Water distribution networks (WDNs) expand their service areas over time. These growth dynamics are poorly understood. One facet of WDNs is that they have loops in general, and closing loops may be a functionally important process for enhancing their robustness and efficiency. We propose a growth model for WDNs which generates networks with loops and is applicable to networks with multiple water sources. We apply the proposed model to four empirical WDNs to show that it produces networks whose structure is similar to that of the empirical WDNs. The comparison between the empirical and modeled WDNs suggests that the empirical WDNs realize a reasonable balance between cost, efficiency, and robustness. We also study the design of pipe diameters based on a biological positive feedback mechanism. Specifically, we apply a model inspired by Physarum polycephalum to find moderate positive correlations between the empirical and modeled pipe diameters. This result suggests that the distribution of pipe diameters in the empirical WDNs is closer to an optimal one than a uniformly random distribution. However, the difference between the empirical and modeled pipe diameters suggests that we may be able to improve the performance of WDNs by following organizing principles of biological flow networks.
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