As the analysis of social networks, or networks of interpersonal and social relationships among social groups, has become an increasingly important method of research in several of the social and behavioral sciences, the gathering of network data has outpaced the development of new methods for its analysis. Addressing the need for new analytical tools, Philippa Pattison presents a number of new algebraic models for the analysis of network data, explaining in the process the rationale for an algebraic approach. Models are developed for both complete networks, meaning those representing the social ties between all pairs of members in a given group, and local networks, meaning those structured around the social ties of one particular group member. Many applications are presented and the ways that these methods can address a number of important issues confronting network analysis are explained.