Connectivity and generalized cliques in sociometric group structure

By using the concepts of antimetry andn-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 ann-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 ofn-cliques by means of the same simple matrix procedures used to obtain the clique structures. The presence of two or morem-cliques, wherem is the number of elements in the group, is proved to mean an almost complete splitting of the group.