Equilibrium statistical mechanics of network structures

Details Equilibrium statistical mechanics of network structures Equilibrium statistical mechanics of network structures

2004-01-30

arxiv.org/abs/cond-mat/0401640v1

Lect. Notes Phys. 650, 163-187 (2004)

Physics

Condensed Matter

Statistical Mechanics

25 pages, 10 figures. Lecture Notes in Physics: "Networks: structure, dynamics, and function", ed by E. Ben-Naim, H. Frauenfel

Scientific paper

10.1007/b98716

In this article we give an in depth overview of the recent advances in the field of equilibrium networks. After outlining this topic, we provide a novel way of defining equilibrium graph (network) ensembles. We illustrate this concept on the classical random graph model and then survey a large variety of recently studied network models. Next, we analyze the structural properties of the graphs in these ensembles in terms of both local and global characteristics, such as degrees, degree-degree correlations, component sizes, and spectral properties. We conclude with topological phase transitions and show examples for both continuous and discontinuous transitions.

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