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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 behavior with changing graph order and temperature. We illustrate our analytical results with numerical simulations for Erd?s-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 Erd?s-Rényi graphs.

SUBMITTER: Glos A

PROVIDER: S-EPMC7801599 | biostudies-literature | 2021 Jan

REPOSITORIES: biostudies-literature

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Asymptotic entropy of the Gibbs state of complex networks.

Glos Adam A Krawiec Aleksandra A Pawela Łukasz Ł

Scientific reports 20210111 1

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 gr ...[more]

PMID: 33431960

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