Topological Taxonomy of Water Distribution Networks

Abstract

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.

A Direct Approach for the Near-Optimal Design of Water Distribution Networks Based on Power Use

“…Conversely, because of the differences in hydraulic behavior between a tree-like network and a real-life looped network, when OPUS is used in small WDSs, the results are not as good as expected because that difference in hydraulics is higher in smaller networks. In addition, Giudicianni (2018) found that there are several topological differences between small, large and synthetic WDNs (Water Distribution Networks) [51,56], thus it is possible to state that one methodology fits for some kind of networks but not for others. In this case, the result was highly influenced by the optimization process and not by the steps based on hydraulic principles, as a result of the fact that the design is executed based on the branched network (spanning tree).…”

Water Network Partitioning into District Metered Areas: A State-Of-The-Art Review

“…The nodal degree, k i , is the number of edges attached to a vertex i. The degree of node i is defined as k i = n j=1 A ij for the adjacency matrix A, and k i = n j=1 W ij for the weighted adjacency matrix W. From a topological point of view and complex network theory, Giudicianni et al [35] treated the WDN as a graph by using several complex network metrics to characterize the topology of typical WDNs. It was a preliminary process for better understanding the network itself, and provided the classical approach for partitioning or/and designing the WDNs.…”

Automatic Multiscale Approach for Water Networks Partitioning into Dynamic District Metered Areas

“…A suitable number of clusters C is taken in order to optimise the overall connectivity of the partitioned network. According to [19], the optimal number of clusters (from a topological point of view) results in C opt ∝ n 0.28 . Thus, without loss of generality, the new number of clusters for Parete is set to C = 4 (see Figure 4(a)).…”