A. P. MASUCCI (Department of Mathematical Sciences, Brunel University, Uxbridge, Middlesex, UB8 3PH, UK) G. J. RODGERS (Department of Mathematical Sciences, Brunel University, Uxbridge, Middlesex, UB8 3PH, UK)
Abstract
In this paper we deal with the structural properties of weighted networks. Starting from an empirical analysis of a linguistic network, we analyze the differences between the statistical properties of a real and a shuffled network. We show that the scale-free degree distribution and the scale-free weight distribution are induced by the scale-free strength distribution, that is Zipf's law. We test the result on a scientific collaboration network, that is a social network, and we define a measure â the vertex selectivity â that can distinguish a real network from a shuffled network. We prove, via an ad hoc stochastic growing network with second order correlations, that this measure can effectively capture the correlations within the topology of the network.
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