Asymptotic quantization of exponential random graphs
Statistics Theory
2016-12-20 v3 Probability
Statistics Theory
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.
Cite
@article{arxiv.1311.1738,
title = {Asymptotic quantization of exponential random graphs},
author = {Mei Yin and Alessandro Rinaldo and Sukhada Fadnavis},
journal= {arXiv preprint arXiv:1311.1738},
year = {2016}
}
Comments
38 pages, 7 figures