Asymptotic entropy of the Gibbs state of complex networks

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 behav...

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Autores principales:	Adam Glos, Aleksandra Krawiec, Łukasz Pawela
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/3989280c9ca54c0694546a4149539f92
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spelling	oai:doaj.org-article:3989280c9ca54c0694546a4149539f922021-12-02T14:12:42ZAsymptotic entropy of the Gibbs state of complex networks10.1038/s41598-020-78626-22045-2322https://doaj.org/article/3989280c9ca54c0694546a4149539f922021-01-01T00:00:00Zhttps://doi.org/10.1038/s41598-020-78626-2https://doaj.org/toc/2045-2322Abstract 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 Erdős–Rényi, Watts–Strogatz, Barabási–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 Erdős–Rényi graphs.Adam GlosAleksandra KrawiecŁukasz PawelaNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-9 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Adam Glos Aleksandra Krawiec Łukasz Pawela Asymptotic entropy of the Gibbs state of complex networks
description	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 Erdős–Rényi, Watts–Strogatz, Barabási–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 Erdős–Rényi graphs.
format	article
author	Adam Glos Aleksandra Krawiec Łukasz Pawela
author_facet	Adam Glos Aleksandra Krawiec Łukasz Pawela
author_sort	Adam Glos
title	Asymptotic entropy of the Gibbs state of complex networks
title_short	Asymptotic entropy of the Gibbs state of complex networks
title_full	Asymptotic entropy of the Gibbs state of complex networks
title_fullStr	Asymptotic entropy of the Gibbs state of complex networks
title_full_unstemmed	Asymptotic entropy of the Gibbs state of complex networks
title_sort	asymptotic entropy of the gibbs state of complex networks
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/3989280c9ca54c0694546a4149539f92
work_keys_str_mv	AT adamglos asymptoticentropyofthegibbsstateofcomplexnetworks AT aleksandrakrawiec asymptoticentropyofthegibbsstateofcomplexnetworks AT łukaszpawela asymptoticentropyofthegibbsstateofcomplexnetworks
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Asymptotic entropy of the Gibbs state of complex networks

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