One of the primary uses of graph theory in social network analysis is the identification of the “most important” actors in a social network. In this chapter, we present and discuss a variety of measures designed to highlight the differences between important and non-important actors. Definitions of importance, or synonymously, prominence, have been offered by many writers. All such measures attempt to describe and measure properties of “actor location” in a social network. Actors who are the most important or the most prominent are usually located in strategic locations within the network. As far back as Moreno (1934), researchers have attempted to quantify the notions of sociometric “stars” and “isolates.”

We will discuss the most noteworthy and substantively interesting definitions of importance or prominence along with the mathematical concepts that the various definitions have spawned. Among the definitions that we will discuss in this chapter are those based on degree, closeness, betweenness, information, and simply the differential status or rank of the actors.

These definitions yield actor indices which attempt to quantify the prominence of an individual actor embedded in a network. The actor indices can also be aggregated across actors to obtain a single, group-level index which summarizes how variable or differentiated the set of actors is as a whole with respect to a given measure. We will show how to calculate both actor and group indices in this chapter.