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Emergent Structures in Large Networks

Part of: Probability theory on algebraic and topological structures Graph theory

Published online by Cambridge University Press:  30 January 2018

David Aristoff  and
Charles Radin
David Aristoff*
Affiliation:
University of Minnesota
Charles Radin*
Affiliation:
The University of Texas at Austin
*
∗ Postal address: Department of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA. Email address: daristof@umn.edu
∗∗ Postal address: Mathematics Department, The University of Texas at Austin, Austin, TX 78712-1202, USA. Email address: radin@math.utexas.edu
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Abstract

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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.

Keywords

Exponential random graph modelcomplex networkphase transition

MSC classification

Primary: 60B99: None of the above, but in this section
Secondary: 05C35: Extremal problems
Type
Research Article
Information
Journal of Applied Probability , Volume 50 , Issue 3 , September 2013 , pp. 883 - 888
Copyright
© Applied Probability Trust 

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