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The Degree Distribution in Random Intersection Graphs

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Challenges at the Interface of Data Analysis, Computer Science, and Optimization

Abstract

We study the degree distribution in a general random intersection graph introduced by Godehardt and Jaworski (Exploratory Data Analysis in Empirical Research, pp. 68–81, Springer, Berlin, 2002). The model has shown to be useful in many applications, in particular in the analysis of the structure of data sets. Recently Bloznelis (Lithuanian Math J 48:38–45, 2008) and independently Deijfen and Kets (Eng Inform Sci 23:661–674, 2009) proved that in many cases the degree distribution in the model follows a power law. We present an enhancement of the result proved by Bloznelis. We are able to strengthen the result by omitting the assumption on the size of the feature set. The new result is of considerable importance, since it shows that a random intersection graph can be used not only as a model of scale free networks, but also as a model of a more important class of networks – complex networks.

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Acknowledgements

This work has been partially supported by the Ministry of Science and Higher Education, grant N N206 2701 33, 2007–2010.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614, Poznań, Poland

    Katarzyna Rybarczyk

Authors
  1. Katarzyna Rybarczyk
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Correspondence to Katarzyna Rybarczyk .

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Editors and Affiliations

  1. Fak. Wirtschaftswissenschaften, Inst. Entscheidungstheorieund, Universität Karlsruhe (TH), Kaiserstr. 12, Karlsruhe, 76128, Germany

    Wolfgang A. Gaul

  2. Insitute for Information Systems, and Management (IISM), Karlsruhe Institute of Technology (KIT), Kaiserstr. 12, Karlsruhe, 76131, Baden-Württemberg, Germany

    Andreas Geyer-Schulz

  3. , Information Systems, University ofHildesheim, Marienburger Platz 22, Hildesheim, 31141, Germany

    Lars Schmidt-Thieme

  4. Institute for Information Systems, and Management (IISM), Karlsruhe Institute of Technology (KIT), Kaiserstraße 12, Karlsruhe, 76128, Germany

    Jonas Kunze

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Rybarczyk, K. (2012). The Degree Distribution in Random Intersection Graphs. In: Gaul, W., Geyer-Schulz, A., Schmidt-Thieme, L., Kunze, J. (eds) Challenges at the Interface of Data Analysis, Computer Science, and Optimization. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24466-7_30

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