Eur. Phys. J. B 38, 163-168 (2004)
https://doi.org/10.1140/epjb/e2004-00111-4

Betweenness centrality in large complex networks

CEA, Département de Physique Théorique et Appliquée, BP12 Bruyères-Le-Châtel, France

Corresponding author: ^a marc.barthelemy@cea.fr

Received: 18 September 2003
Revised: 11 December 2003
Published online: 14 May 2004

Abstract

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 while a larger density of loops leads to . 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 . If the scale free network is a tree, then we have the equality .