

This on-line textbook introduces many of the basics of formal approaches to the analysis of social networks.

• 2: Why Formal Methods?

The basic idea of a social network is very simple. A social network is a set of actors (or points, or nodes, or agents) that may have relationships (or edges, or ties) with one another. Networks can have few or many actors, and one or more kinds of relations between pairs of actors. To build a useful understanding of a social network, a complete and rigorous description of a pattern of social relationships is a necessary starting point for analysis.

• 5: Using Matrices to Represent Social Relations

Graphs are very useful ways of presenting information about social networks. However, when there are many actors and/or many kinds of relations, they can become so visually complicated that it is very difficult to see patterns. It is also possible to represent information about social networks in the form of matrices. Representing the information in this way also allows the application of mathematical and computer tools to summarize and find patterns.

• 7: Connection

In this chapter we will examine some of the most obvious and least complex ideas of formal network analysis methods. Despite the simplicity of the ideas and definitions, there are good theoretical reasons (and some empirical evidence) to believe that these basic properties of social networks have very important consequences. For both individuals and for structures, one main question is connections.

• 10: Centrality and Power

Social network analysis methods provide some useful tools for addressing one of the most important (but also one of the most complex and difficult) aspects of social structure: the sources and distribution of power. The network perspective suggests that the power of individual actors is not an individual attribute, but arises from their relations with others.
• 11: Cliques and Sub-groups

One of the most common interests of structural analysts is in the "sub-structures" that may be present in a network. The dyads, triads, and ego-centered neighborhoods that we examined earlier can all be though of as sub-structures. In this chapter, we'll consider some approaches to identifying larger groupings.

• 13: Measures of Similarity and Structural Equivalence

In this rather lengthy chapter we are going to do three things. First, we will focus on how we can measure the similarity of actors in a network based on their relations to other actors.Second, we will very quickly look at two tools that are very commonly used for visualizing the patterns of similarity and dissimilarity/distance among actors. Third, we will examine the most commonly used approaches for finding structural equivalence classes.
• 14: Automorphic Equivalence

Automorphic equivalence is not as demanding a definition of similarity as structural equivalence, but is more demanding than regular equivalence. There is a hierarchy of the three equivalence concepts: any set of structural equivalences are also automorphic and regular equivalences. Any set of automorphic equivalences are also regular equivalences. Not all regular equivalences are necessarily automorphic or structural; and not all automorphic equivalences are necessarily structural.
• 15: Regular Equivalence

Regular equivalence is the least restrictive of the three most commonly used definitions of equivalence. It is, however, probably the most important for the sociologist. This is because the concept of regular equivalence, and the methods used to identify and describe regular equivalence sets correspond quite closely to the sociological concept of a "role". The notion of social roles is a centerpiece of most sociological theorizing.
• 16: Multiplex Networks

In this chapter we will look at some of the tools that social network analysts have used to grapple with the complexity of analyzing simultaneous multiple relations among actors. We'll begin by examining some basic data structures for multiplex data, and how they can be visualized. To be useful in analysis, however, the information about multiple relations among a set of actors must somehow be represented in summary form.

• 18: Some Statistical Tools

In this chapter we will look at some of the most basic and common approaches to applying statistical analysis to the attributes of actors embedded in networks, the relations among these actors, and the similarities between multiple relational networks connecting the same actors.