Identifying Critical Components in Infrastructure Networks Using Network Topology

Abstract

This paper applies graph theory metrics to network flow models, with the aim of assessing the possibility of using these metrics to identify vulnerable areas within infrastructure systems. To achieve this, a reduced complexity flow model that can be used to simulate flows in infrastructure networks is developed. The reason for developing this model is not to make the analysis easier, but to reduce the physical problem to its most basic level and therefore produce the most general flow model (i.e., applicable to the widest range of infrastructure networks). An initial assessment of the applicability of graph theory metrics to infrastructure networks is made by comparing the distribution of flows, calculated using this model, to the shortest average path length in three of the most recognized classes of network—scale-free networks, small-world networks, and random graph models—and it is demonstrated that for all three classes of network there is a strong correlation. This suggests that at least parts of graph theory may be used to inform one about the behavior of physical networks. The authors further demonstrate the utility of graph theory metrics by using them to improve their predictive skill in identifying vulnerable areas in a specific type of infrastructure system. This is done using a hydraulic model to calculate the flows in a sample water distribution network and then to show that using a combination of graph theory metrics and flow gives superior predictive skill over just one of these measures in isolation.