Tame sparse exponential random graphs

Bernoulli, vol. 32, pp. 1665–1685

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. We compute the logarithm of this probability up to second order, which 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 a large deviation principle for the number of edges. As a byproduct, we propose a consistent estimator of the tuning parameter.

Authors 3

1. Suman Chakraborty
   Affiliation as printed

   Pijnacker, Netherlands

2. Remco van der Hofstad

   Eindhoven University of Technology

   Affiliation as printed

   Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, Netherlands

3. Frank den Hollander Aachen Mathematical Institute

   Leiden University

   Affiliation as printed

   Mathematical Institute, Leiden University, Leiden, Netherlands