Assessment of the Water Distribution Networks in the Kingdom of Saudi Arabia: A Mathematical Model

Graph theory is a branch of mathematics that is crucial to modelling applicable systems and networks using matrix representations. In this article, a novel graph-theoretic model was used to assess an urban water distribution system (WDS) in Saudi Arabia. This graph model is based on representing its elements through nodes and links using a weighted adjacency matrix. The nodes represent the points where there can be a water input or output (sources, treatment plants, tanks, reservoirs, consumers, connections), and links represent the edges of the graph that carry water from one node to another (pipes, pumps, valves). Four WDS benchmarks, pumps, tanks, reservoirs, and external sources were used to validate the framework at first. This validation showed that the worst-case scenarios for vulnerability were provided by the fault sequence iterating the calculation of the centrality measurements. The vulnerability framework's application to the Saudi Arabian WDS enabled the identification of the system's most vulnerable junctions and zones. As anticipated, the regions with the fewest reservoirs were most at risk from unmet demand, indicating that this system is vulnerable to the removal of junctions and pipes that are intricately associated with their neighbours. Different centrality metrics were computed, from which the betweenness centrality offered the worst vulnerability prediction measures. The aspects and zones of the WDS that can more significantly impact the water supply in the event of a failure were identified by the vulnerability framework utilising attack tactics.