Skip to main content

Random Intersection Graphs and Classification

  • Conference paper

Abstract

We study properties of random intersection graphs generated by a random bipartite graph. We focus on the connectedness of these random intersection graphs and give threshold functions for this property and results for the size of the largest components in such graphs. The application of intersection graphs to find clusters and to test their randomness in sets of non-metric data is shortly discussed.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • BOCK, H.-H. (1996): Probabilistic Models in Cluster Analysis. Computational Statistics and Data Analysis, 23, 5–28.

    Article  MATH  Google Scholar 

  • GODEHARDT, E. (1990): Graphs as Structural Models. Vieweg, Braunschweig.

    Google Scholar 

  • GODEHARDT, E. and JAWORSKI, J. (1996): On the Connectivity of a Random Interval Graph. Random Structures and Algorithms, 9, 137–161.

    Article  MathSciNet  MATH  Google Scholar 

  • GODEHARDT, E. and JAWORSKI, J. (2002): Two Models of Random Intersection Graphs for Classification. In: M. Schwaiger and O. Opitz (Eds.): Exploratory Data Analysis in Empirical Research. Springer, Berlin, 68–81.

    Google Scholar 

  • JANSON, S., ŁUCZAK, T. and RUCIŃSKI, A. (2001): Random Graphs. Wiley, New York.

    Google Scholar 

  • JAWORSKI, J., KAROŃSKI, M. and STARK, D. (2006): The Degree of a Typical Vertex in Generalized Random Intersection Graph Models. Discrete Mathematics, 306,18, 2152–2165.

    Article  MathSciNet  MATH  Google Scholar 

  • JAWORSKI, J. and PALKA, Z. (2002): Remarks on a general model of a random digraph. Ars Combinatoria, 65, 135–144.

    MathSciNet  MATH  Google Scholar 

  • JAWORSKI, J. and SMIT, I. (1987): On a Random Digraph. Annals of Discrete Mathematics, 33, 111–127.

    MathSciNet  Google Scholar 

  • KAROŃSKI, M., SCHEINERMAN, E.R. and SINGER-COHEN, K.B. (1999): On Random Intersection Graphs: The Subgraph Problem. Combinatorics, Probability and Computing, 8, 131–159.

    Article  MathSciNet  MATH  Google Scholar 

  • KORDECKI, W. (1985): On the Connectedness of Random Hypergraphs. Commentaciones Mathematicae, 25, 265–283.

    MathSciNet  MATH  Google Scholar 

  • RYBARCZYK, K. (2005): O pewnych zastosowaniach hipergrafów losowych. MA Thesis, Faculty of Mathematics, Adam Mickiewicz University, Poznań.

    Google Scholar 

  • SCHMIDT-PRUZAN, J. and SHAMIR, E. (1985): Component Structure in the Evolution of Random Hypergraphs. Combinatorica, 5.1, 81–94.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Godehardt, E., Jaworski, J., Rybarczyk, K. (2007). Random Intersection Graphs and Classification. In: Decker, R., Lenz, H.J. (eds) Advances in Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70981-7_8

Download citation

Publish with us

Policies and ethics