  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 that 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 modelled WDNs suggests
that the empirical WDNs may realize a reasonable balance between cost,
efficiency and robustness in terms of the network structure. 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 modelled pipe
diameters. The difference between the empirical and modelled pipe diameters
suggests that we may be able to improve the performance of WDNs by following
organizing principles of biological flow networks.
