Algebraic Systems for Normal and Hierarchical Sociograms

Abstract

Sociometric techniques have proved very fruitful for questions directed within the parts of a social structure, but the potential of sociometry for studying total social structures has been neglected. Since this neglect seems in large part due to the conceptual difficulties involved in describing total social structures, it is proposed that relational algebras can facilitate progress in this direction. The first two sections develop an algebra, appropriate for the familiar mutual-choice sociogram, which allows both identification of cliques and preservation of the essential relationships between cliques. Then, since most sociological ideas about group structure imply hierarchy, a procedure for inferring hierarchy in sociograms is presented. Finally, an algebra appropriate for studying hierarchical sociograms is considered, and some of the parallels between this algebra and Friedell's semilattice algebra for organizations are developed.