English

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.

Keywords

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

R2 v1 2026-06-22T02:03:08.554Z