General metrics for segmenting infrastructure networks

The classic modularity index for community detection in complex networks was recently tailored to water distribution networks (WDNs) and extended in order to be cut-position sensitive. Next, the WDN-oriented modularity index was enhanced in order to overcome the resolution limit of the classic modularity. Nonetheless, the modularity-based metrics developed so far allow the networks to be segmented into modules/segments that are similar to each other according to specific pipe characteristics (e.g., pipe lengths, distributed demand, background leakages, etc.). The present work extends and proves the strategy to overcome the resolution limits focusing on an infrastructure index that drives WDN segmentation toward modules that are internally similar with respect to given attributes (e.g., pipe diameters, average pipe pressures, average pipe elevations, etc.), since this aim is suitable for several practical purposes. The introduction of the attribute-based infrastructure index permits a comprehensive discussion and comparison of the metrics for infrastructure network segmentation through simple examples. Finally, the practical implications of increasing the resolution of internally similar modules are demonstrated on a well-known benchmark WDN considering various pipe attributes.