The Annals of Applied Probability

Asymptotic quantization of exponential random graphs

Mei Yin, Alessandro Rinaldo, and Sukhada Fadnavis

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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.

Article information

Ann. Appl. Probab., Volume 26, Number 6 (2016), 3251-3285.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05C80: Random graphs [See also 60B20]
Secondary: 62F99: None of the above, but in this section 82B26: Phase transitions (general)

Exponential random graphs graph limits normal cone asymptotic quantization


Yin, Mei; Rinaldo, Alessandro; Fadnavis, Sukhada. Asymptotic quantization of exponential random graphs. Ann. Appl. Probab. 26 (2016), no. 6, 3251--3285. doi:10.1214/16-AAP1175.

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