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In general, partitioning networks into district metered areas (DMA) is known as a practical method to manage the pressure and reduce water leakage in Water Distribution Networks (WDNs). Different methods such as engineering judgment, optimization techniques, and graph theory are proposed to determine the DMA. The graph theory is a traditional method for partitioning networks including several algorithms. One of these algorithms is the Girvan-Newman (GN) algorithm which is based on the mathematical parameters without considering the characteristics of networks. In other words, the hydraulic quality and quantity condition of WDNs are not used for DMA determination. Therefore, in this research, a new method is proposed to improve the performance of the GN algorithm for DMA determination considering the quantities of water networks. For this purpose, the average values of nodal pressure and residual chlorine concentration are calculated and used simultaneously for the junction’s weight determination. Then, the edge scores are calculated based on the junction’s weights, and the edges with the maximum scores are removed until to reach the desired number of DMAs. For comparison purposes, here, the Demand-Driven Simulation Method (DDSM) and Head-Driven Simulation Method (HDSM) analyses are used for the analysis of the Poulakis WDN, selected as a case study. A comparison of the results shows that by using the proposed method, the average pressure values are decreased and the average residual chlorine concentration values are increased. In other words, the pressure values are decreased from 16.32% to 26.23% and the average residual chlorine concentration values are increased from 2.5% to 18.37% in comparison with the results of the standard form of the GN algorithm using both DDSM and HDSM analyses. Furthermore, by using the proposed method, in all scenarios, the hybrid reliability values increase in comparison with the GN algorithm. The results indicate the unique performance of the proposed method in comparison with the standard form of the GN algorithm for DMA determination of WDNs.

Implementing an inter-regional synergistic control policy for fine particulate matter (PM 2.5 ) and ground-level ozone (O 3 ) could improve regional air quality. However, little is known about the effectiveness and accuracy of synergistic control region delineation. This study aimed to construct a network model and apply it to a case study of regional delineation in China at different scales to quantify the interactions between regions. Firstly, the Cumulative Risk Index (CRI) was proposed and quantified from a health risk perspective based on the daily mean PM 2.5 and daily maximum 8-h average O 3 concentrations from 2015 to 2020 in China. Then, the complex network topology parameters were introduced to determine the optimal threshold for different network constructions, and the Girvan-Newman (GN) algorithm was used to divide the network into independent regions. Results showed that the correlation between cities is more robust than that between provinces. There are four-seven major provincial-scale regions with strong synchronicity in CRI, suggesting that PM 2.5 and O 3 synergistic control policies shall be implemented jointly within these demarcated regions. Moreover, urban-scale CRI network analysis indicated that the existing key control areas (2 + 26 cities) need to be expanded to 40-50 cities and refined into seven independent urban regions. Meanwhile, the Fen-Wei Plain can be focused on six cities: Xi'an, Baoji, Xianyang, Weinan, Yuncheng, and Tongchuan. This study could improve our understanding of the synergistic control regions for PM 2.5 and O 3 pollution, and the results could be used to develop joint control policies for both pollutants., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022 Elsevier B.V. All rights reserved.)