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The European Physical Journal B

, Volume 38, Issue 2, pp 163–168 | Cite as

Betweenness centrality in large complex networks

  • M. Barthélemy
Article

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 \(\eta\). We find that for trees or networks with a small loop density \(\eta = 2\) while a larger density of loops leads to \(\eta < 2\). For scale-free networks characterized by an exponent \(\gamma\) which describes the connectivity distribution decay, the BC is also distributed according to a power law with a non universal exponent \(\delta\). We show that this exponent \(\delta\) must satisfy the exact bound \(\delta\geq (\gamma + 1)/2\). If the scale free network is a tree, then we have the equality \(\delta = (\gamma + 1)/2\).

Keywords

Complex Network Betweenness Centrality Scale Free Network Large Density Large Complex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin/Heidelberg 2004

Authors and Affiliations

  1. 1.Département de Physique Théorique et AppliquéeCEABruyéres-Le-ChâtelFrance

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