Social network data consist of measurements on a variety of relations for one or more sets of actors. In a network data set we may also have recorded information on attributes of the actors. We will need notation for the set of actors, the relations themselves, and the actor attributes so that we can refer to important network concepts in a unified manner.

In this chapter, we introduce notation and illustrate with examples. We start by defining notation for a single, dichotomous relation. We then move to more complicated network data sets involving more than one set of actors and/or more than one relation. We will need a notational system flexible enough to handle the wide range of network data sets that are encountered in practice. We note that the only type of structural variable discussed in this chapter is relational. Chapter 8 presents notation and methodology for affiliational networks.

For the reader who already is familiar with social networks and the ways in which social network data can be denoted, or the reader who is only interested in specific techniques, we recommend a quick reading of the material in this chapter. Specifically, such readers can glance at Section 2 and the examples used in this chapter (perhaps skipping the material on multiple relations), and return to this chapter as needed.

There are many ways to describe social network data mathematically. We will introduce three different notational schemes.