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# Betweenness Centrality in Large Complex Networks

1 DPTA - Département de Physique Théorique et Appliquée
DAM/DIF - DAM Île-de-France : DAM/DIF
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 $\\delta=(\\gamma+1)/2$.
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Journal articles
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https://hal.archives-ouvertes.fr/hal-00014380
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Submitted on : Thursday, November 24, 2005 - 1:54:35 PM
Last modification on : Monday, December 13, 2021 - 11:34:06 AM

### Citation

Marc Barthelemy. Betweenness Centrality in Large Complex Networks. The European Physical Journal B: Condensed Matter and Complex Systems, Springer-Verlag, 2004, 38, pp.163-168. ⟨10.1140/epjb/e2004-00111-4⟩. ⟨hal-00014380⟩

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