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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- 1.C. Bergé, Graphs and Hypergraphs, 2nd edn. (North-Holland, Amsterdam, 1976)Google Scholar
- 2.J. Clark, D.A. Holton, A first look at graph theory (World Scientific, 1991)Google Scholar
- 8.S. Wasserman, K. Faust, Social Network Analysis: Methods and applications (Cambridge University Press, 1994)Google Scholar
- 10.D. Wilkinson, B.A. Huberman, cond-mat/0210147Google Scholar
- 12.M.E.J. Newman, cond-mat/0309045Google Scholar
- 16.For networks with peaked connectivity distributions such as the random graph, the centrality is also peaked and the exponent \(\delta\) is not definedGoogle Scholar
- 18.L.P. Kadanoff, Statistical Physics: Statics, Dynamics and Renormalization (World Scientific, 2000)Google Scholar
- 24.B. Bollobas, Random Graph (Academic Press, New York, 1985)Google Scholar
- 25.A. Renyi, Probability theory (New York, Elsevier, 1980)Google Scholar
- 27.It would be interesting to quantify for different types of networks the degree of anisotropy--measured by the N i‘s--versus the connectivityGoogle Scholar