Análise dos efeitos da dimensionalidade em redes com estatística de Tsallis

Abstract

In this work, a study was carried out on the effects of the dimensionality of networks with Tsallis statistics, having these networks degree distribution in the form P(k) ∼ e−k/λ q , being the q-exponential in the form ez q ≡ [1+(1−q)z]1/(1−q) and in the thermodynamic limit has the form P(k) ∼ kγ . Networks with power-law degree distribution are known as scale-free networks. Among the models capable of generating these networks, are the configuration models and the preferential attachment growth model, proposed by Samurai itshape et. al, being the model of focus of the work. The Tsallis statistic was developed by Constatino Tsallis and comes from the generalization of the Boltzmann-Gibbs entropy. In the growth model of the preferential connection, a change is made in the preferential connection proposed by Barabási, where a d-dimensional Euclidean distance term appears, obtaining a degree distribution that optimizes the entropy that defines the Tsallis statistic. We focus on studying the properties of the average length of the shortest path, the diameter and the assortativity of this network, analyzing the effects of dimensionality on these network properties.