Abstract
We develop and test a rewiring method (originally proposed by Newman) which allows to build random networks having pre-assigned degree distribution and two-point correlations. For the case of scale-free degree distributions, we discretize the tail of the distribution according to the general prescription by Dorogovtsev and Mendes. The application of this method to Barabasi-Albert (BA) networks is possible thanks to recent analytical results on their correlations, and allows to compare the ensemble of random networks generated in the configuration model with that of “real” networks obtained from preferential attachment. For β≥2 (β is the number of parent nodes in the preferential attachment scheme) the networks obtained with the configuration model are completely connected (giant component equal to 100%). In both generation schemes a clear disassortativity of the small degree nodes is demonstrated from the computation of the function knn. We also develop an efficient rewiring method which produces tunable variations of the assortativity coefficient r, and we use it to obtain maximally disassortative networks having the same degree distribution of BA networks with given β. Possible applications of this method concern assortative social networks.
Highlights
In spite of the large number of existing studies on Barabasi-Albert (BA) networks, their two-point correlation functions have been completely analysed only recently by Fotouhi and Rabbat (2013), who have given the full expressions of the conditional probabilities
By computing the function knn(k) of BA networks we have shown in (Bertotti and Modanese 2019) that it is strongly decreasing for small k and slowly increasing for large k
The values of r obtained will depend on the degree distribution, on the scale-free exponent γ in the case of a pure power law, or on β for a “BA-like” degree distribution P(k) = 2β(β + 1)/[ k(k + 1)(k + 2)]. We use this degree distribution as a variation of the pure power law γ = 3, in order to investigate the role of the details of the degree distribution at small k; we recall that these details influence the average degree and may have a strong impact, for instance, on the giant component of random networks in the configuration model (Newman 2010)
Summary
In spite of the large number of existing studies on Barabasi-Albert (BA) networks, their two-point correlation functions have been completely analysed only recently by Fotouhi and Rabbat (2013), who have given the full expressions of the conditional probabilitiesP(h|k) in the large network limit for any value of the parameter β (the number of parent nodes in the preferential attachment process).Concerning the assortativity properties of BA networks, in previous work some estimates of the Newman coefficient r were found (Newman 2002). The configuration model (Newman 2010) is a method for the generation of random networks having an assigned degree distribution.
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