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The Information Theoretic Entropy Function as a Total Expected Participation Index for Communication Network Experiments

Published online by Cambridge University Press:  01 January 2025

Kenneth D. Mackenzie
Kenneth D. Mackenzie*
Affiliation:
Carnegie Institute of Technology
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Abstract

This paper shows how the concept of an incidence matrix of communications can be used to define the entropy of a finite scheme. The properties of the entropy function are examined and the function is found to be best interpreted as a total expected participation index. Data is presented showing the relationship between structural centrality and the new total expected participation index. In general, as the network becomes more centralized the smaller the value of the participation index and as the network becomes more structurally decentralized the greater the participation index.

Type
Original Paper
Information
Psychometrika , Volume 31 , Issue 2 , June 1966 , pp. 249 - 254
Copyright
Copyright © 1966 Psychometric Society

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Footnotes

*

This research was supported in part by Ford Foundation Grant 1-40055 to the Graduate School of Industrial Administration at Carnegie Institute of Technology for Research in Organizational Behavior.

†

The author wishes to acknowledge the aid of Terry B. Marbach in the preparation of data.

References

Cherry, C. On human communications, New York: Science Editions, 1961.Google Scholar
Khinchin, A. I. Mathematical foundations of information theory, New York: Dover, 1957.Google Scholar
Mackenzie, K. D. Structural centrality in communications networks. Psychometrika, 1966, 31, 17–25.CrossRefGoogle Scholar
Wolfowitz, J. Coding theorems of information theory, Englewood Cliffs, N. J.: Prentice-Hall, 1961.Google Scholar