Adam Glos, Aleksandra Krawiec, Łukasz Pawela
Published 2020-03-18Version 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 show that for a large number of graph models this approach does not distinguish the models asymptotically. 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. We conclude saying that, from this perspective, these models are boring.
On the singularity of adjacency matrices for random regular digraphs
Nonsingularity of adjacency matrices of random $r$-regular graphs
Large number of queues in tandem: Scaling properties under back-pressure algorithm
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