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

Chatterjee, Diaconis and Sly (2011) recently established the consistency of the maximum likelihood estimate in the $\beta$-model when the number of vertices goes to infinity. By approximating the inverse of the Fisher information matrix, we obtain its asymptotic normality under mild conditions. Simulation studies and a data example illustrate the theoretical results.