Connectivity and Generalized Cliques in Sociometric Group Structure

A generalized concept of clique, called ann-clique, is introduced and n-cliques are shown to have a very close relationship to the existence of cliques in an artificial structure defined on the same set of elements, thus permitting the determination ofn-Cliques by means of the same simple matrix procedures used to obtain the clique structures.

Abstract

By using the concepts of antimetry and n -chain it is possible to define and to investigate some properties of connectivity in a sociometric group. It is shown that the number of elements in a group, the number of antimetries, and the degree of connectivity must satisfy certain inequalities. Using the ideas of connectivity, a generalized concept of clique, called an n -clique, is introduced. n -cliques are shown to have a very close relationship to the existence of cliques in an artificial structure defined on the same set of elements, thus permitting the determination of n -cliques by means of the same simple matrix procedures used to obtain the clique structures. The presence of two or more m -cliques, where m is the number of elements in the group, is proved to mean an almost complete splitting of the group.