Identifying Critical Nodes in Cross-Border Transportation Networks Under Geopolitical Risk

Cross-border transportation networks show considerable complexity and vulnerability under the influence of geopolitical risks. To identify critical nodes and simulate the propagation paths of failure risk within cross-border transportation networks, this study develops a multilayer cross-border transportation network model that integrates four transport modes: waterway, road, rail, and air transport. First, composite edge weights are calculated using the Criteria Importance Through Intercriteria Correlation (CRITIC) method based on inter-node transport distance, transport time, and geopolitical risk (GPR) exposure score. These weights capture the joint effects of transport efficiency and risk exposure across different transport corridors. Second, an Improved Weighted K-shell (IWKS) model is proposed for critical-node identification by integrating three network topological indicators: degree centrality, weighted degree, and closeness centrality. Third, an edge-risk-based Susceptible–Infected–Recovered (SIR) propagation model is introduced. Monte Carlo simulations are then used to estimate the simulation-based propagation influence of each node. Finally, the identification performance of the IWKS model is compared with that of conventional centrality indicators. The IWKS scores are also significantly correlated with the simulation-based propagation influence under three types of correlation tests. The findings support the applicability of the proposed IWKS model in critical-node identification and system vulnerability research of multilayer cross-border integrated transportation networks.