Prune the Unnecessary: Parallel Pull-Push Louvain Algorithms with Automatic Edge Pruning

Community detection algorithms try to identify the underlying community structure (i.e., clearly distinguishable closely interacting groups of vertices) in a graph representing complex systems such as social networks, protein-protein interaction networks, and the World-Wide-Web. The Louvain algorithm iteratively moves vertices from one community to another to construct disjoint sets of vertices to form communities such that the vertices within the same community have more edges within themselves compared to their connections to the vertices outside the community. A property of the Louvain algorithm is that the number of vertex moves drops significantly just after the first few iterations because the community-membership also stabilizes quickly. In this paper, we present a parallel pull-and-push Louvain algorithm that exploits this property to prune unnecessary edge explorations without sacrificing the quality of the solution. We present a collection of parallel Louvain algorithms that prune many edges and vertices, speeding up convergence by an order of magnitude over the previously best-known implementation of the Louvain algorithm from Grappolo, while producing similar or better results.