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A Method of Matrix Analysis of Group Structure

Published online by Cambridge University Press:  01 January 2025

R. Duncan Luce  and
Albert D. Perry
R. Duncan Luce
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology
Albert D. Perry
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology
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Abstract

Matrix methods may be applied to the analysis of experimental data concerning group structure when these data indicate relationships which can be depicted by line diagrams such as sociograms. One may introduce two concepts, n-chain and clique, which have simple relationships to the powers of certain matrices. Using them it is possible to determine the group structure by methods which are both faster and more certain than less systematic methods. This paper describes such a matrix method and applies it to the analysis of practical examples. At several points some unsolved problems in this field are indicated.

Type
Original Paper
Information
Psychometrika , Volume 14 , Issue 2 , June 1949 , pp. 95 - 116
Copyright
Copyright © 1949 The Psychometric Society

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Footnotes

*

Some of these examples have been worked out by the Research Center for Group Dynamics, Massachusetts Institute of Technology, in conjunction with some of its research.