In the previous chapter we discussed how the formal property of structural equivalence could be used to define a partition of actors in a social network into equivalence classes, called positions. Each position contains actors who relate in similar ways to and from other actors in the network. In this chapter we examine how to model the relationships among these positions. Our emphasis is on how to interpret the results of a positional analysis when the results are presented as a blockmodel. The methods in this chapter are primarily descriptive and focus on properties of subsets of actors. Stochastic blockmodels are discussed in Chapter 16 along with statistical methods for assessing the goodness-of-fit of a given blockmodel. Related methods that focus on associations among relations rather than on subsets of actors are presented in Chapter 11.

We begin by defining and illustrating the concept of a blockmodel. We then show how blockmodels can be used to model network positional systems. The most interesting and useful features of blockmodels are their theoretical interpretations, their potential for validating structural theories, and their usefulness for comparing structural patterns across populations.

Blockmodels were introduced by White, Boorman, and Breiger (1976) for the descriptive algebraic analysis of social roles.