Psychometrika

, Volume 17, Issue 2, pp 195–208 | Cite as

On the determination of redundancies in sociometric chains

  • Ian C. Ross
  • Frank Harary
Article

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.

Keywords

Public Policy Statistical Theory Redundant Path 

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References

  1. 1.
    Festinger, Leon. The analysis of sociograms using matrix algebra.Human Relations, 1949,2, 153–158.Google Scholar
  2. 2.
    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.Google Scholar
  3. 3.
    Luce, R. D., and Perry, A. D. A method of matrix analysis of group structure.Psychometrika, 1949,14, 95–116.Google Scholar
  4. 4.
    Weiss, Marie J. Higher algebra for the undergraduate. Wiley, 1949, pp. 90–144.Google Scholar

Copyright information

© Psychometric Society 1952

Authors and Affiliations

  • Ian C. Ross
    • 1
  • Frank Harary
    • 1
  1. 1.University of MichiganUSA

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