Abstract
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.
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References
Birkhoff, G. Lattice theory. New York: American Mathematical Society, 1948.
Wedderburn, J. H. M. Boolean matrices.Annals of Math., 1934,35, 185–194.
Luce, R. Duncan, and Perry, Albert D. A method of matrix analysis of group structure.Psychometrika, 1949,14, 95–116.
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Luce, R.D. Connectivity and generalized cliques in sociometric group structure. Psychometrika 15, 169–190 (1950). https://doi.org/10.1007/BF02289199
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DOI: https://doi.org/10.1007/BF02289199