Network structure classification and features of water distribution systems

The network connectivity structure of water distribution systems (WDSs) represents the domain where hydraulic processes occur, driving the emerging behavior of such systems, for example with respect to robustness and vulnerability. In complex network theory (CNT), a common way of classifying the network structure and connectivity is the association of the nodal degree distribution to specific probability distribution models, and during the last decades, researchers classified many real networks using the Poisson or Pareto distributions. In spite of the fact that degree-based network classification could play a crucial role to assess WDS vulnerability, this task is not easy because the network structure of WDSs is strongly constrained by spatial characteristics of the environment where they are constructed. The consequence of these spatial constraints is that the nodal degree spans very small ranges in WDSs hindering a reliable classification by the standard approach based on the nodal degree distribution. This work investigates the classification of the network structure of 22 real WDSs, built in different environments, demonstrating that the Poisson distribution generally models the degree distributions very well. In order to overcome the problem of the reliable classification based on the standard nodal degree, we define the “neighborhood” degree, equal to the sum of the nodal degrees of the nearest topological neighbors (i.e., the adjacent nodes). This definition of “neighborhood” degree is consistent with the fact that the degree of a single node is not significant for analysis of WDSs.