Asymptotic entropy of the Gibbs state of complex networks
Probability
2021-01-12 v2 Quantum Physics
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.
Keywords
Cite
@article{arxiv.2003.08411,
title = {Asymptotic entropy of the Gibbs state of complex networks},
author = {Adam Glos and Aleksandra Krawiec and Łukasz Pawela},
journal= {arXiv preprint arXiv:2003.08411},
year = {2021}
}