A novel infrastructure modularity index for the segmentation of water dis-tribution networks

The search for suitable segmentations is a challenging and urgent issue for the analysis, planning and management of complex water distribution networks (WDNs). In fact, complex and large size hydraulic systems require the division into modules in order to simplify the analysis and the management tasks. In the complex network theory, modularity index has been proposed as a measure of the strength of the network division into modules and its maximization is used in order to identify community of nodes (i.e., modules) which are characterized by strong interconnections. Nevertheless, modularity index needs to be revised considering the specificity of the hydraulic systems as infrastructure systems. To this aim, the classic modularity index has been recently modified and tailored for WDNs. Nevertheless, the WDN-oriented modularity is affected by the resolution limit stemming from classic modularity index. Such a limit hampers the identification/design of small modules and this is a major drawback for technical tasks requiring a detailed resolution of the network segmentation. In order to get over this problem, we propose a novel infrastructure modularity index that is not affected by the resolution limit of the classic one. The rationale and good features of the proposed index are theoretically demonstrated and discussed using two real hydraulic networks.