A Spectral Measure for Network Robustness: Assessment, Design, and Evolution

Shengmin Jin, Rui Ma, Jiayu Li, Sara Eftekharnejad, Reza Zafarani

Abstract: A robust system should perform well under random failures or targeted attacks, and networks have been widely used to model the underlying structure of complex systems such as communication, infrastructure, and transportation networks. Hence, network robustness becomes critical to understanding system robustness. In this paper, we propose a spectral measure for network robustness: the second spectral moment $m_{2}$ of the network. Our results show that a smaller second spectral moment $m_{2}$ indicates a more robust network. We demonstrate both theoretically and with extensive empirical studies that the second spectral moment can help (1) capture various traditional measures of network robustness; (2) assess the robustness of networks; (3) design networks with controlled robustness; and (4) study how complex networked systems (e.g., power systems) behave under cascading failures.