Graph-Theoretic Models for Testing the Homogeneity of Data

  • E. Godehardt
  • A. Horsch
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


In cluster analysis, the random graph model G n,p and G n,p-based multigraph models have been used for purposes of statistical modelling of data and testing the randomness of outlined clusters. While being appropriate for non-metric data, such models supposing independence of all edges do not take into account the triangle inequality which is valid for metric data. We will introduce graph models I n,dand I t,n,(d1,…,dt) for random intersection graphs in R 1 and multigraphs in R t under which the triangle inequality holds. We derive limit theorems for the distribution of random variables which describe important properties of these random intersection graphs. While being asymptotically equivalent for some properties like the limit distribution of the number of isolated points, the G n,p-model and the I n,d-model differ in numerous aspects.


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Copyright information

© Springer-Verlag Berlin · Heidelberg 1996

Authors and Affiliations

  • E. Godehardt
    • 1
  • A. Horsch
    • 1
  1. 1.AG Biometrie der Klinik für Thorax- und Kardiovaskular-ChirurgieHeinrich Heine-UniversitätDüsseldorfGermany

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