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A Hierarchical Clustering Approach to Modularity Maximization

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Algorithms from and for Nature and Life

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Abstract

The problem of uncovering clusters of objects described by relationships that can be represented with the help of graphs is an application, which arises in fields as diverse as biology, computer science, and sociology, to name a few. To rate the quality of clusterings of undirected, unweighted graphs, modularity is a widely used goodness-of-fit index. As finding partitions of a graph’s vertex set, which maximize modularity, is NP-complete, various cluster heuristics have been proposed. However, none of these methods uses classical cluster analysis, where clusters based on (dis-)similarity data are sought. We consider the lengths of shortest paths between all vertex pairs as dissimilarities between the pairs of objects in order to apply standard cluster analysis methods. To test the performance of our approach we use popular real-world as well as computer generated benchmark graphs with known optimized cluster structure. Our approach is simple and compares favourably w.r.t. results known from the literature.

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Authors and Affiliations

  1. Institute of Decision Theory and Management Science, Karlsruhe Institute of Technology (KIT), Kaiserstr. 12, 76128, Karlsruhe, Germany

    Wolfgang Gaul & Rebecca Klages

Authors
  1. Wolfgang Gaul
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  2. Rebecca Klages
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Correspondence to Wolfgang Gaul .

Editor information

Editors and Affiliations

  1. University of Essex Department of Mathematical Sciences, Colchester, United Kingdom

    Berthold Lausen

  2. Ghent University Department of Marketing, Ghent, Belgium

    Dirk Van den Poel

  3. University of Marburg Databionics, FB 12, Marburg, Germany

    Alfred Ultsch

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Gaul, W., Klages, R. (2013). A Hierarchical Clustering Approach to Modularity Maximization. In: Lausen, B., Van den Poel, D., Ultsch, A. (eds) Algorithms from and for Nature and Life. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Cham. https://doi.org/10.1007/978-3-319-00035-0_7

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