Onion structure optimizes attack robustness of interdependent networks

Recently, attack vulnerability of interdependent systems composed of multiple networks has attracted a great number of efforts. In this paper, how to improve the robustness of interdependent systems under attacks is addressed. With the aim of improving the robustness concerning malicious attacks on high-degree nodes, different from previous works on adjusting the coupling patterns between networks, new optimization models based on changing the inner structures of each network component are proposed. Through numerical simulations, the performance of optimization models is presented and compared with initial system without any optimization. It is found that the optimized onion structure of target network plays a positive role in improving attack robustness of the entire system. However, as more interdependent links are added between two networks, the existence of interdependent links greatly accelerates the collapse of both networks, just gradually neglecting the impact of optimized onion structure in resisting targeted attacks. Current results can help to deeply understand the structural complexity of real-world complex networks, as well as to provide practical principles in designing robust systems.