Graph Theory-Based Algorithm to Define District Metered Areas Considering Hydraulic Conditions

Graph theory-based methods are widely used to partition water distribution networks (WDNs) into district metered areas (DMAs). In general, the Girvan–Newman (GN) algorithm partitions networks based solely on the edge betweenness, a purely topological criterion, without considering the intrinsic hydraulic characteristics of WDNs. To address this limitation, in this study, an improved approach, named the improved Girvan–Newman (IGN) algorithm, is proposed, which integrates hydraulic parameters into the partitioning process. Specifically, pressure (as a quantity parameter) and chlorine concentration (as a quality parameter) are incorporated into the algorithm. The IGN method involves modeling the WDN as a graph, simulating it using either the demand-driven simulation method or the head-driven simulation method during a 24-h extended period simulation (EPS), and assigning nodal weights based on hydraulic values. Edge scores are then calculated using these nodal weights, and the edge with the lowest score is iteratively removed, with corresponding links closed in the hydraulic model. Then, the WDN is reanalyzed to update the hydraulic parameters. This iterative process continues until the desired number of DMAs is achieved. Two case studies, a small-scale WDN, named Poulakis, and a large-scale real WDN of Baharestan city in Isfahan, Iran, are used to investigate the performance of the IGN algorithm. In Poulakis WDN, by using IGN, the average nodal pressure decreases by 1.6%, the chlorine concentration increases by 9.1%, and the hybrid reliability improves by 3.7% compared to the standard GN algorithm. In addition, in Baharestan WDN, the related values are 5.1%, 3.4%, and 4.2%, respectively. The IGN method also enables flexible and time-dependent DMA configurations during EPS, in which the final configuration is selected based on a floating index. Here, a novel integration of hydraulic features into the GN algorithm is proposed, offering a more effective and reliable approach to WDN partitioning and management.