  We propose a new method to estimate a root-directed spanning tree from
extreme data. A prominent example is a river network, to be discovered from
extreme flow measured at a set of stations. Our new algorithm utilizes
qualitative aspects of a max-linear Bayesian network, which has been designed
for modelling causality in extremes. The algorithm estimates bivariate scores
and returns a root-directed spanning tree. It performs extremely well on
benchmark data and new data. We prove that the new estimator is consistent
under a max-linear Bayesian network model with noise. We also assess its
strengths and limitations in a small simulation study.
