  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.
