Social network analysts study the structural patterning of the ties that link social actors. For the most part, they seek to uncover two kinds of patterns: (1) those that reveal subsets of actors that are organized into cohesive social groups, and (2) those that reveal subsets of actors that occupy equivalent social positions, or roles.

To uncover patterns of those kinds, network analysts collect and examine data on actor-to-actor ties. Such data record who is connected to whom and/or how closely they are connected. Typically, the data are organized into square, N-dimensional, N by-N matrices, where the N rows and the N columns both refer to the social actors being studied. Cell entries in these matrices indicate either the presence/absence or the strength of some social relationship linking the row actor to the column actor. In this chapter, we deal only with symmetric relationships where, given a connection from actor i to actor j, actor j is also connected to i in the same way.

Network analysts sometimes use standard statistical procedures in examining their actor-by-actor matrices. Although there are several statistical modeling tools that have been developed specifically for network data (Holland and Leinhardt 1981; Wasserman and Pattison 1996), these tools were designed primarily for testing hypotheses. They do not provide a simple direct way to explore the patterning of network data – one that will permit an investigator to “see” groups and positions.