On finding graph clusterings with maximum modularity

Authors:
Ulrik Brandes;Daniel Delling;Marco Gaertler;Robert Görke;Martin Hoefer;Zoran Nikoloski;Dorothea Wagner
Affiliations:
Department of Computer and Information Science, University of Konstanz;Faculty of Informatics, Universität Karlsruhe, TH;Faculty of Informatics, Universität Karlsruhe, TH;Faculty of Informatics, Universität Karlsruhe, TH;Department of Computer and Information Science, University of Konstanz;Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Prague;Faculty of Informatics, Universität Karlsruhe, TH
Venue:
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Year:
2007

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Abstract

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.