توسعه مفاهیم مرکزیت گراف در تحلیل و اولویت‌بندی اجزاء شبکه‌های حمل‌ونقلی

Identifying key components of urban transportation networks to enhance resilience, reduce vulnerability, and optimize traffic flow is a fundamental issue in transportation planning. In this study, an analytical framework based on graph-theoretical centrality concepts and matrix–tensor structures was developed to determine and prioritize the relative importance of network components. To this end, three incidence matrices—route–street, street–intersection, and route–intersection—were defined, and a three-dimensional tensor was constructed to represent the multilayer relationships of the network simultaneously. Degree, betweenness, and eigenvector centrality measures were then computed based on these structures and integrated through normalization and weighted aggregation. The proposed framework was implemented on the benchmark Nguyen–Dupuis network consisting of 13 nodes and 38 links. The results indicated that nodes 6, 11, and 5 exhibit the highest composite centrality values, and selecting the top five nodes covers 92.3% of the network routes. Sensitivity analysis further revealed that the tensor-based criterion can highlight inter-layer nodes that are not identified by classical methods. The findings suggest that the combined use of incidence matrices and tensor structures provides deeper insight into the functional organization of transportation networks and can support more effective strategies for maintenance prioritization, alternative route design, and system resilience enhancement.