In the fast local move procedure in the Leiden algorithm, only nodes whose neighbourhood has changed are visited. In general, Leiden is both faster than Louvain and finds better partitions. Sign up for the Nature Briefing newsletter what matters in science, free to your inbox daily. Communities in Networks. The resolution limit describes a limitation where there is a minimum community size able to be resolved by optimizing modularity (or other related functions). Traag, V. A., Waltman, L. & van Eck, N. J. networkanalysis. Cluster your data matrix with the Leiden algorithm. Once no further increase in modularity is possible by moving any node to its neighboring community, we move to the second phase of the algorithm: aggregation. J. To overcome the problem of arbitrarily badly connected communities, we introduced a new algorithm, which we refer to as the Leiden algorithm. 8, the Leiden algorithm is significantly faster than the Louvain algorithm also in empirical networks. The percentage of disconnected communities even jumps to 16% for the DBLP network. Nonlin. This way of defining the expected number of edges is based on the so-called configuration model. As can be seen in Fig. The Louvain local moving phase consists of the following steps: This process is repeated for every node in the network until no further improvement in modularity is possible. Article Duch, J. The horizontal axis indicates the cumulative time taken to obtain the quality indicated on the vertical axis. PubMedGoogle Scholar. Wolf, F. A. et al. E 76, 036106, https://doi.org/10.1103/PhysRevE.76.036106 (2007). Later iterations of the Louvain algorithm only aggravate the problem of disconnected communities, even though the quality function (i.e. Luecken, M. D. Application of multi-resolution partitioning of interaction networks to the study of complex disease. MathSciNet Speed and quality of the Louvain and the Leiden algorithm for benchmark networks of increasing size (two iterations). Performance of modularity maximization in practical contexts. Are you sure you want to create this branch? Phys. The Leiden community detection algorithm outperforms other clustering methods. Traag, V.A., Waltman, L. & van Eck, N.J. From Louvain to Leiden: guaranteeing well-connected communities. We find that the Leiden algorithm is faster than the Louvain algorithm and uncovers better partitions, in addition to providing explicit guarantees. In this stage we essentially collapse communities down into a single representative node, creating a new simplified graph. This can be a shared nearest neighbours matrix derived from a graph object. 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. To do this we just sum all the edge weights between nodes of the corresponding communities to get a single weighted edge between them, and collapse each community down to a single new node. Theory Exp. Phys. For each community, modularity measures the number of edges within the community and the number of edges going outside the community, and gives a value between -1 and +1. Random moving can result in some huge speedups, since Louvain spends about 95% of its time computing the modularity gain from moving nodes. USA 104, 36, https://doi.org/10.1073/pnas.0605965104 (2007). In an experiment containing a mixture of cell types, each cluster might correspond to a different cell type. This package implements the Leiden algorithm in C++ and exposes it to python.It relies on (python-)igraph for it to function. Any sub-networks that are found are treated as different communities in the next aggregation step. 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"). For larger networks and higher values of , Louvain is much slower than Leiden. 2004. For the Amazon and IMDB networks, the first iteration of the Leiden algorithm is only about 1.6 times faster than the first iteration of the Louvain algorithm. E Stat. Google Scholar. Based on this partition, an aggregate network is created (c). Subpartition -density is not guaranteed by the Louvain algorithm. & Bornholdt, S. Statistical mechanics of community detection. Traag, V. A., Van Dooren, P. & Nesterov, Y. Waltman, L. & van Eck, N. J. Ozaki, N., Tezuka, H. & Inaba, M. A Simple Acceleration Method for the Louvain Algorithm. As far as I can tell, Leiden seems to essentially be smart local moving with the additional improvements of random moving and Louvain pruning added. ADS Elect. Runtime versus quality for empirical networks. In this way, Leiden implements the local moving phase more efficiently than Louvain. Nodes 16 have connections only within this community, whereas node 0 also has many external connections. We here introduce the Leiden algorithm, which guarantees that communities are well connected. This function takes a cell_data_set as input, clusters the cells using . Directed Undirected Homogeneous Heterogeneous Weighted 1. The fast local move procedure can be summarised as follows. Louvain algorithm. 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. For example, nodes in a community in biological or neurological networks are often assumed to share similar functions or behaviour25. Importantly, the number of communities discovered is related only to the difference in edge density, and not the total number of nodes in the community. As such, we scored leiden-clustering popularity level to be Limited. Somewhat stronger guarantees can be obtained by iterating the algorithm, using the partition obtained in one iteration of the algorithm as starting point for the next iteration. Clustering the neighborhood graph As with Seurat and many other frameworks, we recommend the Leiden graph-clustering method (community detection based on optimizing modularity) by Traag *et al. Traag, V. A. leidenalg 0.7.0. Node mergers that cause the quality function to decrease are not considered. In this section, we analyse and compare the performance of the two algorithms in practice. This is very similar to what the smart local moving algorithm does. A Simple Acceleration Method for the Louvain Algorithm. Int. We name our algorithm the Leiden algorithm, after the location of its authors. The property of -connectivity is a slightly stronger variant of ordinary connectivity. Moreover, when no more nodes can be moved, the algorithm will aggregate the network. The Leiden algorithm provides several guarantees. The Leiden algorithm consists of three phases: (1) local moving of nodes, (2) refinement of the partition and (3) aggregation of the network based on the refined partition, using the non-refined. In this new situation, nodes 2, 3, 5 and 6 have only internal connections. IEEE Trans. E 74, 036104, https://doi.org/10.1103/PhysRevE.74.036104 (2006). Hence, in general, Louvain may find arbitrarily badly connected communities. Bullmore, E. & Sporns, O. However, it is also possible to start the algorithm from a different partition15. Communities may even be internally disconnected. PubMed From Louvain to Leiden: guaranteeing well-connected communities, $$ {\mathcal H} =\frac{1}{2m}\,{\sum }_{c}({e}_{c}-{\rm{\gamma }}\frac{{K}_{c}^{2}}{2m}),$$, $$ {\mathcal H} ={\sum }_{c}[{e}_{c}-\gamma (\begin{array}{c}{n}_{c}\\ 2\end{array})],$$, https://doi.org/10.1038/s41598-019-41695-z. We keep removing nodes from the front of the queue, possibly moving these nodes to a different community. Such algorithms are rather slow, making them ineffective for large networks. The difference in computational time is especially pronounced for larger networks, with Leiden being up to 20 times faster than Louvain in empirical networks. 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. The inspiration for this method of community detection is the optimization of modularity as the algorithm progresses. We then created a certain number of edges such that a specified average degree \(\langle k\rangle \) was obtained. Default behaviour is calling cluster_leiden in igraph with Modularity (for undirected graphs) and CPM cost functions. Algorithmics 16, 2.1, https://doi.org/10.1145/1963190.1970376 (2011). It does not guarantee that modularity cant be increased by moving nodes between communities. Therefore, clustering algorithms look for similarities or dissimilarities among data points. Leiden consists of the following steps: Local moving of nodes Partition refinement Network aggregation The refinement step allows badly connected communities to be split before creating the aggregate network. Presumably, many of the badly connected communities in the first iteration of Louvain become disconnected in the second iteration. Sci. If we move the node to a different community, we add to the rear of the queue all neighbours of the node that do not belong to the nodes new community and that are not yet in the queue. The second iteration of Louvain shows a large increase in the percentage of disconnected communities. Finally, we compare the performance of the algorithms on the empirical networks. Centre for Science and Technology Studies, Leiden University, Leiden, The Netherlands, You can also search for this author in 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. Figure4 shows how well it does compared to the Louvain algorithm. contrastive-sc works best on datasets with fewer clusters when using the KMeans clustering and conversely for Leiden. We start by initialising a queue with all nodes in the network. 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. Leiden consists of the following steps: The refinement step allows badly connected communities to be split before creating the aggregate network. Google Scholar. You will not need much Python to use it. All experiments were run on a computer with 64 Intel Xeon E5-4667v3 2GHz CPUs and 1TB internal memory. Neurosci. Clustering with the Leiden Algorithm in R 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 https://github.com/vtraag/leidenalg Install Modularity is used most commonly, but is subject to the resolution limit. In the initial stage of Louvain (when all nodes belong to their own community), nearly any move will result in a modularity gain, and it doesnt matter too much which move is chosen. V.A.T. Furthermore, by relying on a fast local move approach, the Leiden algorithm runs faster than the Louvain algorithm. Clearly, it would be better to split up the community. B 86 (11): 471. https://doi.org/10.1140/epjb/e2013-40829-0. E 84, 016114, https://doi.org/10.1103/PhysRevE.84.016114 (2011). ADS If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate. Again, if communities are badly connected, this may lead to incorrect inferences of topics, which will affect bibliometric analyses relying on the inferred topics. We prove that the Leiden algorithm yields communities that are guaranteed to be connected. To install the development version: The current release on CRAN can be installed with: First set up a compatible adjacency matrix: An adjacency matrix is any binary matrix representing links between nodes (column and row names). Even worse, the Amazon network has 5% disconnected communities, but 25% badly connected communities. The larger the increase in the quality function, the more likely a community is to be selected. The Beginner's Guide to Dimensionality Reduction. In this post, I will cover one of the common approaches which is hierarchical clustering. We first applied the Scanpy pipeline, including its clustering method (Leiden clustering), on the PBMC dataset. This should be the first preference when choosing an algorithm. However, after all nodes have been visited once, Leiden visits only nodes whose neighbourhood has changed, whereas Louvain keeps visiting all nodes in the network. Modularity optimization. Modularity scores of +1 mean that all the edges in a community are connecting nodes within the community. Publishers note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Moreover, when the algorithm is applied iteratively, it converges to a partition in which all subsets of all communities are guaranteed to be locally optimally assigned. On the other hand, after node 0 has been moved to a different community, nodes 1 and 4 have not only internal but also external connections. We demonstrate the performance of the Leiden algorithm for several benchmark and real-world networks. For empirical networks, it may take quite some time before the Leiden algorithm reaches its first stable iteration. Raghavan, U., Albert, R. & Kumara, S. Near linear time algorithm to detect community structures in large-scale networks. E Stat. One of the most popular algorithms to optimise modularity is the so-called Louvain algorithm10, named after the location of its authors. 9, the Leiden algorithm also performs better than the Louvain algorithm in terms of the quality of the partitions that are obtained. Rev. Slider with three articles shown per slide. In our experimental analysis, we observe that up to 25% of the communities are badly connected and up to 16% are disconnected. Class wrapper based on scanpy to use the Leiden algorithm to directly cluster your data matrix with a scikit-learn flavor. We can guarantee a number of properties of the partitions found by the Leiden algorithm at various stages of the iterative process. According to CPM, it is better to split into two communities when the link density between the communities is lower than the constant. J. In this iterative scheme, Louvain provides two guarantees: (1) no communities can be merged and (2) no nodes can be moved. 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. As we prove in SectionC1 of the Supplementary Information, even when node mergers that decrease the quality function are excluded, the optimal partition of a set of nodes can still be uncovered. In short, the problem of badly connected communities has important practical consequences. We used modularity with a resolution parameter of =1 for the experiments. J. Comput. The authors act as bibliometric consultants to CWTS B.V., which makes use of community detection algorithms in commercial products and services. We provide the full definitions of the properties as well as the mathematical proofs in SectionD of the Supplementary Information. In practice, this means that small clusters can hide inside larger clusters, making their identification difficult. Initially, \({{\mathscr{P}}}_{{\rm{refined}}}\) is set to a singleton partition, in which each node is in its own community. However, so far this problem has never been studied for the Louvain algorithm. Louvain community detection algorithm was originally proposed in 2008 as a fast community unfolding method for large networks. (We ensured that modularity optimisation for the subnetwork was fully consistent with modularity optimisation for the whole network13) The Leiden algorithm was run until a stable iteration was obtained. Local Resolution-Limit-Free Potts Model for Community Detection. Phys. 2(b). Louvain pruning is another improvement to Louvain proposed in 2016, and can reduce the computational time by as much as 90% while finding communities that are almost as good as Louvain (Ozaki, Tezuka, and Inaba 2016). The resulting clusters are shown as colors on the 3D model (top) and t -SNE embedding . A major goal of single-cell analysis is to study the cell-state heterogeneity within a sample by discovering groups within the population of cells. Rev. Newman, M. E. J. Leiden is faster than Louvain especially for larger networks. 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. Nonetheless, some networks still show large differences. With one exception (=0.2 and n=107), all results in Fig. At this point, it is guaranteed that each individual node is optimally assigned. We now compare how the Leiden and the Louvain algorithm perform for the six empirical networks listed in Table2. Nat. For higher values of , Leiden finds better partitions than Louvain. Fortunato, S. Community detection in graphs. For each network, Table2 reports the maximal modularity obtained using the Louvain and the Leiden algorithm. Package 'leiden' October 13, 2022 Type Package Title R Implementation of Leiden Clustering Algorithm Version 0.4.3 Date 2022-09-10 Description Implements the 'Python leidenalg' module to be called in R. Enables clustering using the leiden algorithm for partition a graph into communities. Guimer, R. & Nunes Amaral, L. A. Functional cartography of complex metabolic networks. See the documentation on the leidenalg Python module for more information: https://leidenalg.readthedocs.io/en/latest/reference.html. 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). In other words, modularity may hide smaller communities and may yield communities containing significant substructure. conda install -c conda-forge leidenalg pip install leiden-clustering Used via. For those wanting to read more, I highly recommend starting with the Leiden paper (Traag, Waltman, and Eck 2018) or the smart local moving paper (Waltman and Eck 2013). In practical applications, the Leiden algorithm convincingly outperforms the Louvain algorithm, both in terms of speed and in terms of quality of the results, as shown by the experimental analysis presented in this paper. Communities were all of equal size. 4. This method tries to maximise the difference between the actual number of edges in a community and the expected number of such edges. Thank you for visiting nature.com. The corresponding results are presented in the Supplementary Fig. The corresponding results are presented in the Supplementary Fig. A score of -1 means that there are no edges connecting nodes within the community, and they instead all connect nodes outside the community. Article Leiden is both faster than Louvain and finds better partitions. To ensure readability of the paper to the broadest possible audience, we have chosen to relegate all technical details to the Supplementary Information. The Leiden algorithm has been specifically designed to address the problem of badly connected communities. Article CAS 10, 186198, https://doi.org/10.1038/nrn2575 (2009). The algorithm moves individual nodes from one community to another to find a partition (b), which is then refined (c). Phys. The problem of disconnected communities has been observed before19,20, also in the context of the label propagation algorithm21. 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. A partition of clusters as a vector of integers Examples Importantly, mergers are performed only within each community of the partition \({\mathscr{P}}\). Google Scholar. The leidenalg package facilitates community detection of networks and builds on the package igraph. Uniform -density means that no matter how a community is partitioned into two parts, the two parts will always be well connected to each other. This is very similar to what the smart local moving algorithm does. Nonlin. The Leiden algorithm is considerably more complex than the Louvain algorithm. where nc is the number of nodes in community c. The interpretation of the resolution parameter is quite straightforward. Technol. Faster Unfolding of Communities: Speeding up the Louvain Algorithm. Phys. http://arxiv.org/abs/1810.08473. Note that if Leiden finds subcommunities, splitting up the community is guaranteed to increase modularity. There is an entire Leiden package in R-cran here ADS CPM has the advantage that it is not subject to the resolution limit. 69 (2 Pt 2): 026113. http://dx.doi.org/10.1103/PhysRevE.69.026113. Hence, by counting the number of communities that have been split up, we obtained a lower bound on the number of communities that are badly connected. For each set of parameters, we repeated the experiment 10 times. A tag already exists with the provided branch name. Once aggregation is complete we restart the local moving phase, and continue to iterate until everything converges down to one node. Bae, S., Halperin, D., West, J. D., Rosvall, M. & Howe, B. Scalable and Efficient Flow-Based Community Detection for Large-Scale Graph Analysis. & Girvan, M. Finding and evaluating community structure in networks. As the use of clustering is highly depending on the biological question it makes sense to use several approaches and algorithms. The algorithm moves individual nodes from one community to another to find a partition (b), which is then refined (c). These nodes are therefore optimally assigned to their current community. 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 In this case we can solve one of the hard problems for K-Means clustering - choosing the right k value, giving the number of clusters we are looking for. Eng. This makes sense, because after phase one the total size of the graph should be significantly reduced. Basically, there are two types of hierarchical cluster analysis strategies - 1. The Leiden algorithm consists of three phases: (1) local moving of nodes, (2) refinement of the partition and (3) aggregation of the network based on the refined partition, using the non-refined partition to create an initial partition for the aggregate network. We conclude that the Leiden algorithm is strongly preferable to the Louvain algorithm. Nonlin. This problem is different from the well-known issue of the resolution limit of modularity14. Such a modular structure is usually not known beforehand. 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).