Maximizing Modularity is hard

Details Maximizing Modularity is hard Maximizing Modularity is hard

2006-08-25

arxiv.org/abs/physics/0608255v2

Physics

Data Analysis, Statistics and Probability

10 pages, 1 figure

Scientific paper

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.

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