Statistical Models for Degree Distributions of Networks
This provides the first statistically grounded analysis of dK-graph models for network researchers, though it appears incremental in formalizing existing concepts.
The authors tackled the problem of statistically modeling network degree distributions by formalizing exponential family models for degree and bi-degree distributions of undirected labeled simple graphs, providing preliminary results for parameter estimation and asymptotic behavior.
We define and study the statistical models in exponential family form whose sufficient statistics are the degree distributions and the bi-degree distributions of undirected labelled simple graphs. Graphs that are constrained by the joint degree distributions are called $dK$-graphs in the computer science literature and this paper attempts to provide the first statistically grounded analysis of this type of models. In addition to formalizing these models, we provide some preliminary results for the parameter estimation and the asymptotic behaviour of the model for degree distribution, and discuss the parameter estimation for the model for bi-degree distribution.