# Section II Methods

## Exponential Random Graph Model Fundamentals

Johan Koskinen and Galina Daraganova

### Outline

This chapter provides a more detailed description of exponential random graph models and aims at answering the following questions:

- • What do the different notions of independence and interdependence imply for the modeling of tie-variables?
- • What are exponential random graph models? What can they tell us?
- • Why and when should we use exponential random graph models?
- • What different model specifications are available? How may these be interpreted?

After presenting some necessary notation, we revisit the concept of statistical independence in order to move to an understanding of interdependence. A network approach implies some level of dependence among the observations. We then explain the exponential random graph model (ERGM) framework akin to more familiar generalized linear models, emphasizing that we now have dependence, not independence, of observations. Next, the exact nature of these departures from independence is explained, and the implications for model specifications are presented. We begin by explaining individual ties because this illustrates the snug fit between individual ties, endogenous dependencies, and the model expressed in terms of the entire graph.