Node Criticality Estimation in Intermodal Networks

The Critical Node Problem (CNP) is a network optimisation challenge focused on identifying a subset of nodes whose removal most significantly impacts network connectivity. This problem has broad applications in areas such as network security, infrastructure resilience, and social network analysis. Its complexity arises from the need to evaluate the influence of node removals on network structure under various constraints and multiple objectives. This study introduces a novel node criticality estimation framework for intermodal networks, integrating centrality measures with congestion-aware freight redistribution. The proposed method combines graph-theoretical indicators (degree, betweenness, closeness) with operational data from an intermodal transhipment problem that accounts for terminal capacities, transport costs and emissions. This integration enables a more realistic assessment of node importance based on both topological and flow-based impacts. A comparative analysis demonstrates the advantages of this model in terms of faster operational recovery of the disrupted network. Using a case study of a European freight transport network, the closure of a single node is simulated through a subnetwork to demonstrate its high impact on the overall network’s efficiency and flow resilience. It addresses the following questions: which node in the network is the most significant? What is the geographical extent of the disruption of that node? The results highlight the importance of highly connected terminals, intermodal transfer points, and their role in maintaining networks’ efficiency.