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“Minimax Length Links” of a Dissimilarity Matrix and Minimum Spanning Trees

Published online by Cambridge University Press:  01 January 2025

J. Douglas Carroll
J. Douglas Carroll*
Affiliation:
Rutgers University
*
Requests for reprints should be sent to J. Douglas Carroll, Faculty of Management, Rutgers University, 181 New Street, Newark, NJ 07102-1895.
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Abstract

A theorem is proved stating that the set of all “minimax links”, defined as links minimizing, over paths, the maximum length of links in any path connecting a pair of objects comprising nodes in an undirected weighted graph, comprise the union of all minimum spanning trees of that graph. This theorem is related to methods of fitting network models to dissimilarity data, particularly a method called “Pathfinder” due to Schvaneveldt and his colleagues, as well as to single linkage clustering, and results concerning the relationship between minimum spanning trees and single linkage hierarchical trees.

Keywords

minimum spanning treeshierarchical clusteringsingle linkagenetwork modelsproximity dataundirected weighted graphs
Type
Original Paper
Information
Psychometrika , Volume 60 , Issue 3 , September 1995 , pp. 371 - 374
Copyright
Copyright © 1995 The Psychometric Society

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Footnotes

Acknowledgments: The author thanks Phipps Arabie, Lawrence J. Hubert, and K. Christoph Klauer for a number of helpful suggestions and comments on various aspects of this paper.

References

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