Betweenness centrality in large complex networks
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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 \(\delta = (\gamma + 1)/2\).
KeywordsComplex Network Betweenness Centrality Scale Free Network Large Density Large Complex
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