Efficient Modularity Optimization: Multi-Step Greedy Algorithm and Vertex Mover Refinement

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  • 7 December 2007
Abstract
Identifying strongly connected substructures in large networks provides insight in their coarse-grained organization. Several approaches based on the optimization of a quality function, e.g. the modularity, have been proposed. We have developed a multi-step extension of the greedy algorithm (MSG) for modularity optimization and combined it with a simplistic refinement procedure called ``Vertex Mover'' (VM) which reassigns vertices to neighboring communities to improve the final modularity value. With an appropriate choice of the step-width in the MSG, the combined MSG&VM algorithm is able to find solutions of higher modularity than those reported previously. The multi-step extension does not alter the running time expectation of the greedy algorithm. It has been reported earlier that the greedy algorithm is the most efficient modularity optimization procedure for a generic (sparse) network (Danon et al., J. Stat. Mech. P09008 (2005)). Therefore, we conclude that the combined MSG&VM algorithm yields network partitions of higher modularity in shorter time than reported previously.

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