Research on the controllability robustness of urban subway networks under node attacks

Urban subway systems are essential for the efficient operation of modern cities, but their operational reliability is vulnerable to a range of risks, including technical failures, natural disasters, and vandalism. This study examines the controllability robustness of urban subway networks, with a particular focus on their ability to remain controllable after partial network failures. Using graph theory and control theory, we evaluate and analyze the controllability robustness by simulating random failures and deliberate attacks on nodes. We introduce the concept of connected component turning points, which is a key factor affecting the controllability robustness of urban subway networks. This hypothesis is verified by simulations of model networks and real-world cases including the urban subway networks of Shanghai, Xi'an and Tianjin.