Betweenness Centrality in Large Complex Networks

Details Betweenness Centrality in Large Complex Networks Betweenness Centrality in Large Complex Networks

2003-09-18

arxiv.org/abs/cond-mat/0309436v2

Eur. Phys. Jour. B, vol 38, 163 (2004)

Physics

Condensed Matter

Disordered Systems and Neural Networks

6 pages, 5 figures, revised version

Scientific paper

10.1140/epjb/e2004-00111-4

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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