Equilibrium Statistical Mechanicsof Network Structures

  • Illés Farkas
  • Imre Derényi
  • Gergely Palla
  • Tamás Vicsek
Part I Network Structure
Part of the Lecture Notes in Physics book series (LNP, volume 650)


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.


Random Graph Degree Distribution Canonical Ensemble Grand Canonical Ensemble Giant Component 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Authors and Affiliations

  • Illés Farkas
    • 1
  • Imre Derényi
    • 2
  • Gergely Palla
    • 1
  • Tamás Vicsek
    • 1
    • 2
  1. 1.Biological Physics Research Group of HAS 
  2. 2.Department of Biological Physics, Eötvös University, Pázmány P. stny. 1A, 1117 BudapestHungary

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