Onion-like network topology enhances robustness against malicious attacks

We develop a method to generate robust networks against malicious attacks, as well as to substantially improve the robustness of a given network by swapping edges and keeping the degree distribution fixed. The method, based on persistence of the size of the largest cluster during attacks, was applied to several types of networks with broad degree distributions, including a real network-the Internet. We find that our method can improve the robustness significantly. Our results show that robust networks have a novel 'onion-like' topology consisting of a core of highly connected nodes hierarchically surrounded by rings of nodes with decreasing degree.