Cluster Inference by using Transitivity Indices in Empirical Graphs
Journal of the American Statistical AssociationPublished 1 December 1982
Ove Frank, Frank Harary
Citations86
SJR quartileQ1
SJR score4.10
SNIP3.08
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
This model is introduced for similarities observed between the objects sampled from an unknown cluster structure and it is shown how some common transitivity indices in empirical graphs can be used for making statistical inferences about cluster structures.
Abstract
Abstract A random graph model is introduced for similarities observed between the objects sampled from an unknown cluster structure. We investigate this model and show how some common transitivity indices in empirical graphs can be used for making statistical inferences about cluster structures.
Keywords
Computer SciencePhysics and Astronomy
Springer series in statisticsMeasures of Association for Cross Classifications
2,260 Citations1979Leo A. Goodman, William Kruskal
Scandinavian Journal of StatisticsScandinavian Journal of Statistics
985 Citations2010Gijbels, Irène, Veraverbeke, Noël +1 more
Sociological MethodologyLocal Structure in Social Networks
431 Citations1976Paul W. Holland, Samuel Leinhardt
This chapter was written when Paul Holland was with the Computer Research Center for Economics and Management Science of the National Bureau of Economic Research, Inc.
PsychometrikaSome Applications of Graph Theory to Clustering
158 Citations1974Lawrence J. Hubert
Several graphtheoretic criteria are proposed for use within a general clustering paradigm as a means of developing procedures “in between” the extremes of complete-link and single-link hierarchical partitioning.
Cambridge University Press eBooksApplications to graph theory
135 Citations2018Cheryl E. Praeger, Csaba Schneider
An overview of the applications of graph theory in various fields to some extent is given but mainly focuses on the computer discipline applications that uses graph theoretical concepts.
Journal of the American Statistical AssociationA Probability Theory of Cluster Analysis
133 Citations1973Robert F. Ling
Journal of the American Statistical AssociationStability of Two Hierarchical Grouping Techniques Case I: Sensitivity to Data Errors
129 Citations1974Frank B. Baker
Empirical sampling distributions of the gamma coefficients indicated that the single linkage grouping technique was more sensitive to the type of data errors employed than the complete linkage technique.
Elsevier eBooksDistribution Problems in Clustering
101 Citations1977J. A. Hartigan
A statistical problem that is encountered in deciding which of the many clusters presented by algorithms are real is discussed, which requires the asymptotic theory to be validated by Monte Carlo experiments.
Sociological MethodologyA Survey of Statistical Methods for Graph Analysis
98 Citations1981Ove Frank
Only recently have statistical models and methods been developed that begin to meet the need for proper handling of sampling variation, measurement errors, and other kinds of uncertainty in network data.
PsychometrikaMonotone Invariant Clustering Procedures
75 Citations1973Lawrence J. Hubert
Several alternative procedures are presented in this paper that also share in the same property of invariance with respect to monotone increasing transformations of the original similarity measures.
Journal of the American Statistical AssociationEstimating an Author's Vocabulary
55 Citations1973Donald R. McNeil
Journal of the American Statistical AssociationProbability Tables for Cluster Analysis Based on a Theory of Random Graphs
49 Citations1976Robert F. Ling, G.G. Killough
Journal of Mathematical SociologyMatrix measures for transitivity and balance*
44 Citations1979Frank Harary, Helene J. Kommel
PsychometrikaSome Extensions of Johnson's Hierarchical Clustering Algorithms
43 Citations1972Lawrence J. Hubert
This paper is an attempt to extend the hierarchical partitioning algorithms proposed by Johnson and to emphasize a general connection between these clustering procedures and the mathematical theory of lattices.
Estimation of the Number of Connected Components in a Graph by Using a Sampled Subgraph
42 Citations1978Ove Frank
The number of connected components in an unknown parent graph is to be estimated by using a sampled subgraph using a transitive graph and a forest.
Journal of Mathematical SociologyTransitivity in stochastic graphs and digraphs
33 Citations1980Ove Frank
Journal of Statistical Computation and SimulationEstimating a graph from triad counts
22 Citations1979Ove Frank
Methods of estimating a transitive graph and a forest are described, and a possible approach for a general graph G is indicated.
Elsevier eBooksAn Empirical Comparison of Baseline Models for Goodness-of-Fit in r-Diameter Hierarchical Clustering
16 Citations1977Lawrence J. Hubert, Frank B. Baker
The class of r-diameter strategies provides a sequence of clustering alternatives that lie between the complete-link and the single-link extremes; at the same time, each such alternative maintains a sole dependence on the rank order of the proximity values assigned to the object pairs and used in constructing the partition hierarchy.
