 This can be used to calculate mean values (expectations) of the flow rates, head losses or any other variables of interest in the pipe network.This analysis has been extended using a reduced-parameter entropic formulation, which ensures consistency of the analysis regardless of the graphical representation of the network.A comparison of Bayesian and maximum entropy probabilistic formulations for the analysis of pipe flow networks has also been presented, showing that under certain assumptions (Gaussian priors), the two approaches lead to equivalent predictions of mean flow rates.