## The Annals of Applied Probability

### Asymptotic quantization of exponential random graphs

#### 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.

#### Article information

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

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

https://projecteuclid.org/euclid.aoap/1481792585

Digital Object Identifier
doi:10.1214/16-AAP1175

Mathematical Reviews number (MathSciNet)
MR3582803

Zentralblatt MATH identifier
1356.05138

#### Citation

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. https://projecteuclid.org/euclid.aoap/1481792585

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