Abstract：
Graph theory (GT) and complex network theory play an increasingly important role in the design, operation, and management of water distribution networks (WDNs) and these tasks were originally often heavily dependent on hydraulic models. Facing the general reality of the lack of high-precision hydraulic models in water utilities, GT has become a promising surrogate or assistive technology. However, there is a lack of a systematic review of how and where the GT techniques are applied to the field of WDNs, along with an examination of potential directions that GT can contribute to addressing WDNs\' challenges. This paper presents such a review and first summarizes the graph construction methods and topological properties of WDNs, which are mathematical foundations for the application of GT in WDNs. Then, main application areas, including state estimation, performance evaluation, partitioning, optimal design, optimal sensor placement, critical components identification, and interdependent networks analysis, are identified and reviewed. GT techniques can provide acceptable results and valuable insights while having a low computational burden compared with hydraulic models. Combining GT with hydraulic model significantly enhances the performance of analysis methods. Four research challenges, namely reasonable abstraction, data availability, tailored topological indicators, and integration with Graph Neural Networks (GNNs), have been identified as key areas for advancing the application and implementation of GT in WDNs. This paper would have a positive impact on promoting the use of GT for optimal design and sustainable management of WDNs.
摘要：
图论(GT)和复杂网络理论在设计中发挥着越来越重要的作用,操作,和水分配网络（WDN）的管理，这些任务最初通常严重依赖于水力模型。面对水务事业缺乏高精度水工模型的普遍现实,GT已成为一种有前途的替代或辅助技术。然而,缺乏对GT技术如何以及在何处应用于WDN领域的系统审查，以及对GT可以帮助解决WDN挑战的潜在方向的研究。本文进行了这样的回顾，首先总结了WDN的图构造方法和拓扑性质，这是GT在WDN中应用的数学基础。然后，主要应用领域,包括状态估计，绩效评估，分区,优化设计，最佳传感器放置，关键部件识别,和相互依赖的网络分析，被识别和审查。与水力模型相比，GT技术可以提供可接受的结果和有价值的见解，同时具有较低的计算负担。GT与水力模型的结合显着提高了分析方法的性能。四个研究挑战，即合理的抽象，数据可用性，量身定制的拓扑指标，并与图神经网络(GNN)集成，已被确定为推进GT在WDN中的应用和实施的关键领域。本文将对促进使用GT进行WDN的优化设计和可持续管理产生积极影响。
