From Louvain to Leiden: guaranteeing well-connected communities

Community detection is often used to understand the structure of large and complex networks. One of the most popular algorithms for uncovering community structure is the so-called Louvain algorithm. We show that this algorithm has a major defect that largely went unnoticed until now: the Louvain algorithm may yield arbitrarily badly connected communities. In the worst case, communities may even be disconnected, especially when running the algorithm iteratively. In our experimental analysis, we observe that up to 25% of the communities are badly connected and up to 16% are disconnected. To address this problem, we introduce the Leiden algorithm. We prove that the Leiden algorithm yields communities that are guaranteed to be connected. In addition, we prove that, when the Leiden algorithm is applied iteratively, it converges to a partition in which all subsets of all communities are locally optimally assigned. Furthermore, by relying on a fast local move approach, the Leiden algorithm runs faster than the Louvain algorithm

In many complex networks, nodes cluster and form relatively dense groups—often called communities [1, 2]. Such a modular structure is usually not known beforehand. Detecting communities in a network is therefore an important problem. One of the best-known methods for community detection is called modularity [3]. This method tries to maximise the difference between the actual number of edges in a community and the expected number of such edges.