Application of Graph Theory to Analyze Gaps in Water and Utility Networks to Enhance the Resilience of Urban Infrastructure

This work investigates the potential application of graph theory to understand the vulnerability of urban water and utility networks (graph theory provides opportunities to enable resilience in urban water and utility networks) and models urban water and utilities as a structurally functional model of the main water and utility components as graphs, with the critical components (water treatment plant, pumping station and/or distribution terminal) being the nodes and the pipes, power lines and/or other conduits connecting one to another being the edges. Graph theory can be used to diagnose systematically and more rigorously the most structurally vulnerable and operationally inefficient points in the last-mile logistics of complex infrastructures. Some of the simplest graph-theoretical applications, including connectivity and centrality, clustering coefficients and network analysis tools, are used to identify critical disconnections, bottlenecks and single points of failure that can impact the performance of a water or utility network under stressors (such as natural disasters, cyberattacks and equipment failure). Data will also measure the level of connectivity of the networks, as well as how much less a utility truly is once a node/edge has been removed, and how to use graph theory to find these nodes/edges. The paper also highlighted practical steps to optimization that service providers can work on to become a resilient and continue providing services in the event of a failure, such as improving network redundancy, re-routing critical paths and prioritizing on upgrading. This work has led to a novel approach to modelling flexible and resilient infrastructural fabric that can withstand and be resilient to disruption in measurable and scalable ways using the incorporation of graph theory and urban planning. The recommendations provide valuable guidance for policymakers, engineers, city planners and others as they seek to advance future-proofing utility networks and services in the face of environmental and human impacts. The study provides a mathematically precise quantification of vulnerability and resilience by representing urban water and utility systems as weighted graphs in the mathematical literature and applying matrix representation, spectral graph theory and flow-based optimization. We are able to give explicit mathematical formulae for these connectivity and centrality metrics, as well as for those of robustness and resilience, which make the assessment of such infrastructure systems reproducible and give principles for improving them.