# The configuration model for Barabasi-Albert networks

## TL;DR

This paper introduces a rewiring method to generate random networks with specific degree distributions and correlations, enabling comparison with real Barabasi-Albert networks and exploring network properties like disassortativity.

## Contribution

The authors develop a novel rewiring technique for creating correlated networks with prescribed degree distributions, specifically applied to Barabasi-Albert networks, and analyze their structural properties.

## Key findings

- Networks with $eta extgreater=2$ are fully connected.
- Small degree nodes exhibit disassortativity.
- The method allows tuning of the assortativity coefficient.

## 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.