The configuration model for Barabasi-Albert networks

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 $\beta \ge 2$ ($\beta$ 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 $k_{nn}$. 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 $\beta$. Possible applications of this method concern assortative social networks.

arXiv comment17 pages, 5 figures

References in corpus (10)

• Assortative mixing in networks
• Mixing patterns in networks
• Class of correlated random networks with hidden variables
• Cut-offs and finite size effects in scale-free networks
• Construction and properties of assortative random networks
• Robustness and Assortativity for Diffusion-like Processes in Scale-free Networks
• Degree Correlation in Scale-Free Graphs
• Exact sampling of graphs with prescribed degree correlations
• The Bass diffusion model on networks with correlations and inhomogeneous advertising
• Assortative and disassortative mixing investigated using the spectra of graphs

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• Diagonal degree correlations vs. epidemic threshold in scale-free networks