Complex network theory (CNT) is an emerging topic based on the paradigm that quite all the natural and man‐made physical systems work as networks, namely, their features derive from the internal connectivity among vertices exchanging information through edges. Water distribution infrastructures are networked systems connecting the vertices named nodes, by edges named pipes, and transferring water to customers. Therefore, water distribution networks (WDNs) fall into CNT and belongs to the class of spatial networks due to their urban constraints. CNT proposed several centrality metrics for quantifying the importance of vertex and, sometime, edges. Those metrics can be potentially very useful for analyzing the key features of the physical domain (i.e., the network) where WDN hydraulics occurs, but they need to be tailored to consider that (i) pipes/edges are the relevant physical components of the WDNs, (ii) some nodes/vertices (reservoirs and tanks) play a completely different hydraulic role from the majority of nodes (demand and connection nodes), and (iii) pipes/edges have different characteristics (length, diameter, hydraulic resistance, etc.). Accordingly, this work presents and discusses the need of tailoring the most suitable centrality metrics for spatial networks: betweenness, closeness, and degree. Then the capacity of the WDN‐tailored edge betweenness is demonstrated and discussed using two real WDNs, showing that it can extract useful information from the domain, that is, the emerging hydraulic behavior due to the network connectivity structure. Therefore, the WDN‐tailored edge betweenness can assist analysis, planning, and management actions before and after the hydraulic analysis.

The division of water distribution networks (WDNs) into district metering areas (DMAs) is a challenging issue and can be effective for analysis, planning, and management purposes. This contribution proposes a novel two-step strategy for DMA planning. The first step is optimal segmentation design by maximizing the WDN-oriented modularity index versus minimizing the number of conceptual cuts (i.e., not accounting for devices). The second step is the actual optimal DMA design, returning the positions of flow meters and closed valves at the conceptual cuts. Since closed valves change the system’s hydraulic paths, the implementation of DMAs could allow reductions in pressure and leakages through the WDN. Optimal DMA design is therefore achieved by solving a three-objective optimization minimizing the number of flow meters and total unsupplied customer demand while maximizing the reduction of background leakages; thus, pressure-driven modeling is mandatory. The effectiveness and flexibility of the procedure is demonstrated using the Apulian and Exnet networks. Results shows that DMA implementation can allow leakage reduction in systems with excess hydraulic capacity.

In real water distribution networks (WDNs) are present thousands nodes and optimal placement of pressure and flow observations is a relevant issue for different management tasks. The planning of pressure observations in terms of spatial distribution and number is named sampling design and it was faced considering model calibration. Nowadays, the design of system monitoring is a relevant issue for water utilities e.g., in order to manage background leakages, to detect anomalies and bursts, to guarantee service quality, etc. In recent years, the optimal location of flow observations related to design of optimal district metering areas (DMAs) and leakage management purposes has been faced considering optimal network segmentation and the modularity index using a multiobjective strategy. Optimal network segmentation is the basis to identify network modules by means of optimal conceptual cuts, which are the candidate locations of closed gates or flow meters creating the DMAs. Starting from the WDN‐oriented modularity index, as a metric for WDN segmentation, this paper proposes a new way to perform the sampling design, i.e., the optimal location of pressure meters, using newly developed sampling‐oriented modularity index. The strategy optimizes the pressure monitoring system mainly based on network topology and weights assigned to pipes according to the specific technical tasks. A multiobjective optimization minimizes the cost of pressure meters while maximizing the sampling‐oriented modularity index. The methodology is presented and discussed using the Apulian and Exnet networks.

The estimate of current real losses in water distribution networks (WDN) is crucial to plan investments for rehabilitation, assess the rise of leakage over time, and possibly drive procedures for failure identification and repair. However, many WDNs worldwide do not have flow/pressure monitoring within the system yet, and the inlet water volume or flowrate is the only recorded data. Developing reliable procedures to estimate real losses in such circumstances is essential to assess the leakage phenomenon and eventually drive the upgrade of existing monitoring systems. This work proposes a simple bottom-up methodology to estimate leakage using WDN inflow data series while only exploiting the seasonal fluctuation of water consumptions. It resorts to a data-assimilation strategy whose formulation is consistent with the physical behavior of WDNs and requires the estimate of only a few numerical parameters. Additionally, the methodology allows the estimation of the user’s daily and night water consumptions, thus being useful to verify or integrate other leakage estimate methods. The methodology is discussed and demonstrated on both synthetic and real WDNs.

Complex network theory (CNT) studies the relevance of elements in networks using centrality metrics. From the CNT standpoint, water distribution networks (WDNs) are infrastructure networks composed by vertices, named nodes, connected to each other by edges, named pipes, that transfer water to customers following a transfer process based on shortest paths. The present paper proposes the domain analysis of several real WDNs using the edge betweenness in order to capture the hydraulic behaviour based on network structure, i.e., for understanding the role of topological features in the emergent hydraulic behaviour. The strategy is obtained by tailoring CNT studies and tools in order to (i) embed the different hydraulic roles of sources and demand nodes, (ii) move the classic concept of centrality from the nodes to the pipes, i.e., the technically relevant components for WDNs and (iii) include information related to the directional devices, because they constrain flow directions. Results show the usefulness of the novel WDN-tailored edge betweenness for the WDN domain analysis. Therefore, the metric can represent a useful tool for supporting WDNs analysis, design and management tasks.