Using arborescences to estimate hierarchicalness in directed complex networks.

Using arborescences to estimate hierarchicalness in directed complex networks.

Blog Article

Complex 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 campicon.com 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; harry potter magsafe case and it is not just a score, but it provides an overall scheme of the underlying hierarchy of any directed complex network.