Measuring the Robustness of the European Rail and Air Networks

Abstract The robustness of international transport services is paramount for ensuring network connectivity under disruptions. We conduct a comparative analysis of the European rail and air networks of 124 main metropolitan areas, assessing their ability to withstand disruptions through the progressive failure of nodes and links. Various strategies for node selection, including targeted and random failures, are explored. During progressive node failures, network response is measured by considering the size of the largest connected component. Additionally, an aggregate network robustness metric is presented to compare networks and strategies responses. Our findings indicate that the air network exhibits significantly greater robustness compared to rail. Furthermore, original metrics are formulated for measuring the impact of nodes on network fragmentation, both at the individual level and as cluster members. Additionally, a new metric is introduced to assess cities' reliance on air transportation, when considering the integrated multi-layer air-rail network during disruptions in air connections. We discuss our findings in terms of the relationship between network structure, robustness, and the role of critical nodes.