Fig. 4
From: Multi-modal and multi-layer robustness analysis of the European rail and air networks
The mean profile of the betweenness centrality (b) for the single node of Paris (left) and aggregated by clusters of nodes (right) is presented. The profile for the Paris node shows that this coefficient is an indicator representing the role of the node within the network as a whole. As can be seen, the metric varies even in response to attacks that are not in the immediate vicinity of Paris. The clusters were generated using the profiles of all nodes, and the main identified patterns are three. C1 (orange) represents the cluster of nodes with higher initial b values, which are immediately impacted by network reduction. C2 (blue) displays an initial increase in b followed by a decline to zero. This suggests that nodes in this cluster compensate for the network reduction initially, but their betweenness decreases as x reaches 20 to 30%. C3 (cyan) consists of nodes at the periphery of the network, showing a nearly constant behavior with b values close to zero across all x values. For the three clusters, distinct breaking points are observed, where the drop in b begins at different values of x.
