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Emergent Structures in Large Networks

Published online by Cambridge University Press:  30 January 2018

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: [email protected]
∗∗ Postal address: Mathematics Department, The University of Texas at Austin, Austin, TX 78712-1202, USA. Email address: [email protected]
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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.

Type
Research Article
Copyright
© Applied Probability Trust 

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