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arXiv · 1311.1738

Asymptotic quantization of exponential random graphs

Mei Yin·Alessandro Rinaldo·Sukhada Fadnavis
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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. 2016-01-11. Asymptotic quantization of exponential random graphs. https://doi.org/10.1214/16-aap1175

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