Analyses based on benchmark networks have only a limited value because these networks are not representative of empirical real-world networks. 8, 207218, https://doi.org/10.17706/IJCEE.2016.8.3.207-218 (2016). Newman, M E J, and M Girvan. The algorithm then locally merges nodes in \({{\mathscr{P}}}_{{\rm{refined}}}\): nodes that are on their own in a community in \({{\mathscr{P}}}_{{\rm{refined}}}\) can be merged with a different community. Raghavan, U., Albert, R. & Kumara, S. Near linear time algorithm to detect community structures in large-scale networks. However, the initial partition for the aggregate network is based on P, just like in the Louvain algorithm. As can be seen in Fig. Large network community detection by fast label propagation, Representative community divisions of networks, Gausss law for networks directly reveals community boundaries, A Regularized Stochastic Block Model for the robust community detection in complex networks, Community Detection in Complex Networks via Clique Conductance, A generalised significance test for individual communities in networks, Community Detection on Networkswith Ricci Flow, https://github.com/CWTSLeiden/networkanalysis, https://doi.org/10.1016/j.physrep.2009.11.002, https://doi.org/10.1103/PhysRevE.69.026113, https://doi.org/10.1103/PhysRevE.74.016110, https://doi.org/10.1103/PhysRevE.70.066111, https://doi.org/10.1103/PhysRevE.72.027104, https://doi.org/10.1103/PhysRevE.74.036104, https://doi.org/10.1088/1742-5468/2008/10/P10008, https://doi.org/10.1103/PhysRevE.80.056117, https://doi.org/10.1103/PhysRevE.84.016114, https://doi.org/10.1140/epjb/e2013-40829-0, https://doi.org/10.17706/IJCEE.2016.8.3.207-218, https://doi.org/10.1103/PhysRevE.92.032801, https://doi.org/10.1103/PhysRevE.76.036106, https://doi.org/10.1103/PhysRevE.78.046110, https://doi.org/10.1103/PhysRevE.81.046106, http://creativecommons.org/licenses/by/4.0/, A robust and accurate single-cell data trajectory inference method using ensemble pseudotime, Batch alignment of single-cell transcriptomics data using deep metric learning, ViralCC retrieves complete viral genomes and virus-host pairs from metagenomic Hi-C data, Community detection in brain connectomes with hybrid quantum computing. Phys. How many iterations of the Leiden clustering algorithm to perform. Higher resolutions lead to more communities and lower resolutions lead to fewer communities, similarly to the resolution parameter for modularity. CPM does not suffer from this issue13. Rep. 6, 30750, https://doi.org/10.1038/srep30750 (2016). We now compare how the Leiden and the Louvain algorithm perform for the six empirical networks listed in Table2. V.A.T. Phys. Then, in order . It starts clustering by treating the individual data points as a single cluster then it is merged continuously based on similarity until it forms one big cluster containing all objects. Soft Matter Phys. 9 shows that more than 10 iterations of the Leiden algorithm can be performed before the Louvain algorithm has finished its first iteration. Phys. Later iterations of the Louvain algorithm only aggravate the problem of disconnected communities, even though the quality function (i.e. Here we can see partitions in the plotted results. By creating the aggregate network based on \({{\mathscr{P}}}_{{\rm{refined}}}\) rather than P, the Leiden algorithm has more room for identifying high-quality partitions. Phys. Louvain algorithm. Below we offer an intuitive explanation of these properties. The nodes are added to the queue in a random order. This enables us to find cases where its beneficial to split a community. Ozaki, N., Tezuka, H. & Inaba, M. A Simple Acceleration Method for the Louvain Algorithm. The algorithm moves individual nodes from one community to another to find a partition (b), which is then refined (c). Reichardt, J. Ayan Sinha, David F. Gleich & Karthik Ramani, Marinka Zitnik, Rok Sosi & Jure Leskovec, Zhenqi Lu, Johan Wahlstrm & Arye Nehorai, Natalie Stanley, Roland Kwitt, Peter J. Mucha, Scientific Reports When the Leiden algorithm found that a community could be split into multiple subcommunities, we counted the community as badly connected. The algorithm may yield arbitrarily badly connected communities, over and above the well-known issue of the resolution limit14. reviewed the manuscript. However, the Louvain algorithm does not consider this possibility, since it considers only individual node movements. The high percentage of badly connected communities attests to this. Faster Unfolding of Communities: Speeding up the Louvain Algorithm. Phys. For each set of parameters, we repeated the experiment 10 times. This should be the first preference when choosing an algorithm. Rather than progress straight to the aggregation stage (as we would for the original Louvain), we next consider each community as a new sub-network and re-apply the local moving step within each community. 2013. E 78, 046110, https://doi.org/10.1103/PhysRevE.78.046110 (2008). Nevertheless, depending on the relative strengths of the different connections, these nodes may still be optimally assigned to their current community. E 84, 016114, https://doi.org/10.1103/PhysRevE.84.016114 (2011). Data Eng. 2016. Rev. Internet Explorer). Scaling of benchmark results for network size. Weights for edges an also be passed to the leiden algorithm either as a separate vector or weights or a weighted adjacency matrix. leiden_clustering Description Class wrapper based on scanpy to use the Leiden algorithm to directly cluster your data matrix with a scikit-learn flavor. There is an entire Leiden package in R-cran here CAS In the case of the Louvain algorithm, after a stable iteration, all subsequent iterations will be stable as well. wrote the manuscript. Using the fast local move procedure, the first visit to all nodes in a network in the Leiden algorithm is the same as in the Louvain algorithm. Louvain can also be quite slow, as it spends a lot of time revisiting nodes that may not have changed neighborhoods. The Leiden algorithm guarantees all communities to be connected, but it may yield badly connected communities. The Louvain algorithm guarantees that modularity cannot be increased by merging communities (it finds a locally optimal solution). On the other hand, Leiden keeps finding better partitions, especially for higher values of , for which it is more difficult to identify good partitions. 9, the Leiden algorithm also performs better than the Louvain algorithm in terms of the quality of the partitions that are obtained. In addition, a node is merged with a community in \({{\mathscr{P}}}_{{\rm{refined}}}\) only if both are sufficiently well connected to their community in \({\mathscr{P}}\). Google Scholar. & Clauset, A. Int. In this way, Leiden implements the local moving phase more efficiently than Louvain. For example, the red community in (b) is refined into two subcommunities in (c), which after aggregation become two separate nodes in (d), both belonging to the same community. IEEE Trans. Fortunato, S. Community detection in graphs. For a full specification of the fast local move procedure, we refer to the pseudo-code of the Leiden algorithm in AlgorithmA.2 in SectionA of the Supplementary Information. By submitting a comment you agree to abide by our Terms and Community Guidelines. For lower values of , the correct partition is easy to find and Leiden is only about twice as fast as Louvain. We then created a certain number of edges such that a specified average degree \(\langle k\rangle \) was obtained. This aspect of the Louvain algorithm can be used to give information about the hierarchical relationships between communities by tracking at which stage the nodes in the communities were aggregated. Such a modular structure is usually not known beforehand. Source Code (2018). The thick edges in Fig. To obtain Nodes 13 should form a community and nodes 46 should form another community. Inf. The above results shows that the problem of disconnected and badly connected communities is quite pervasive in practice. Leiden is both faster than Louvain and finds better partitions. Node optimality is also guaranteed after a stable iteration of the Louvain algorithm. It means that there are no individual nodes that can be moved to a different community. leidenalg. For both algorithms, 10 iterations were performed. This can be a shared nearest neighbours matrix derived from a graph object. The random component also makes the algorithm more explorative, which might help to find better community structures. Speed and quality of the Louvain and the Leiden algorithm for benchmark networks of increasing size (two iterations). 10008, 6, https://doi.org/10.1088/1742-5468/2008/10/P10008 (2008). Note that this code is . Phys. ADS Two ways of doing this are graph modularity (Newman and Girvan 2004) and the constant Potts model (Ronhovde and Nussinov 2010). An aggregate. We first applied the Scanpy pipeline, including its clustering method (Leiden clustering), on the PBMC dataset. Article Guimer, R. & Nunes Amaral, L. A. Functional cartography of complex metabolic networks. We therefore require a more principled solution, which we will introduce in the next section. The Louvain algorithm is illustrated in Fig. As shown in Fig. Leiden algorithm. A community is subset optimal if all subsets of the community are locally optimally assigned. The corresponding results are presented in the Supplementary Fig. 92 (3): 032801. http://dx.doi.org/10.1103/PhysRevE.92.032801. Empirical networks show a much richer and more complex structure. Node mergers that cause the quality function to decrease are not considered. In particular, it yields communities that are guaranteed to be connected. An iteration of the Leiden algorithm in which the partition does not change is called a stable iteration. The property of -separation is also guaranteed by the Louvain algorithm. On Modularity Clustering. This contrasts to benchmark networks, for which Leiden often converges after a few iterations. V.A.T. Waltman, L. & van Eck, N. J. Elect. Hence, no further improvements can be made after a stable iteration of the Louvain algorithm. However, modularity suffers from a difficult problem known as the resolution limit (Fortunato and Barthlemy 2007). Usually, the Louvain algorithm starts from a singleton partition, in which each node is in its own community. 69 (2 Pt 2): 026113. http://dx.doi.org/10.1103/PhysRevE.69.026113. Hence, the Leiden algorithm effectively addresses the problem of badly connected communities. Ozaki, Naoto, Hiroshi Tezuka, and Mary Inaba. A Smart Local Moving Algorithm for Large-Scale Modularity-Based Community Detection. Eur. Not. This may have serious consequences for analyses based on the resulting partitions. Finally, we compare the performance of the algorithms on the empirical networks. S3. If nothing happens, download Xcode and try again. http://iopscience.iop.org/article/10.1088/1742-5468/2008/10/P10008/meta, http://dx.doi.org/10.1073/pnas.0605965104, http://dx.doi.org/10.1103/PhysRevE.69.026113, https://pdfs.semanticscholar.org/4ea9/74f0fadb57a0b1ec35cbc5b3eb28e9b966d8.pdf, http://dx.doi.org/10.1103/PhysRevE.81.046114, http://dx.doi.org/10.1103/PhysRevE.92.032801, https://doi.org/10.1140/epjb/e2013-40829-0, Assign each node to a different community. Wolf, F. A. et al. Slider with three articles shown per slide. For example an SNN can be generated: For Seurat version 3 objects, the Leiden algorithm has been implemented in the Seurat version 3 package with Seurat::FindClusters and algorithm = "leiden"). Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Leiden consists of the following steps: The refinement step allows badly connected communities to be split before creating the aggregate network. We prove that the Leiden algorithm yields communities that are guaranteed to be connected. The Louvain algorithm10 is very simple and elegant. Anyone you share the following link with will be able to read this content: Sorry, a shareable link is not currently available for this article. Due to the resolution limit, modularity may cause smaller communities to be clustered into larger communities. We gratefully acknowledge computational facilities provided by the LIACS Data Science Lab Computing Facilities through Frank Takes. The percentage of disconnected communities is more limited, usually around 1%. Modularity is a popular objective function used with the Louvain method for community detection. In other words, communities are guaranteed to be well separated. Such algorithms are rather slow, making them ineffective for large networks. Once aggregation is complete we restart the local moving phase, and continue to iterate until everything converges down to one node. It only implies that individual nodes are well connected to their community. After running local moving, we end up with a set of communities where we cant increase the objective function (eg, modularity) by moving any node to any neighboring community. 2 represent stronger connections, while the other edges represent weaker connections. We now consider the guarantees provided by the Leiden algorithm. Good, B. H., De Montjoye, Y. A number of iterations of the Leiden algorithm can be performed before the Louvain algorithm has finished its first iteration. Speed and quality for the first 10 iterations of the Louvain and the Leiden algorithm for benchmark networks (n=106 and n=107). In the meantime, to ensure continued support, we are displaying the site without styles The algorithm then moves individual nodes in the aggregate network (e). U. S. A. The constant Potts model might give better communities in some cases, as it is not subject to the resolution limit. N.J.v.E. Phys. This will compute the Leiden clusters and add them to the Seurat Object Class. We generated networks with n=103 to n=107 nodes. Introduction The Louvain method is an algorithm to detect communities in large networks. To use Leiden with the Seurat pipeline for a Seurat Object object that has an SNN computed (for example with Seurat::FindClusters with save.SNN = TRUE). Provided by the Springer Nature SharedIt content-sharing initiative. This problem is different from the well-known issue of the resolution limit of modularity14. To find an optimal grouping of cells into communities, we need some way of evaluating different partitions in the graph. Is modularity with a resolution parameter equivalent to leidenalg.RBConfigurationVertexPartition? Table2 provides an overview of the six networks. The solution provided by Leiden is based on the smart local moving algorithm. E 72, 027104, https://doi.org/10.1103/PhysRevE.72.027104 (2005). We start by initialising a queue with all nodes in the network. The horizontal axis indicates the cumulative time taken to obtain the quality indicated on the vertical axis. Cluster cells using Louvain/Leiden community detection Description. Disconnected community. Louvain pruning keeps track of a list of nodes that have the potential to change communities, and only revisits nodes in this list, which is much smaller than the total number of nodes. Use the Previous and Next buttons to navigate the slides or the slide controller buttons at the end to navigate through each slide. Even worse, the Amazon network has 5% disconnected communities, but 25% badly connected communities. We show that this algorithm has a major defect that largely went unnoticed until now: the Louvain algorithm may yield arbitrarily badly connected communities. They show that the original Louvain algorithm that can result in badly connected communities (even communities that are completely disconnected internally) and propose an alternative method, Leiden, that guarantees that communities are well connected. We name our algorithm the Leiden algorithm, after the location of its authors. Waltman, L. & van Eck, N. J. The Leiden algorithm is considerably more complex than the Louvain algorithm. Porter, M. A., Onnela, J.-P. & Mucha, P. J. Rev. Article 2004. 81 (4 Pt 2): 046114. http://dx.doi.org/10.1103/PhysRevE.81.046114. These nodes are therefore optimally assigned to their current community. This package allows calling the Leiden algorithm for clustering on an igraph object from R. See the Python and Java implementations for more details: https://github.com/CWTSLeiden/networkanalysis. where nc is the number of nodes in community c. The interpretation of the resolution parameter is quite straightforward. Later iterations of the Louvain algorithm are very fast, but this is only because the partition remains the same. We will use sklearns K-Means implementation looking for 10 clusters in the original 784 dimensional data. Google Scholar. As can be seen in the figure, Louvain quickly reaches a state in which it is unable to find better partitions. The Leiden algorithm also takes advantage of the idea of speeding up the local moving of nodes16,17 and the idea of moving nodes to random neighbours18. We typically reduce the dimensionality of the data first by running PCA, then construct a neighbor graph in the reduced space. 68, 984998, https://doi.org/10.1002/asi.23734 (2017). 8 (3): 207. https://pdfs.semanticscholar.org/4ea9/74f0fadb57a0b1ec35cbc5b3eb28e9b966d8.pdf. Note that Leiden clustering directly clusters the neighborhood graph of cells, which we already computed in the previous section. We provide the full definitions of the properties as well as the mathematical proofs in SectionD of the Supplementary Information. There are many different approaches and algorithms to perform clustering tasks. Phys. 1 I am using the leiden algorithm implementation in iGraph, and noticed that when I repeat clustering using the same resolution parameter, I get different results. Finding communities in large networks is far from trivial: algorithms need to be fast, but they also need to provide high-quality results. & Moore, C. Finding community structure in very large networks. By moving these nodes, Louvain creates badly connected communities. Importantly, the first iteration of the Leiden algorithm is the most computationally intensive one, and subsequent iterations are faster. Article As discussed earlier, the Louvain algorithm does not guarantee connectivity. The refined partition \({{\mathscr{P}}}_{{\rm{refined}}}\) is obtained as follows. 2.3. Resolution Limit in Community Detection. Proc. Eng. Centre for Science and Technology Studies, Leiden University, Leiden, The Netherlands, You can also search for this author in Agglomerative clustering is a bottom-up approach. The algorithm optimises a quality function such as modularity or CPM in two elementary phases: (1) local moving of nodes; and (2) aggregation of the network. Note that nodes can be revisited several times within a single iteration of the local moving stage, as the possible increase in modularity will change as other nodes are moved to different communities. These are the same networks that were also studied in an earlier paper introducing the smart local move algorithm15. E 70, 066111, https://doi.org/10.1103/PhysRevE.70.066111 (2004). This contrasts with optimisation algorithms such as simulated annealing, which do allow the quality function to decrease4,8.