American Physical Society, Physical review E: Statistical, nonlinear, and soft matter physics, 3(92)
DOI: 10.1103/physreve.92.032801
Full text: Download
Many complex networks exhibit a modular structure of densely connected groups of nodes. Usually, such a modular structure is uncovered by the optimisation of some quality function. Although flawed, Modularity remains one of the most popular quality functions. The Louvain algorithm was originally developed for optimising Modularity, but has been applied to a variety of methods. As such, speeding up the Louvain algorithm, enables the analysis of larger graphs in a shorter time for various methods. We here suggest to consider moving nodes to the community of a random neighbour, instead of the best neighbouring community. Although incredibly simple, it reduces the theoretical runtime complexity from $O(m)$ to $O(n \log )$ in networks with a clear community structure. In benchmark networks, resembling real networks more closely, it speeds up the algorithm roughly 2-3 times. This is due to two factors: (1) a random neighbour is likely to be in a "good" community; and (2) random neighbours are likely to be hubs, helping the convergence. Finally, the performance gain only slightly diminishes the quality, thus providing an excellent quality-performance ratio. However, these gains do not seem to hold up when detecting small communities in large graphs.