“Region” and ‘subgroup”: Organizing concepts in social network analysis

This paper provides a conceptual framework within which one can discuss the identification and comparison of subsets of actors and relations in social networks. Consider the adjacency matrix of a social network: Let a region be any subset of elements in the matrix and a subgroup be any subset of units (rows and corresponding columns). Then, a subgroup defines four regions: all possible relations among subgroup members, all possible relations between subgroup members and nonmembers (two regions), and all possible relations among nonmembers. This paper uses the properties of regions formed by subgroups to: (1) construct consistent and general definitions of degree and density in mathematical graphs; (2) discuss the relationship between subgroups produced by relational analyses and those produced by positional analyses; (3) show how to use region and subgroup to analyze egocentric networks; and (4) indicate directions for the further development of an analytical framework based on region and subgroup.