An Ultra-Fast Modularity-Based Graph Clustering Algorithm

In this paper, we propose a multilevel graph partitioning scheme to speed up a modularity-based graph clustering technique. The modularity-based algorithm was proposed by Newman for partitioning graphs into communities without the input of the number of clusters. The algorithm seeks to maximize a modularity measure. However, its worst-time complexity on sparse graphs is O(n), where n is the number of vertices, which can be prohibitive for many applications. The multilevel graph partitioning scheme consists of three phases: (i) reduction of the size (coarsen) of original graph by collapsing vertices and edges, (ii) partitioning the coarsened graph, and (iii) uncoarsen it to obtain a partition for the original graph. The rationale behind this strategy is to apply a computationally expensive method in a coarsened graph, i.e., with a significantly reduced number of vertices and edges. Empirical evaluation using this approach demonstrate a significant speed up of the modularity-based algorithm, keeping a good quality clusters partitioning.