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Divisive heuristic for modularity density maximization. (English) Zbl 1349.90850
Summary: In this paper we consider a particular method of clustering for graphs, namely the modularity density maximization. We propose a hierarchical divisive heuristic which works by splitting recursively a cluster into two new clusters by maximizing the modularity density, and we derive four reformulations for the mathematical programming model used to obtain the optimal splitting. We report computational results of the eight algorithms (four reformulations with two different symmetry breaking strategies) obtained on some instances from the literature. Statistical tests show that the best model in terms of computational time is the one that is obtained with a dual reformulation of the bilinear terms arising in the objective function. Moreover, the hierarchical divisive heuristic provides generally near-optimal solutions in terms of modularity density.

MSC:
90C59 Approximation methods and heuristics in mathematical programming
05C85 Graph algorithms (graph-theoretic aspects)
62H30 Classification and discrimination; cluster analysis (statistical aspects)
90C35 Programming involving graphs or networks
Software:
BARON; CPLEX
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