9 - Structural Equivalence

Summary

Many methods for the description of network structural properties are concerned with the dual notions of social position and social role. In social network terms these translate into procedures for analyzing actors' structural similarities and patterns of relations in multirelational networks. These methods, which have been referred to as positional, role, or relational approaches, are the topic of Part IV. Although these methods are mathematically and formally diverse, they share a common goal of representing patterns in complex social network data in simplified form to reveal subsets of actors who are similarly embedded in networks of relations and to describe the associations among relations in multirelational networks.

The diversity of methods and potential complexity of mathematics has influenced our organization of topics in the following chapters. We begin this chapter with an overview of the theoretical and historical background for network role and positional analysis. We then discuss the basics of positional analysis. These basics will occupy Chapter 9 and the first part of Chapter 10. Chapters 9 and 10 discuss how to perform basic positional analysis using measures based on the mathematical notion of structural equivalence. In Chapters 11 and 12 we take up more advanced approaches to the notions of role and position and explore alternative formal definitions of these concepts. These chapters are concerned with the algebraic analysis of role systems using relational algebras (Chapter 11) and more general definitions of equivalence (Chapter 12).