Hierarchy Measures in Complex Networks

2003/08/31 by Ala Trusina, Sergei Maslov, Petter Minnhagen +1 · 7 citations
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Bioinformatics and Genomic Networks #Complex Network Analysis Techniques #Opinion Dynamics and Social Influence #cond-mat.soft #q-bio.MN

paper · pdf · doi:10.1103/physrevlett.92.178702

published as Phys. Rev. Lett. 92, 178702 (2004) · 4 pages, 4 figures

arxiv created 2004/02/19 · openalex publication_date 2004/04/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 gamma, the exponent of a degree distribution, reaching its highest possible value for gamma</=2 and quickly approaching zero for gamma>3.

Citations

• Detection of topological patterns in complex networks: correlation profile of the internet

Cited by

• The effects of degree correlations on network topologies and robustness
• On the basic computational structure of gene regulatory networks
• Topology regulates pattern formation capacity of binary cellular automata on graphs
• Maximal planar networks with large clustering coefficient and power-law degree distribution
• Radial structure of the Internet
• Self-assembly of information in networks
• Generating Hierarchically Modular Networks via Link Switching