Abstract
We generate correlated scale-free networks in the configuration model through a new rewiring algorithm that allows one to tune the Newman assortativity coefficient r and the average degree of the nearest neighbors K (in the range , ). At each attempted rewiring step, local variations and are computed and then the step is accepted according to a standard Metropolis probability , where T is a variable temperature. We prove a general relation between and , thus finding a connection between two variables that have very different definitions and topological meaning. We describe rewiring trajectories in the r-K plane and explore the limits of maximally assortative and disassortative networks, including the case of small minimum degree (), which has previously not been considered. The size of the giant component and the entropy of the network are monitored in the rewiring. The average number of second neighbors in the branching approximation is proven to be constant in the rewiring, and independent from the correlations for Markovian networks. As a function of the degree, however, the number of second neighbors gives useful information on the network connectivity and is also monitored.
Highlights
Rewiring algorithms are often employed in network science to build “synthetic networks” for the mathematical modeling of dynamics or diffusion processes [1,2,3,4,5]
The method of assortative and disassortative rewiring at variable T that we presented in this work appeared to be quite effective for the generation of correlated scale-free networks
At each step of the rewiring process, our algorithm permitted a control of the variations of the assortativity coefficient r and of the average degree of the nearest neighbors K
Summary
Rewiring algorithms are often employed in network science to build “synthetic networks” for the mathematical modeling of dynamics or diffusion processes [1,2,3,4,5]. Erdös-Renyi which yields uncorrelated networks having a pre-assigned (typically scale-free) degree distribution. It is known, that assortative and disassortative correlations play an important role in dynamics and diffusion on networks [7,8,9,10,11]. That assortative and disassortative correlations play an important role in dynamics and diffusion on networks [7,8,9,10,11] For this reason some algorithms have been devised, which are able to perform a degree-conserving rewiring while modifying the pair correlations in the direction of increasing assortativity or disassortativity.
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