Asymptotic quantization of exponential random graphs

11 Jan 2016  ·  Yin Mei, Rinaldo Alessandro, Fadnavis Sukhada ·

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. read more

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Statistics Theory Probability Statistics Theory