" Finding Statistically Significant Communities in Networks," Andrea Lancichinetti & Filippo Radicchi & José J Ramasco & Santo Fortunato, 2011.The European Physical Journal B: Condensed Matter and Complex Systems, Springer EDP Sciences, vol. " Modularity-maximizing graph communities via mathematical programming," " Reformulation of a model for hierarchical divisive graph modularity maximization,"Īnnals of Operations Research, Springer, vol. Sonia Cafieri & Alberto Costa & Pierre Hansen, 2014." MILP formulations for the modularity density maximization problem,"Įuropean Journal of Operational Research, Elsevier, vol. Physica A: Statistical Mechanics and its Applications, Elsevier, vol. " Weighting links based on edge centrality for community detection," " Finding community structures in complex networks using mixed integer optimisation," " Modularity functions maximization with nonnegative relaxation facilitates community detection in networks," Ground truth experiments in artificial random graphs were performed and suggest that our heuristics lead to better cluster detection than both CNM and Louvain. Hypothesis tests suggest that four proposed heuristics are state-of-the-art since they are scalable for hundreds of thousands of nodes for the modularity density problem, and they find the high objective value partitions for the largest instances. This feature was confirmed by an amortized complexity analysis which reveals average linear time for three of our heuristics. Our seven heuristics were tested with real graphs from the Stanford Large Network Dataset Collection and the experiments show that they are scalable. Our experiments also show that some of our heuristics surpassed the objective function value reported by iMeme-Net, Hain, and BMD-λ for some real graphs. The results suggest that our seven heuristics are faster than GAOD, iMeme-Net, HAIN, and BMD-λ modularity density heuristics. The results are also compared with CNM and Louvain, which are scalable heuristics for modularity maximization. This paper presents seven scalable heuristics for modularity density and compares them with literature results from exact mixed integer linear programming and GAOD, iMeme-Net, HAIN, and BMD-λ heuristics.
Modularity density maximization is a community detection optimization problem which improves the resolution limit degeneracy of modularity maximization.
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