Journal of Applied Probability

Emergent structures in large networks

David Aristoff and Charles Radin

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Abstract

We consider a large class of exponential random graph models and prove the existence of a region of parameter space corresponding to the emergent multipartite structure, separated by a phase transition from a region of disordered graphs. An essential feature is the formalism of graph limits as developed by Lovász et al. for dense random graphs.

Article information

Source
J. Appl. Probab., Volume 50, Number 3 (2013), 883-888.

Dates
First available in Project Euclid: 5 September 2013

Permanent link to this document
https://projecteuclid.org/euclid.jap/1378401243

Digital Object Identifier
doi:10.1239/jap/1378401243

Mathematical Reviews number (MathSciNet)
MR3102521

Zentralblatt MATH identifier
1276.05106

Subjects
Primary: 60B99: None of the above, but in this section
Secondary: 05C35: Extremal problems [See also 90C35]

Keywords
Exponential random graph model complex network phase transition

Citation

Aristoff, David; Radin, Charles. Emergent structures in large networks. J. Appl. Probab. 50 (2013), no. 3, 883--888. doi:10.1239/jap/1378401243. https://projecteuclid.org/euclid.jap/1378401243


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