Graph Theory and Its Role in Vulnerability Evaluation of Infrastructure Networks

Infrastructure Networks (INs) have reached a level of complexity where conventional vulnerability analysis methods cannot fulfil the challenges for the management of this increasing complexity. There is, therefore, a need for a complementary approach through which the structural complexity and the level of interaction among the components are studied. In this context, researchers have increasingly looked into graph theory for help in understanding the structure, efficiency, and vulnerability of INs. The desire to employ the graph theory has resulted in the proliferation of a wide range of topological metrics. To gain a better appreciation for how various graph theory quantities have been used for vulnerability evaluation of INs, this chapter documents a variety of concepts from graph theory in one place and presents an overview of the application of graph theory in the field of INs. It also reviews the conceptions of the four widely used vulnerability-averse indicators of INs, which are reliability, resilience, robustness, and redundancy. The conventional graph theory methods are criticized on several grounds and the future evolution of graph theory tools is forecast.