A central limit theorem in the $\beta$-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. 
Ting Yan and Jinfeng Xu
math.ST stat.TH