@misc{Brandes2006,
  abstract = {Several algorithms have been proposed to compute partitions of networks
	into communities that score high on a graph clustering index called
	modularity. While publications on these algorithms typically contain
	experimental evaluations to emphasize the plausibility of results,
	none of these algorithms has been shown to actually compute optimal
	partitions. We here settle the unknown complexity status of modularity
	maximization by showing that the corresponding decision version is
	NP-complete in the strong sense. As a consequence, any efficient,
	i.e. polynomial-time, algorithm is only heuristic and yields suboptimal
	partitions on many instances.},
  author = {Brandes, U. and Delling, D. and Gaertler, M. and Goerke, R. and Hoefer, M. and Nikoloski, Z. and Wagner, D.},
  interhash = {3e2bf460cff3138de1e855a7cf5d659d},
  intrahash = {b5185cbb85b90294fa15dd2e8ea53f5e},
  note = {cite arxiv:physics/0608255 Comment: 10 pages, 1 figure},
  title = {Maximizing Modularity is hard},
  url = {http://arxiv.org/abs/physics/0608255},
  year = 2006
}

@article{brandes2008modularity,
  abstract = {Modularity is a recently introduced quality measure for graph clusterings. It has immediately received considerable attention in several disciplines, particularly 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 agglomerative approach.},
  author = {Brandes, U. and Delling, D. and Gaertler, M. and Gorke, R. and Hoefer, M. and Nikoloski, Z. and Wagner, D.},
  doi = {10.1109/TKDE.2007.190689},
  interhash = {b7195d25a851617a48d4f15bef5ad789},
  intrahash = {9e2e5f9d06d2f83be98083175560c835},
  issn = {1041-4347},
  journal = {Knowledge and Data Engineering, IEEE Transactions on},
  month = {feb. },
  number = 2,
  pages = {172 -188},
  title = {On Modularity Clustering},
  url = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4358966&tag=1},
  volume = 20,
  year = 2008
}