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On the Determination of Redundancies in Sociometric Chains

Published online by Cambridge University Press:  01 January 2025

Ian C. Ross  and
Frank Harary
Ian C. Ross
Affiliation:
University of Michigan
Frank Harary
Affiliation:
University of Michigan
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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.

Type
Original Paper
Information
Psychometrika , Volume 17 , Issue 2 , June 1952 , pp. 195 - 208
Copyright
Copyright © 1952 The Psychometric Society

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Footnotes

*

The research leading to this paper was supported by a grant from the Rockefeller Foundation.

References

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