Coscia, Michele2018-06-202018Coscia, Michele. 2018. “Using Arborescences to Estimate Hierarchicalness in Directed Complex Networks.” Edited by Constantine Dovrolis. PLOS ONE 13 (1) (January 30): e0190825. doi:10.1371/journal.pone.0190825.1932-6203http://nrs.harvard.edu/urn-3:HUL.InstRepos:37140312Complex networks are a useful tool for the understanding of complex systems. One of the emerging properties of such systems is their tendency to form hierarchies: networks can be organized in levels, with nodes in each level exerting control on the ones beneath them. In this paper, we focus on the problem of estimating how hierarchical a directed network is. We propose a structural argument: a network has a strong top-down organization if we need to delete only few edges to reduce it to a perfect hierarchy—an arborescence. In an arborescence, all edges point away from the root and there are no horizontal connections, both characteristics we desire in our idealization of what a perfect hierarchy requires. We test our arborescence score in synthetic and real-world directed networks against the current state of the art in hierarchy detection: agony, flow hierarchy and global reaching centrality. These tests highlight that our arborescence score is intuitive and we can visualize it; it is able to better distinguish between networks with and without a hierarchical structure; it agrees the most with the literature about the hierarchy of well-studied complex systems; and it is not just a score, but it provides an overall scheme of the underlying hierarchy of any directed complex network.en-USJournal Article2018-01-2320182018-06-2010.1371/journal.pone.0190825