2003/09/30 by Marc Barthelemy, M. Barthélemy · 4 citations
Mathematics · Physics and Astronomy · #Betweenness centrality #Centrality #Complex Network Analysis Techniques #Complex network #Complex system #Distribution (mathematics) #Exponent #Graph theory and applications #Loop (graph theory) #Power law #Theoretical and Computational Physics #Upper and lower bounds #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1140/epjb/e2004-00111-4
published as Eur. Phys. Jour. B, vol 38, 163 (2004) · 6 pages, 5 figures, revised version
openalex publication_date 2004/03/01 · arxiv created 2004/05/13 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We analyze the betweenness centrality (BC) of nodes in large complex networks. In general, the BC is increasing with connectivity as a power law with an exponent η. We find that for trees or networks with a small loop density η=2 while a larger density of loops leads to η<2. For scale-free networks characterized by an exponent γ which describes the connectivity distribution decay, the BC is also distributed according to a power law with a non universal exponent δ. We show that this exponent δ must satisfy the exact bound δ≥ (γ+1)/2. If the scale free network is a tree, then we have the equality δ=(γ+1)/2.