Tame sparse exponential random graphs

Suman Chakraborty; Remco van der Hofstad; Frank den Hollander

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arXiv · 2406.17390

Tame sparse exponential random graphs

Suman Chakraborty·Remco van der Hofstad·Frank den Hollander

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Abstract

In this paper, we obtain a precise estimate of the probability that the sparse binomial random graph contains a large number of vertices in a triangle. The estimate of log of this probability is correct up to second order, and enables us to propose an exponential random graph model based on the number of vertices in a triangle. Specifically, by tuning a single parameter, we can with high probability induce any given fraction of vertices in a triangle. Moreover, in the proposed exponential random graph model we derive the large deviation principle for the number of edges. As a byproduct, we propose a consistent estimator of the tuning parameter.

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BibTeX RIS

Suman Chakraborty, Remco van der Hofstad, Frank den Hollander. 2024-06-25. Tame sparse exponential random graphs. https://arxiv.org/abs/2406.17390

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