A central limit theorem in the β-model for undirected random graphs with a diverging number of vertices

Abstract

Chatterjee et al. (2011) established the consistency of the maximum likelihood estimator in the β -model for undirected random graphs when the number of vertices goes to infinity. By approximating the inverse of the Fisher information matrix, we prove asymptotic normality of the maximum likelihood estimator under mild conditions. Simulation studies and a data example illustrate the theoretical results.