  Water distribution networks (WDNs) are one of the most important man-made
infrastructures. Resilience, the ability to respond to disturbances and recover
to a desirable state, is of vital importance to our society. There is
increasing evidence that the resilience of networked infrastructures with
dynamic signals depends on their network topological properties. Whilst
existing literature has examined a variety of complex network centrality and
spectral properties, very little attention has been given to understand
multi-scale flow-based feedback loops and its impact on overall stability.
Here, resilience arising from multi-scale feedback loops is inferred using a
proxy measure called trophic coherence. This is hypothesised to have a strong
impact on both the pressure deficit and the water age. Our results show that
trophic coherence is positively correlated with the time to recovery (0.62 to
0.52), while it is negatively correlated with the diffusion of a disruption
(-0.66 to -0.52). Finally, we apply random forest analysis to combine
resilience measures, showing that the new resilience ensemble provides a more
accurate measure for networked resilience.
