The results of the hierarchy null model test for many real world networks.

If the observed score is at least 2 standard deviations higher than the null models’ scores then we say we found a hierarchy (symbol +). If the observed score is 2 standard deviations lower than the null models, we say we found an anti-hierarchy (symbol −). Otherwise there is no hierarchy (symbol ×). * marks networks for which we first calculated the network’s backbone using [41]. If the last column has a ✓, it means that there is at least a three-to-one agreement on the structure of the network and our arborescence method is in the majority. For all networks, we report the number of nodes (V), edges (E), edges in the reduced graph (E*) and arborescence runtime in seconds (t).