OPEN ACCESS
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.
betweenness centrality, efficiency, quantitative graph theory, vulnerability analysis
[1] Rinaldi, S.M., Modeling and simulating critical infrastructures and their interdependencies. In: Proceedings of the 37th annual Hawaii international conference on System sciences, pp. 1–8, 2004. https://doi.org/10.1109/hicss.2004.1265180
[2] ICE-Netz. Deutsche Bahn, 2016, available at https://www.bahn.de/p/view/service/fahrplaene/streckennetz.shtml (accessed 07 March, 2017).
[3] Dehmer, M. & Emmert-Streib, F., Quantitative Graph Theory: Mathematical Foundations and Applications. CRC Press, 2014.
[4] Dehmer, M., Emmert-Streib, F. & Pickl, S., Computational Network Theory: Theoretical foundations and applications. Wiley-VCH Verlang GmbH & Co. KGaA, Weinheim, 2015.
[5] Freeman, L.C., Centrality in social networks conceptual clarification. Social Networks, 1, pp. 215–239, 1978. https://doi.org/10.1016/0378-8733(78)90021-7
[6] Latora, V. & Marchiori, M., Economic small-world behavior in weighted networks. The European Physical Journal B-Condensed Matter and Complex Systems, 32(2), pp. 249–263, 2003. https://doi.org/10.1140/epjb/e2003-00095-5
[7] Nistor, M.S., Pickl, S., Raap, M. & Zsifkovits, M., Network efficiency and vulnerability analysis using the flow-weighted efficiency measure. International Transactions in Operational Research, 2017. https://doi.org/10.1111/itor.12384
[8] Dangalchev, C., Residual closeness in networks. Physica A: Statistical Mechanics and its Applications, 365, pp. 556–564, 2006. https://doi.org/10.1016/j.physa.2005.12.020
[9] Buldyrev, S. V., Parshani, R., Paul, G., Stanley, H.E. & Havlin, S., Catastrophic cascade of failures in interdependent networks. Nature, 464, pp. 1025–1028, 2010. https://doi.org/10.1038/nature08932
[10] Gao, J., Buldyrev, S.V., Havlin, S. & Stanley, H.E., Robustness of a network of networks. Physical Review Letters, 107(19), 2011. https://doi.org/10.1103/physrevlett.107.195701