Graph Theory Approach to the Vulnerability of Transportation Networks

Abstract

Nowadays, transport is the basis for the functioning of national, continental, and global economies. Thus, many governments recognize it as a critical element in ensuring the daily existence of societies in their countries. Those responsible for the proper operation of the transport sector must have the right tools to model, analyze, and optimize its elements. One of the most critical problems is the need to prevent bottlenecks in transport networks. Thus, the main aim of the article was to define the parameters characterizing the transportation network vulnerability and select algorithms to support their search. The parameters proposed are based on characteristics related to domination in graph theory. The domination, edge-domination concepts, and related topics, such as bondage-connected and weighted bondage-connected numbers, were applied as the tools for searching and identifying the bottlenecks in transportation networks. Furthermore, the algorithms for finding the minimal dominating set and minimal (maximal) weighted dominating sets are proposed. This way, the exemplary academic transportation network was analyzed in two cases: stationary and dynamic. Some conclusions are presented. The main one is the fact that the methods given in this article are universal and applicable to both small and large-scale networks. Moreover, the approach can support the dynamic analysis of bottlenecks in transport networks.