in protecting the real-world networks.