Social Structure from Multiple Networks. II. Role Structures

Abstract

Role structures in small populations are given operational meaning as algebras generated from the sociometric blockmodels of Part I by Boolean multiplication (matrix multiplication employing binary arithmetic). Many different sociometric structures can yield the same algebraic multiplication table, which captures a different level of social structure. Elements of the algebras are interpreted concretely as compound roles, and interlock among these roles is studied through investigation of their algebraic properties (equations and inclusions). Similarities and differences among algebras from six case studies are explored by means of homomorphisms as well as by multidimensional scaling on a derivative numerical distance measure. Results for particular populations, including reliability and stability tests, are summarized through simple target tables reporting aggregations of more complicated role structures.