Analyzing vulnerabilities of the German highspeed train network using quantitative graph theory

The German high-speed train system (ICE) as one of the critical infrastructures is mapped into a distance-weighted undirected network.The aim of the analysis is to make full use of quantitative graph theory in order to analyze the vulnerabilities of the network and to detect the centers and hubs of the system.When conducting network analysis of railways, there is a tradition of such an analysis that the betweenness centrality measure and the efficiency measure would be applied; however, based on these two measures, we offer a new promising one that we call betweenness-efficiency vulnerability measure, which can be used to detect the most vulnerable nodes on an aggregated level.By analyzing and comparing the results of these three measures, highly vulnerable stations are identified, which therefore have more potential to harm the overall system in case of disruption.This can help decision-makers to understand the structure, behavior and vulnerabilities of the network more directly from the point of view of quantitative graph theory.Finally, the problem of adapting a new vulnerability measure to this kind of system is discussed.