A Method of Matrix Analysis of Group Structure
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TL;DR
This paper describes a matrix method, n-chain and clique, which has simple relationships to the powers of certain matrices and applies it to the analysis of practical examples of group structure.
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.