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Network Rewiring in the r-K Plane

Faculty of Science and Technology, Free University of Bozen-Bolzano, 39100 Bolzano, Italy
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Entropy 2020, 22(6), 653; https://doi.org/10.3390/e22060653
Received: 15 April 2020 / Revised: 10 June 2020 / Accepted: 11 June 2020 / Published: 13 June 2020
(This article belongs to the Special Issue Generalized Statistical Thermodynamics)
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 1 r 1 , K k ). At each attempted rewiring step, local variations Δ r and Δ K are computed and then the step is accepted according to a standard Metropolis probability exp ( ± Δ r / T ) , where T is a variable temperature. We prove a general relation between Δ r and Δ K , 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 ( k m i n 1 ), 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 z ¯ 2 , B 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. View Full-Text
Keywords: scale-free networks; network rewiring; network assortativity; network entropy scale-free networks; network rewiring; network assortativity; network entropy
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Bertotti, M.L.; Modanese, G. Network Rewiring in the r-K Plane. Entropy 2020, 22, 653.

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