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December 2016 Asymptotic quantization of exponential random graphs
Mei Yin, Alessandro Rinaldo, Sukhada Fadnavis
Ann. Appl. Probab. 26(6): 3251-3285 (December 2016). DOI: 10.1214/16-AAP1175

Abstract

We describe the asymptotic properties of the edge-triangle exponential random graph model as the natural parameters diverge along straight lines. We show that as we continuously vary the slopes of these lines, a typical graph drawn from this model exhibits quantized behavior, jumping from one complete multipartite graph to another, and the jumps happen precisely at the normal lines of a polyhedral set with infinitely many facets. As a result, we provide a complete description of all asymptotic extremal behaviors of the model.

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Mei Yin. Alessandro Rinaldo. Sukhada Fadnavis. "Asymptotic quantization of exponential random graphs." Ann. Appl. Probab. 26 (6) 3251 - 3285, December 2016. https://doi.org/10.1214/16-AAP1175

Information

Received: 1 January 2015; Revised: 1 July 2015; Published: December 2016
First available in Project Euclid: 15 December 2016

zbMATH: 1356.05138
MathSciNet: MR3582803
Digital Object Identifier: 10.1214/16-AAP1175

Subjects:
Primary: 05C80
Secondary: 62F99 , 82B26

Keywords: asymptotic quantization , exponential random graphs , Graph limits , normal cone

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.26 • No. 6 • December 2016
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