Hierarchy Measures in Complex Networks

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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 $γ>3$.
4 pages, 4 figures

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Soft Condensed Matter, Molecular Networks

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http://salesiana.dossiersoluciones.com/handle/123456789/163452

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/cond-mat/0308339
 http://arxiv.org/abs/cond-mat/0308339
 Phys. Rev. Lett. 92, 178702 (2004)
 doi:10.1103/PhysRevLett.92.178702

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arXiv