New specifications for exponential random graph models

The most promising class of statistical models for expressing struc-tural properties of social networks observed at one moment in time is the class of exponential random graph models (ERGMs), also known as p models. The strong point of these models is that they can represent a variety of structural tendencies, such as transitivity, that define complicated dependence patterns not easily modeled by more basic probability models. Recently, Markov chain Monte Carlo (MCMC) algorithms have been developed that produce ap-proximate maximum likelihood estimators. Applying these models in their traditional specification to observed network data often has led to problems, however, which can be traced back to the fact that important parts of the parameter space correspond to nearly de-generate distributions, which may lead to convergence problems of estimation algorithms, and a poor fit to empirical data. This paper proposes new specifications of exponential random graph models. These specifications represent structural propertie