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A Graph-Theoretic Formulation of Exploratory Blockmodeling

Authors Alexander Bille, Niels Grüttemeier , Christian Komusiewicz , Nils Morawietz

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Author Details

Alexander Bille
  • Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Germany
Niels Grüttemeier
  • System Technologies and Image Exploitation, Fraunhofer IOSB, Lemgo, Fraunhofer Institute of Optronics, Germany
Christian Komusiewicz
  • Institute of Computer Science, Friedrich Schiller Universität Jena, Germany
Nils Morawietz
  • Institute of Computer Science, Friedrich Schiller Universität Jena, Germany

Funding

  • Morawietz, Nils: Supported by the Deutsche Forschungsgemeinschaft (DFG), project OPERAH, KO 3669/5-1.

Acknowledgements

We would like to thank the anonymous reviewers of SEA for their helpful comments which have improved the presentation of our results.

Cite As Get BibTex

Alexander Bille, Niels Grüttemeier, Christian Komusiewicz, and Nils Morawietz. A Graph-Theoretic Formulation of Exploratory Blockmodeling. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 14:1-14:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.SEA.2023.14

Abstract

We present a new simple graph-theoretic formulation of the exploratory blockmodeling problem on undirected and unweighted one-mode networks. Our formulation takes as input the network G and the maximum number t of blocks for the solution model. The task is to find a minimum-size set of edge insertions and deletions that transform the input graph G into a graph G' with at most t neighborhood classes. Herein, a neighborhood class is a maximal set of vertices with the same neighborhood. The neighborhood classes of G' directly give the blocks and block interactions of the computed blockmodel.
We analyze the classic and parameterized complexity of the exploratory blockmodeling problem, provide a branch-and-bound algorithm, an ILP formulation and several heuristics. Finally, we compare our exact algorithms to previous ILP-based approaches and show that the new algorithms are faster for t ≥ 4.

Subject Classification

ACM Subject Classification
  • Theory of computation → Social networks
  • Theory of computation → Parameterized complexity and exact algorithms
  • Theory of computation → Branch-and-bound
Keywords
  • Clustering
  • Exact Algorithms
  • ILP-Formulation
  • Branch-and-Bound
  • Social Networks

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