From Louvain to Leiden: guaranteeing well-connected communities

TL;DR

This paper identifies a flaw in the Louvain community detection algorithm where communities can be disconnected, and introduces the Leiden algorithm, which guarantees connected communities and improves speed and partition quality.

Contribution

The paper presents the Leiden algorithm, a novel community detection method that guarantees connected communities and converges to locally optimal partitions, outperforming Louvain.

Findings

Up to 25% of communities are badly connected in Louvain.

Leiden guarantees connected communities and faster convergence.

Leiden uncovers better partitions than Louvain.

Abstract

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. We demonstrate the performance of the Leiden algorithm for several benchmark and real-world networks. We find that the Leiden algorithm is faster than the Louvain algorithm and uncovers better partitions, in addition to providing explicit guarantees.