Statistical mechanics of networks.

By Juyong Park, Mark Newman. Physical review. E, Statistical, nonlinear, and soft matter physics, 2004

610 citations recorded by the source corpus.

We study the family of network models derived by requiring the expected properties of a graph ensemble to match a given set of measurements of a real-world network, while maximizing the entropy of the ensemble. Models of this type play the same role in the study of networks as is played by the Boltzmann distribution in classical statistical mechanics; they offer the best prediction of network properties subject to the constraints imposed by a given set of observations. We give exact solutions of models within this class that incorporate arbitrary degree distributions and arbitrary but independent edge probabilities. We also discuss some more complex examples with correlated edges that can be solved approximately or exactly by adapting various familiar methods, including mean-field theory, perturbation theory, and saddle-point expansions.

Subfields: Experimental and Cognitive Psychology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0b430953d6116fd82ab05c6304425b14d75e9aad

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In Experimental and Cognitive Psychology

In Statistical and Nonlinear Physics

Citations in the corpus

The statistical physics of real-world networks (2018, methodology): “Besides very simple models like the well-known Erdös-Rényi random graph [39], this happens for the important constraints describing the local network structure from the viewpoint of each individual node—namely, degrees k∗ and strengths s∗ [26].”
A Sequential Importance Sampling Algorithm for Generating Random Graphs with Prescribed Degrees (2011, methodology): “Second, they use a variant of the pairing model, modiﬁed from an algorithm in Newman, Strogatz and Watts [59].”
A Survey of Statistical Network Models (2009, background): “Barabási, Newman, and Watts, among others, produced what we can think of as variations on the Erdös-RényiGilbert model which either controlled the growth of the network or allowed for differential probabilities for edge addition and/or deletion.”
Applications of Stein's method for concentration inequalities (2009, background): “(B) The equation h′(s) = 0 has a unique root at s = 0 where h(s) := s 2 2 − log ∫ exp(sx) dρ(x) for s ∈ R.”
Multilayer networks (2013, background): “Bianconi [45, 227] introduced microcanonical and canonical network ensembles [256, 316] for multiplex networks.”
Random graphs with a given degree sequence (2010, methodology): “This model was considered by Holland and Lienhardt [27] in the directed case and by Park and Newman [43] and Blitzstein and Diaconis [12] in the undirected case.”