Related papers: Asymptotic entropy of the Gibbs state of complex networks

Asymptotic entropy of the Gibbs state of complex networks

URL: http://arxiv.org/abs/2003.08411v2
Date: Mon, 11 Jan 2021 15:46:23 GMT
Title: Asymptotic entropy of the Gibbs state of complex networks
Authors: Adam Glos, Aleksandra Krawiec, {\L}ukasz Pawela
Abstract summary: The Gibbs state is obtained from the Laplacian, normalized Laplacian or adjacency matrices associated with a graph. We calculated the entropy of the Gibbs state for a few classes of graphs and studied their behavior with changing graph order and temperature. Our results show that the behavior of Gibbs entropy as a function of the temperature differs for a choice of real networks when compared to the random ErdHos-R'enyi graphs.
Score: 68.8204255655161
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: In this work we study the entropy of the Gibbs state corresponding to a graph. The Gibbs state is obtained from the Laplacian, normalized Laplacian or adjacency matrices associated with a graph. We calculated the entropy of the Gibbs state for a few classes of graphs and studied their behavior with changing graph order and temperature. We illustrate our analytical results with numerical simulations for Erd\H{o}s-R\'enyi, Watts-Strogatz, Barab\'asi-Albert and Chung-Lu graph models and a few real-world graphs. Our results show that the behavior of Gibbs entropy as a function of the temperature differs for a choice of real networks when compared to the random Erd\H{o}s-R\'enyi graphs.

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