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arXiv · 2003.08411

Asymptotic entropy of the Gibbs state of complex networks

Adam Glos·Aleksandra Krawiec·Łukasz Pawela
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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.

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Adam Glos, Aleksandra Krawiec, Łukasz Pawela. 2021-01-11. Asymptotic entropy of the Gibbs state of complex networks. https://doi.org/10.1038/s41598-020-78626-2

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