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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.
Computations on discrete structures, Knowledge and data engineering tools and techniques, Graphs and networks, Inter programming, G.1.6.a Constrained optimization, Combinatorial algorithms, Graph Theory, Clustering, Clustering, Mathematics and statistics
Daniel Delling, Robert G?rke, Zoran Nikoloski, Marco Gaertler, Ulrik Brandes, Dorothea Wagner, Martin Hoefer, "On Modularity Clustering", IEEE Transactions on Knowledge & Data Engineering, vol. 20, no. , pp. 172-188, February 2008, doi:10.1109/TKDE.2007.190689
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