A graph‐theoretic generalization of the clique concept

For at least twenty‐five years, the concept of the clique has had a prominent place in sociometric and other kinds of sociological research. Recently, with the advent of large, fast computers and with the growth of interest in graph‐theoretic social network studies, research on the definition and investigation of the graph theoretic properties of clique‐like structures has grown. In the present paper, several of these formulations are examined, and their mathematical properties analyzed. A family of new clique‐like structures is proposed which captures an aspect of cliques which is seldom treated in the existing literature. The new structures, when used to complement existing concepts, provide a new means of tapping several important properties of social networks. Notes The network research on which this paper is based, was carried out under support from the National Science Foundation, Grant No. BNS 76–05023. The Thai data were gathered by Foster in Thailand from August 1970 through December 1971; the field research was supported by the Foreign Area Fellowship Program of the Social Science Research Council and the American Council of Learned Societies.