Abstract
The use of a matrix to represent a relationship between the members of a group is well known in sociometry. If this matrix is raised to a certain power, the elements appearing give the total number of connecting paths between each pair of members. In general, some of these paths will be redundant. Methods of finding the number of such redundant paths have been developed for three- and four-step chains by Luce and Perry (3) and Katz (2), respectively. We have derived formulas for the number of redundant paths of five and six steps; and in addition, an algorithm for determining the number of redundant paths of any given length.
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References
Festinger, Leon. The analysis of sociograms using matrix algebra.Human Relations, 1949,2, 153–158.
Katz, Leo. An application of matrix algebra to the study of human relations within organizations. Institute of Statistics, University of North Carolina, Mimeograph Series, 1950.
Luce, R. D., and Perry, A. D. A method of matrix analysis of group structure.Psychometrika, 1949,14, 95–116.
Weiss, Marie J. Higher algebra for the undergraduate. Wiley, 1949, pp. 90–144.
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The research leading to this paper was supported by a grant from the Rockefeller Foundation.
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Ross, I.C., Harary, F. On the determination of redundancies in sociometric chains. Psychometrika 17, 195–208 (1952). https://doi.org/10.1007/BF02288782
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DOI: https://doi.org/10.1007/BF02288782