On Finding Graph Clusterings with Maximum Modularity

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2007
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Delling, Daniel
Gaertler, Marco
Görke, Robert
Hoefer, Martin
Nikoloski, Zoran
Wagner, Dorothea
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BRANDSTÄDT, Andreas, ed., Dieter KRATSCH, ed., Haiko MÜLLER, ed.. Graph-Theoretic Concepts in Computer Science. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007, pp. 121-132. Lecture Notes in Computer Science. ISBN 978-3-540-74838-0. Available under: doi: 10.1007/978-3-540-74839-7_12
Zusammenfassung

Modularity is a recently introduced quality measure for graph clusterings. It has immediately received considerable attention in several disciplines, and in particular in the complex systems literature, although its properties are not well understood. We study the problem of finding clusterings with maximum modularity, thus providing theoretical foundations for past and present work based on this measure. More precisely, we prove the conjectured hardness of maximizing modularity both in the general case and with the restriction to cuts, and give an Integer Linear Programming formulation. This is complemented by first insights into the behavior and performance of the commonly applied greedy agglomaration approach.

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ISO 690BRANDES, Ulrik, Daniel DELLING, Marco GAERTLER, Robert GÖRKE, Martin HOEFER, Zoran NIKOLOSKI, Dorothea WAGNER, 2007. On Finding Graph Clusterings with Maximum Modularity. In: BRANDSTÄDT, Andreas, ed., Dieter KRATSCH, ed., Haiko MÜLLER, ed.. Graph-Theoretic Concepts in Computer Science. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007, pp. 121-132. Lecture Notes in Computer Science. ISBN 978-3-540-74838-0. Available under: doi: 10.1007/978-3-540-74839-7_12
BibTex
@inproceedings{Brandes2007Findi-5883,
  year={2007},
  doi={10.1007/978-3-540-74839-7_12},
  title={On Finding Graph Clusterings with Maximum Modularity},
  isbn={978-3-540-74838-0},
  publisher={Springer Berlin Heidelberg},
  address={Berlin, Heidelberg},
  series={Lecture Notes in Computer Science},
  booktitle={Graph-Theoretic Concepts in Computer Science},
  pages={121--132},
  editor={Brandstädt, Andreas and Kratsch, Dieter and Müller, Haiko},
  author={Brandes, Ulrik and Delling, Daniel and Gaertler, Marco and Görke, Robert and Hoefer, Martin and Nikoloski, Zoran and Wagner, Dorothea}
}
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