Structural equivalence of individuals in social networks

TLDR

Social structure is investigated beyond ideal types, with functorial mapping from category theory serving as a key analytical tool. The study seeks to clarify how relations interrelate within concrete social groups. By algebraically extracting global relational patterns through functorial mappings, the authors delineate equivalence classes of individuals and illustrate the approach on two social networks.

Abstract

The aim of this paper is to understand the interrelations among relations within concrete social groups. Social structure is sought, not ideal types, although the latter are relevant to interrelations among relations. From a detailed social network, patterns of global relations can be extracted, within which classes of equivalently positioned individuals are delineated. The global patterns are derived algebraically through a ‘functorial’ mapping of the original pattern. Such a mapping (essentially a generalized homomorphism) allows systematically for concatenation of effects through the network. The notion of functorial mapping is of central importance in the ‘theory of categories,’ a branch of modern algebra with numerous applications to algebra, topology, logic. The paper contains analyses of two social networks, exemplifying this approach.