A method of matrix analysis of group structure

  title={A method of matrix analysis of group structure},
  author={R. Duncan Luce and Albert D. Perry},
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… 

Direct Factor Analysis of Sociometric Data

Electronic computation allows cliques or subgroups within a larger group to be separated by "direct" factor analysis of sociometric choices, followed by analytic rotation. Information on the


The method described here was developed for defining the structure of a social group, although it can be applied to grouping problems in many other areas. Essentially, it considers a given group of

Brokerage Roles between Cliques: A Secondary Clique Analysis

The roles the actors play in the cohesive structure using the brokerage ideas of Gould and Fernandez is examined, as it is possible to identify what actors play important roles (and which kind of role) in bridging the gaps between the cohesive subgroups.

Structural analysis and the generation of sociograms.

A method for analyzing sociometric information using a modified mutual choice sociomatrix with Replication of individuals permitted, enabling a person to be placed in proximity to all subgroups to which he belongs.

A Review of Mathematical Methods in Sociometry

Current mathematical and computer methods for the analysis of group and organizational structures of communication and evaluation are reviewed. Sociometric data collection, the detection of cliques

The preliminary analysis of emergent social structure in groups

The problem of detecting emergent social structure in small groups is examined in terms of establishing a baseline or expected structure. The standard proposed here is equalitarianism; that is to

Analyzing Clique Overlap

There are a large number of techniques that try and determine areas within a network in which individuals are more closely linked to each other than outsiders. However, once these cohesive subgraphs

Informal Structure in Elementary Schools

To study the informal structures in these schools, sociometric procedures were used (3). Matrix multiplication was applied to sociometric data. This allowed for analysis of group structures by means

A graph theory interpretation of nodal regions

ConclusionsThe techniques defined in this paper will divide a set of cities into subgroups which specify a central place and its subordinate hierarchy. The association between cities is not the only


Connectivity and generalized cliques in sociometric group structure

  • R. Luce
  • Mathematics
  • 1950
A generalized concept of clique, called ann-clique, is introduced and n-cliques are shown to have a very close relationship to the existence of cliques in an artificial structure defined on the same set of elements, thus permitting the determination ofn-Cliques by means of the same simple matrix procedures used to obtain the clique structures.