Hostname: page-component-745bb68f8f-5r2nc Total loading time: 0 Render date: 2025-01-08T10:22:12.567Z Has data issue: false hasContentIssue false
  • English
  • Français

A Graph Theoretic Approach to Similarity Relations

Published online by Cambridge University Press:  01 January 2025

Frank Harary
Frank Harary*
Affiliation:
University of Michigan
Get access Rights & Permissions [Opens in a new window]

Summary

A similarity relation is reflexive and symmetric. A graph may be regarded as a geometric representation of an irreflexive symmetric relation; an r-graph then coincides with a similarity relation. For the realization of psychophysical phenomena, the points of a graph stand for the stimuli and a line for indistinguishability of a stimulus pair. Not all graphs, however, are likely to arise as similarity relations in a real situation. A special class of graphs, called interval graphs, does have this realistic property. These graphs are described and characterized.

Type
Original Paper
Information
Psychometrika , Volume 29 , Issue 2 , June 1964 , pp. 143 - 151
Copyright
Copyright © 1964 Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

The preparation of this article was supported by Grant NSF-G-17771 from the National Science Foundation.

References

Cartwright, D. and Harary, F. Structural balance: A generalization of Heider's theory. Psychol. Rev., 1956, 63, 277–293.CrossRefGoogle ScholarPubMed
Coombs, C. H. The theory of data, New York: Wiley, 1964.Google Scholar
Galanter, E. H. An axiomatic and experimental study of sensory order and measure. Psychol. Rev., 1956, 63, 16–28.CrossRefGoogle ScholarPubMed
Gilmore, P. C. and Hoffman, A. J. A characterization of comparability graphs and of interval graphs, Yorktown Heights, New York: IBM Research Center, 1962.Google Scholar
Goodman, N. The structure of appearance, Cambridge, Mass.: Harvard Univ. Press, 1951.Google Scholar
Harary, F. Graph theoretic methods in the management sciences. Mgmt Sci., 1959, 5, 387–403.CrossRefGoogle Scholar
Harary, F., Norman, R. Z., and Cartwright, D. Structural models: An introduction to the theory of directed graphs, New York: Wiley, 1964.Google Scholar
Lekkerkerker, C. G. and Boland, J. C. Representation of a finite graph by a set of intervals on the real line. Fundamenta Mathematicae, 1962, 51, 45–64.CrossRefGoogle Scholar
Restle, F. A metric and an ordering on sets. Psychometrika, 1959, 24, 207–220.CrossRefGoogle Scholar