## Analysis of social networks – An introduction to Exponential Random Graph Models

**Prof. Dr. Göran Kauermann**

We will give an introduction to statistical models for network data. Starting from the so-called p1 and p2 model we will concentrate on Exponential Random Graph Models (ERGMs) as common tools for social network data analyses. ERGMs describe the distribution of a network graph with an exponential family distribution, where the statistics are, for example, counts of edges, k stars or triangles, for instance. This facilitates meaningful interpretations of network data.

Though the model class mirrors welcome properties of exponential families, the fitting of ERGMs is numerical a burden due to a non-feasible normalization constant in the exponential model. We will discuss the state of the art of MCMC based sampling strategies for estimation and suggest approximate alternatives. We will also include random nodal effects to compensate for heterogeneity in the nodes of a network, combining different model classes.