Cities depend on multiple heterogeneous, interconnected infrastructures to provide safe water to consumers. Given this complexity, efficient numerical techniques are needed to support optimal control and management of a water distribution network (WDN). This paper introduces a holistic analysis framework to support water utilities on the decision making process for an efficient supply management. The proposal is based on graph spectral techniques that take advantage of eigenvalues and eigenvectors properties of matrices that are associated with graphs. Instances of these matrices are the adjacency matrix and the Laplacian, among others. The interest for this application is to work on a graph that specifically represents a WDN. This is a complex network that is made by nodes corresponding to water sources and consumption points and links corresponding to pipes and valves. The aim is to face new challenges on urban water supply, ranging from computing approximations for network performance assessment to setting device positioning for efficient and automatic WDN division into district metered areas. It is consequently created a novel tool-set of graph spectral techniques adapted to improve main water management tasks and to simplify the identification of water losses through the definition of an optimal network partitioning.Two WDNs are used to analyze the proposed methodology. Firstly, the well-known network of C-Town is investigated for benchmarking of the proposed graph spectral framework. This allows for comparing the obtained results with others coming from previously proposed approaches in literature. The second case-study corresponds to an operational network. It shows the usefulness and optimality of the proposal to effectively manage a WDN.

Water Distribution Networks (WDNs) can be regarded as complex networks and modeled as graphs. In this paper, Complex Network Theory is applied to characterize the behavior of WDNs from a topological point of view, reviewing some basic metrics, exploring their fundamental properties and the relationship between them. The crucial aim is to understand and describe the topology of WDNs and their structural organization to provide a novel tool of analysis which could help to find new solutions to several arduous problems of WDNs. The aim is to understand the role of the topological structure in the WDNs functioning. The methodology is applied to 21 existing networks and 13 literature networks. The comparison highlights some topological peculiarities and the possibility to define a set of best design parameters for ex-novo WDNs that could also be used to build hypothetical benchmark networks retaining the typical structure of real WDNs. Two well-known types of network ((a) square grid; and (b) random graph) are used for comparison, aiming at defining a possible mathematical model for WDNs. Finally, the interplay between topology and some performance requirements of WDNs is discussed.

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In order to improve the management and to better locate water losses, Water Distribution Networks can be physically divided into District Meter Areas (DMAs), inserting hydraulic devices on proper pipes and thus simplifying the control of water budget and pressure regime. Traditionally, the water network division is based on empirical suggestions and on ‘trial and error’ approaches, checking results step by step through hydraulic simulation, and so making it very difficult to apply such approaches to large networks. Recently, some heuristic procedures, based on graph and network theory, have shown that it is possible to automatically identify optimal solutions in terms of number, shape and dimension of DMAs. In this paper, weighted spectral clustering methods have been used to define the optimal layout of districts in a real water distribution system, taking into account both geometric and hydraulic features, through weighted adjacency matrices. The obtained results confirm the feasibility of the use of spectral clustering to address the arduous problem of water supply network partitioning with an elegant mathematical approach compared to other heuristic procedures proposed in the literature. A comparison between different spectral clustering solutions has been carried out through topological and energy performance indices, in order to identify the optimal water network partitioning procedure.

Water distribution networks (WDNs) must keep a proper level of service under a wide range of operational conditions, and, in particular, the analysis of their resilience to pipe failures is essential to improve their design and management. WDNs can be regarded as large sparse planar graphs showing fractal and complex network properties. In this paper, the relationship linking the geometrical and topological features of a WDN to its resilience to the failure of a pipe is investigated. Some innovative indices have been borrowed from fractal geometry and complex network theory to study WDNs. Considering all possible network configurations obtained by suppressing one link, the proposed indices are used to quantify the impact of pipe failure on the system's resilience. This approach aims to identify critical links, in terms of resilience, with the help of topological metrics only, and without recourse to hydraulic simulations, which require complex calibration processes and come with a computational burden. It is concluded that the proposed procedure, which has been successfully tested on two real WDNs located in southern Italy, can provide valuable information to water utilities about which pipes have a significant role in network performance, thus helping in their design, planning and management.