From Louvain to Leiden: guaranteeing well-connected communities

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.

PARC: ultrafast and accurate clustering of phenotypic data of millions of single cells

“…Hence, the data-driven pruning procedure offers a two-fold impact in reducing the sample size of edges and improving the k-NN graph representation of the underlying data structure, both of which critically improve the subsequent community detection step in speed and robustness. Third, a newly developed community-detection approach, Leiden algorithm (Traag et al, 2019), is employed to partition the large pruned networks in the graph into communities. In contrast to the popular Louvain algorithm (Blondel et al 2008), Leiden algorithm demonstrates superior performance in faster computation time, scalability, and minimising badly connected communities (Traag et al 2019).…”

“…Third, a newly developed community-detection approach, Leiden algorithm (Traag et al, 2019), is employed to partition the large pruned networks in the graph into communities. In contrast to the popular Louvain algorithm (Blondel et al 2008), Leiden algorithm demonstrates superior performance in faster computation time, scalability, and minimising badly connected communities (Traag et al 2019).…”

“…Having constructed a network representation of the single cells, i.e a collection of cells that have strong links to each other but fewer links to the remaining network, we apply a new modularity optimization algorithm called Leiden algorithm, for community-detection-based clustering (Traag et al 2019). Leiden method has very recently been demonstrated to show superior performance in speed as well as reducing internally disconnected (or poorly connected) communities, to the popular Louvain algorithm in clustering social network datasets.…”

“…Asides from the 'resolution limit' issue of the modularity optimization function which tends to merge small sub-structures, the Louvain algorithm applied to any quality function suffers from a separate issue of poorly connected or even internally disconnected communities (Traag et al 2019). Recall that the Louvain algorithm essentially consists of repeating two steps: 1) re-assigning nodes to communities based on improvement in modularity and 2) once nodes can no longer be moved, aggregate nodes in a community and allow each community to become a 'node' in the next pass of the same steps.…”

Refining modules to determine functionally significant clusters in molecular networks

“…The quality function (surprise), = ( ||< >) where is the number of edges, is the fraction of internal edges , < > is the expected fraction of internal edges and is the binary Kullback-Leibler divergence. The quality function is optimised using the Louvain algorithm implemented using the python package Louvain-igraph 46 . MCODE 10 : It detects dense protein complexes in PPIN.…”