On the growth of directed complex networks with preferential attachment: Effect upon the prohibition of multiple links

Several real-world directed networks do not have multiple links. For example, in a paper citation network a paper does not cite two identical references, and in a network of friends there exists only a single link between two individuals. This suggest that the growth and evolution models of complex networks should take into account such feature in order to approximate the topological properties of this class of networks. The aim of this paper is to propose a growth model of directed complex networks that takes into account the prohibition of the existence multiple links. It is shown through numerical experiments that when multiple links are forbidden, the exponent γ of the in-degree connectivity distribution, $P(k-{{\rm in}}) \sim k-{{\rm in}}^{-\gamma}$, takes values ranging from 1 to ∞. In particular, the proposed multi-link free (MLF) model is able to predict exponents occurring in real-world complex networks, which range 1.05 < γ < 3.51. As an example, the MLF reproduces somxe topological properties exhibited by the network of flights between airports of the world (NFAW); i.e. γ ≈ 1.74. With this result, we believe that the multiple links prohibition might be one of the local processes accounting for the existence of exponents γ < 2 found in some real complex networks. © 2015 World Scientific Publishing Company.

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