Identification of Critical Nodes in Urban Subway Network Using Temporal Network ConceptCase Study: Tehran Urban Subway Network

The urban subway network is one of the most vital infrastructures that plays a pivotal role in the sustainable development of cities; therefore, network robustness or maintaining the proper performance in various conditions has great importance. Considering financial and functional limitations, identifying critical nodes is required to prioritize robustness enhance projects. Critical nodes are nodes that their removal deeply affects the connectivity and efficiency of the network. Network robustness and identification of critical nodes in the face of cascading disruptions have been studied, focusing on the network's structural features. On the one hand, cascading disturbances affect several stations simultaneously, which is less likely to occur than concentrated disturbances that affect only one station. On the other hand, focusing on the network structure leads to the loss of dynamic information, resulting in underestimating the length and overestimating the number of paths between network nodes. In this study, the critical nodes in the face of centralized disturbances have been identified using temporal network concepts, which consider both structural and temporal features. The results reveal that Darvazeh-Shemiran, Shadman, Shahid Beheshti, and Mohammadieh Square stations are the critical stations from both efficiency and connectivity points of view. The critical nodes have high values of static and temporal centrality indices, which increase network vulnerability against malicious attacks. In contrast, due to the high ratio of non-critical nodes to critical nodes, the network is robust against random failures. The method developed in this research can be generalized to other transportation networks.