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.

FICTURE: scalable segmentation-free analysis of submicron-resolution spatial transcriptomics

“…Baysor is moderately affected by the over-specification with 2.6% (12-cluster model) to 15.7% (20-cluster model) pixels assigned to the extra clusters, while GraphST tends to over-cluster to reach the target number of clusters and assigns a large fraction (9.2~35.0%) of pixels to the extra factors. This is similar to observations from other graph-based methods that use community detection algorithms such as Louvain 31 and Leiden 32 .…”

FICTURE: scalable segmentation-free analysis of submicron-resolution spatial transcriptomics

“…Baysor is moderately affected by the over-specification with 2.6% (12-cluster model) to 15.7% (20-cluster model) pixels assigned to the extra clusters, while GraphST tends to over-cluster to reach the target number of clusters and assigns a large fraction (9.2~35.0%) of pixels to the extra factors. This is similar to observations from other graph-based methods that use community detection algorithms such as Louvain 31 and Leiden 32 .…”

FICTURE: Scalable segmentation-free analysis of submicron resolution spatial transcriptomics

“…On the other hand, GraphST tends to over-cluster to achieve the target number of clusters and assignied a large fraction (20~50%) of pixels to the extra factors. This is similar to observations from other graph-based methods that use community detection algorithms such as Louvain 28 and Leiden 29 .…”

Single-cell RNA profiling of Plasmodium vivax -infected hepatocytes reveals parasite- and host- specific transcriptomic signatures and therapeutic targets

“…Given that the population of cells profiled at day 9 post-infection, from which schizonts were chemically removed, overlapped with one of the two cell populations profiled at 5 days post-infection, we deduced that the non-overlapping population of cells encoded for schizonts. Consistent with our reasoning, an unsupervised clustering algorithm (Traag et al, 2019) unbiasedly assigned the cells to one of the two clusters ( Fig. 2B and Fig.…”

FICTURE: scalable segmentation-free analysis of submicron-resolution spatial transcriptomics

“…Baysor is moderately affected by the over-specification with 2.6% (12-cluster model) to 15.7% (20-cluster model) pixels assigned to the extra clusters, while GraphST tends to over-cluster to reach the target number of clusters and assigns a large fraction (9.2~35.0%) of pixels to the extra factors. This is similar to observations from other graph-based methods that use community detection algorithms such as Louvain 31 and Leiden 32 .…”

FICTURE: Scalable segmentation-free analysis of submicron resolution spatial transcriptomics

“…On the other hand, GraphST tends to over-cluster to achieve the target number of clusters and assignied a large fraction (20~50%) of pixels to the extra factors. This is similar to observations from other graph-based methods that use community detection algorithms such as Louvain 28 and Leiden 29 .…”

Single-cell RNA profiling of Plasmodium vivax -infected hepatocytes reveals parasite- and host- specific transcriptomic signatures and therapeutic targets

“…Given that the population of cells profiled at day 9 post-infection, from which schizonts were chemically removed, overlapped with one of the two cell populations profiled at 5 days post-infection, we deduced that the non-overlapping population of cells encoded for schizonts. Consistent with our reasoning, an unsupervised clustering algorithm (Traag et al, 2019) unbiasedly assigned the cells to one of the two clusters ( Fig. 2B and Fig.…”

FICTURE: scalable segmentation-free analysis of submicron-resolution spatial transcriptomics

“…Baysor is moderately affected by the over-specification with 2.6% (12-cluster model) to 15.7% (20-cluster model) pixels assigned to the extra clusters, while GraphST tends to over-cluster to reach the target number of clusters and assigns a large fraction (9.2~35.0%) of pixels to the extra factors. This is similar to observations from other graph-based methods that use community detection algorithms such as Louvain 31 and Leiden 32 .…”

FICTURE: Scalable segmentation-free analysis of submicron resolution spatial transcriptomics

“…On the other hand, GraphST tends to over-cluster to achieve the target number of clusters and assignied a large fraction (20~50%) of pixels to the extra factors. This is similar to observations from other graph-based methods that use community detection algorithms such as Louvain 28 and Leiden 29 .…”

Single-cell RNA profiling of Plasmodium vivax -infected hepatocytes reveals parasite- and host- specific transcriptomic signatures and therapeutic targets

“…Given that the population of cells profiled at day 9 post-infection, from which schizonts were chemically removed, overlapped with one of the two cell populations profiled at 5 days post-infection, we deduced that the non-overlapping population of cells encoded for schizonts. Consistent with our reasoning, an unsupervised clustering algorithm (Traag et al, 2019) unbiasedly assigned the cells to one of the two clusters ( Fig. 2B and Fig.…”