The development of stochastic models for the analysis of social networks is an important growth area in contemporary statistics. The last few decades have witnessed the rapid development of a variety of statistical models capable of representing the global structure of an observed network in terms of underlying generating mechanisms. The distinctive feature of statistical models for social networks is their ability to represent directly the dependence relations that these mechanisms entail. In this review, we focus on models for single network observations, particularly on the family of exponential random graph models. After defining the models, we discuss issues of model specification, estimation and assessment. We then review model extensions for the analysis of other types of network data, provide an empirical example, and give a selective overview of empirical studies that have adopted the basic model and its many variants. We conclude with an outline of the current analytical challenges.


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