Identification of Critical Risk Nodes and Vulnerability Analysis in Railway Networks

As the importance of railway networks in regional transportation and economic development continues to grow, identifying critical risk nodes and assessing network vulnerability is crucial for enhancing the stability and resilience of railway systems. This study focuses on the railway network of Shandong Province, constructing a topological model to systematically analyze the structural characteristics of the network, with a particular emphasis on key nodes. To identify these critical risk nodes, four modified weighted indicators were employed, combined with the mean-square deviation TOPSIS method to quantify node importance. The analysis identified Jinan, Linyi, and Yantai as key risk nodes, as they consistently ranked high across multiple indicators. Further vulnerability analysis reveals that the failure of these critical nodes would lead to significant declines in network efficiency and connectivity, with particularly high vulnerability observed when nodes with high weighted betweenness centrality and PageRank values fail.