On Finding Graph Clusterings with Maximum Modularity

  • Ulrik Brandes
  • Daniel Delling
  • Marco Gaertler
  • Robert Görke
  • Martin Hoefer
  • Zoran Nikoloski
  • Dorothea Wagner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4769)


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.


Greedy Algorithm Integer Linear Program Community Detection Approximation Factor Element Node 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Ulrik Brandes
    • 1
  • Daniel Delling
    • 2
  • Marco Gaertler
    • 2
  • Robert Görke
    • 2
  • Martin Hoefer
    • 1
  • Zoran Nikoloski
    • 3
  • Dorothea Wagner
    • 2
  1. 1.Department of Computer and Information Science, University of Konstanz 
  2. 2.Faculty of Informatics, Universität Karlsruhe (TH) 
  3. 3.Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Prague 

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