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Using arborescences to estimate hierarchicalness in directed complex networks

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  • Michele Coscia

Abstract

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 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.

Suggested Citation

  • Michele Coscia, 2018. "Using arborescences to estimate hierarchicalness in directed complex networks," PLOS ONE, Public Library of Science, vol. 13(1), pages 1-18, January.
  • Handle: RePEc:plo:pone00:0190825
    DOI: 10.1371/journal.pone.0190825
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    References listed on IDEAS

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    1. Yong-Yeol Ahn & James P. Bagrow & Sune Lehmann, 2010. "Link communities reveal multiscale complexity in networks," Nature, Nature, vol. 466(7307), pages 761-764, August.
    2. Michele Coscia & Ricardo Hausmann, 2015. "Evidence That Calls-Based and Mobility Networks Are Isomorphic," PLOS ONE, Public Library of Science, vol. 10(12), pages 1-15, December.
    3. Marcus Kaiser & Claus C Hilgetag, 2006. "Nonoptimal Component Placement, but Short Processing Paths, due to Long-Distance Projections in Neural Systems," PLOS Computational Biology, Public Library of Science, vol. 2(7), pages 1-11, July.
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    1. Vasiliauskaite, Vaiva & Evans, Tim S. & Expert, Paul, 2022. "Cycle analysis of Directed Acyclic Graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).

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