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Hierarchy Measures in Complex Networks

Ala Trusina·Sergei Maslov·Petter Minnhagen·Kim Sneppen
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Abstract

Using each node's degree as a proxy for its importance, the topological hierarchy of a complex network is introduced and quantified. We propose a simple dynamical process used to construct networks which are either maximally or minimally hierarchical. Comparison with these extremal cases as well as with random scale-free networks allows us to better understand hierarchical versus modular features in several real-life complex networks. For random scale-free topologies the extent of topological hierarchy is shown to smoothly decline with $γ$ -- the exponent of a degree distribution -- reaching its highest possible value for $γ\leq 2$ and quickly approaching zero for $γ>3$.

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Ala Trusina, Sergei Maslov, Petter Minnhagen, Kim Sneppen. 2004-02-19. Hierarchy Measures in Complex Networks. https://doi.org/10.1103/physrevlett.92.178702

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