Asymptotics in undirected random graph models parameterized by the strengths of vertices

摘要: To capture the heterozygous of vertex degrees networks and understand their distributions, a class random graph models parameterized by strengths vertices, are proposed. These equipped in framework mutually independent edges, where number parameters matches with size networks. The asymptotic properties maximum likelihood estimator have been derived some special such as β-model, but general results lacking. In these models, equations identical to moment equations. this paper, we establish unified result including consistency normality instead estimator, when goes infinity. We apply it generalized entropy Poisson models.