In this stage we essentially collapse communities down into a single representative node, creating a new simplified graph. For all networks, Leiden identifies substantially better partitions than Louvain. The PyPI package leiden-clustering receives a total of 15 downloads a week. Speed and quality for the first 10 iterations of the Louvain and the Leiden algorithm for six empirical networks. 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. The Louvain algorithm guarantees that modularity cannot be increased by merging communities (it finds a locally optimal solution). 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. We find that the Leiden algorithm commonly finds partitions of higher quality in less time. Modularity optimization. Ph.D. thesis, (University of Oxford, 2016). & Clauset, A. MathSciNet In this way, Leiden implements the local moving phase more efficiently than Louvain. Google Scholar. We keep removing nodes from the front of the queue, possibly moving these nodes to a different community. Importantly, the problem of disconnected communities is not just a theoretical curiosity. This is not the case when nodes are greedily merged with the community that yields the largest increase in the quality function. The smart local moving algorithm (Waltman and Eck 2013) identified another limitation in the original Louvain method: it isnt able to split communities once theyre merged, even when it may be very beneficial to do so. This should be the first preference when choosing an algorithm. Introduction The Louvain method is an algorithm to detect communities in large networks. 2004. We here introduce the Leiden algorithm, which guarantees that communities are well connected. You will not need much Python to use it. Zenodo, https://doi.org/10.5281/zenodo.1466831 https://github.com/CWTSLeiden/networkanalysis. The minimum resolvable community size depends on the total size of the network and the degree of interconnectedness of the modules. Conversely, if Leiden does not find subcommunities, there is no guarantee that modularity cannot be increased by splitting up the community. & Arenas, A. Inf. However, Leiden is more than 7 times faster for the Live Journal network, more than 11 times faster for the Web of Science network and more than 20 times faster for the Web UK network. The 'devtools' package will be used to install 'leiden' and the dependancies (igraph and reticulate). Nonlin. I tracked the number of clusters post-clustering at each step. When a disconnected community has become a node in an aggregate network, there are no more possibilities to split up the community. The thick edges in Fig. The Leiden algorithm is clearly faster than the Louvain algorithm. The horizontal axis indicates the cumulative time taken to obtain the quality indicated on the vertical axis. Then the Leiden algorithm can be run on the adjacency matrix. Edges were created in such a way that an edge fell between two communities with a probability and within a community with a probability 1. An aggregate network (d) is created based on the refined partition, using the non-refined partition to create an initial partition for the aggregate network. Rev. Thank you for visiting nature.com. In that case, nodes 16 are all locally optimally assigned, despite the fact that their community has become disconnected. E 76, 036106, https://doi.org/10.1103/PhysRevE.76.036106 (2007). Furthermore, by relying on a fast local move approach, the Leiden algorithm runs faster than the Louvain algorithm. E 69, 026113, https://doi.org/10.1103/PhysRevE.69.026113 (2004). ADS Due to the resolution limit, modularity may cause smaller communities to be clustered into larger communities. The docs are here. In other words, communities are guaranteed to be well separated. Rev. The Leiden algorithm is typically iterated: the output of one iteration is used as the input for the next iteration. However, in the case of the Web of Science network, more than 5% of the communities are disconnected in the first iteration. Not. Hence, in general, Louvain may find arbitrarily badly connected communities. Randomness in the selection of a community allows the partition space to be explored more broadly. to use Codespaces. 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. Sci Rep 9, 5233 (2019). Rev. MathSciNet This is similar to what we have seen for benchmark networks. This is well illustrated by figure 2 in the Leiden paper: When a community becomes disconnected like this, there is no way for Louvain to easily split it into two separate communities. Bullmore, E. & Sporns, O. Such algorithms are rather slow, making them ineffective for large networks. Louvain community detection algorithm was originally proposed in 2008 as a fast community unfolding method for large networks. However, values of within a range of roughly [0.0005, 0.1] all provide reasonable results, thus allowing for some, but not too much randomness. The value of the resolution parameter was determined based on the so-called mixing parameter 13. Internet Explorer). The resulting clusters are shown as colors on the 3D model (top) and t -SNE embedding . The Leiden algorithm is considerably more complex than the Louvain algorithm. GitHub on Feb 15, 2020 Do you think the performance improvements will also be implemented in leidenalg? Phys. Google Scholar. 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. J. Assoc. The differences are not very large, which is probably because both algorithms find partitions for which the quality is close to optimal, related to the issue of the degeneracy of quality functions29. Waltman, Ludo, and Nees Jan van Eck. Note that communities found by the Leiden algorithm are guaranteed to be connected. However, the initial partition for the aggregate network is based on P, just like in the Louvain algorithm. 104 (1): 3641. As shown in Fig. Wolf, F. A. et al. Technol. As can be seen in Fig. performed the experimental analysis. They identified an inefficiency in the Louvain algorithm: computes modularity gain for all neighbouring nodes per loop in local moving phase, even though many of these nodes will not have moved. In other words, modularity may hide smaller communities and may yield communities containing significant substructure. E Stat. The algorithm moves individual nodes from one community to another to find a partition (b), which is then refined (c). 2(a). Nodes 06 are in the same community. 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. Traag, V. A., Van Dooren, P. & Nesterov, Y. Hence, no further improvements can be made after a stable iteration of the Louvain algorithm. Moreover, when no more nodes can be moved, the algorithm will aggregate the network. the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in These nodes are therefore optimally assigned to their current community. Below, the quality of a partition is reported as \(\frac{ {\mathcal H} }{2m}\), where H is defined in Eq. There are many different approaches and algorithms to perform clustering tasks. While current approaches are successful in reducing the number of sequence alignments performed, the generated clusters are . To address this important shortcoming, we introduce a new algorithm that is faster, finds better partitions and provides explicit guarantees and bounds. A score of 0 would mean that the community has half its edges connecting nodes within the same community, and half connecting nodes outside the community. It therefore does not guarantee -connectivity either. The high percentage of badly connected communities attests to this. Article The algorithm continues to move nodes in the rest of the network. 92 (3): 032801. http://dx.doi.org/10.1103/PhysRevE.92.032801. As the use of clustering is highly depending on the biological question it makes sense to use several approaches and algorithms. USA 104, 36, https://doi.org/10.1073/pnas.0605965104 (2007). The Louvain algorithm10 is very simple and elegant. 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. Acad. 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). This enables us to find cases where its beneficial to split a community. Proc. The DBLP network is somewhat more challenging, requiring almost 80 iterations on average to reach a stable iteration. & Fortunato, S. Community detection algorithms: A comparative analysis. 81 (4 Pt 2): 046114. http://dx.doi.org/10.1103/PhysRevE.81.046114. MathSciNet Presumably, many of the badly connected communities in the first iteration of Louvain become disconnected in the second iteration. To overcome the problem of arbitrarily badly connected communities, we introduced a new algorithm, which we refer to as the Leiden algorithm. Such a modular structure is usually not known beforehand. An alternative quality function is the Constant Potts Model (CPM)13, which overcomes some limitations of modularity. The authors show that the total computational time for Louvain depends a lot on the number of phase one loops (loops during the first local moving stage). After the refinement phase is concluded, communities in \({\mathscr{P}}\) often will have been split into multiple communities in \({{\mathscr{P}}}_{{\rm{refined}}}\), but not always. Article Weights for edges an also be passed to the leiden algorithm either as a separate vector or weights or a weighted adjacency matrix. This is similar to ideas proposed recently as pruning16 and in a slightly different form as prioritisation17. Speed and quality of the Louvain and the Leiden algorithm for benchmark networks of increasing size (two iterations). Finally, we demonstrate the excellent performance of the algorithm for several benchmark and real-world networks. AMS 56, 10821097 (2009). 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. running Leiden clustering finished: found 16 clusters and added 'leiden_1.0', the cluster labels (adata.obs, categorical) (0:00:00) running Leiden clustering finished: found 12 clusters and added 'leiden_0.6', the cluster labels (adata.obs, categorical) (0:00:00) running Leiden clustering finished: found 9 clusters and added 'leiden_0.4', the Mech. In an experiment containing a mixture of cell types, each cluster might correspond to a different cell type. The increase in the percentage of disconnected communities is relatively limited for the Live Journal and Web of Science networks. Article The algorithm moves individual nodes from one community to another to find a partition (b). Finally, we compare the performance of the algorithms on the empirical networks. Technol. 2010. The percentage of disconnected communities even jumps to 16% for the DBLP network. Nodes 16 have connections only within this community, whereas node 0 also has many external connections. It implies uniform -density and all the other above-mentioned properties. A partition of clusters as a vector of integers Examples CAS Knowl. We consider these ideas to represent the most promising directions in which the Louvain algorithm can be improved, even though we recognise that other improvements have been suggested as well22. We prove that the new algorithm is guaranteed to produce partitions in which all communities are internally connected. Soft Matter Phys. 2018. where >0 is a resolution parameter4. Our analysis is based on modularity with resolution parameter =1. 8, the Leiden algorithm is significantly faster than the Louvain algorithm also in empirical networks. The Leiden algorithm starts from a singleton partition (a). The Louvain algorithm is illustrated in Fig. and L.W. Waltman, L. & van Eck, N. J. Google Scholar. This can be a shared nearest neighbours matrix derived from a graph object. Reichardt, J. In particular, in an attempt to find better partitions, multiple consecutive iterations of the algorithm can be performed, using the partition identified in one iteration as starting point for the next iteration. This represents the following graph structure. Performance of modularity maximization in practical contexts. Default behaviour is calling cluster_leiden in igraph with Modularity (for undirected graphs) and CPM cost functions. The main ideas of our algorithm are explained in an intuitive way in the main text of the paper. All communities are subpartition -dense. These nodes can be approximately identified based on whether neighbouring nodes have changed communities. 2013. Starting from the second iteration, Leiden outperformed Louvain in terms of the percentage of badly connected communities. Zenodo, https://doi.org/10.5281/zenodo.1469357 https://github.com/vtraag/leidenalg. 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. * (2018). ADS We first applied the Scanpy pipeline, including its clustering method (Leiden clustering), on the PBMC dataset. Basically, there are two types of hierarchical cluster analysis strategies - 1. Rep. 6, 30750, https://doi.org/10.1038/srep30750 (2016). Computer Syst. 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 For each network, we repeated the experiment 10 times. Leiden is faster than Louvain especially for larger networks. https://leidenalg.readthedocs.io/en/latest/reference.html. The Beginner's Guide to Dimensionality Reduction. Besides the Louvain algorithm and the Leiden algorithm (see the "Methods" section), there are several widely-used network clustering algorithms, such as the Markov clustering algorithm [], Infomap algorithm [], and label propagation algorithm [].Markov clustering and Infomap algorithm are both based on flow . Value. Higher resolutions lead to more communities, while lower resolutions lead to fewer communities. In many complex networks, nodes cluster and form relatively dense groupsoften called communities1,2. Biological sequence clustering is a complicated data clustering problem owing to the high computation costs incurred for pairwise sequence distance calculations through sequence alignments, as well as difficulties in determining parameters for deriving robust clusters. It only implies that individual nodes are well connected to their community. A score of -1 means that there are no edges connecting nodes within the community, and they instead all connect nodes outside the community. Newman, M. E. J. Here is some small debugging code I wrote to find this. It identifies the clusters by calculating the densities of the cells. The Web of Science network is the most difficult one. This is not too difficult to explain. An aggregate. Article Luecken, M. D. Application of multi-resolution partitioning of interaction networks to the study of complex disease. Both conda and PyPI have leiden clustering in Python which operates via iGraph. The random component also makes the algorithm more explorative, which might help to find better community structures. 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. Rev. By moving these nodes, Louvain creates badly connected communities. In fact, by implementing the refinement phase in the right way, several attractive guarantees can be given for partitions produced by the Leiden algorithm. ADS ADS Google Scholar. The larger the increase in the quality function, the more likely a community is to be selected. Traag, V. A. leidenalg 0.7.0. In terms of the percentage of badly connected communities in the first iteration, Leiden performs even worse than Louvain, as can be seen in Fig. Scaling of benchmark results for network size. Unlike the Louvain algorithm, the Leiden algorithm uses a fast local move procedure in this phase. See the documentation on the leidenalg Python module for more information: https://leidenalg.readthedocs.io/en/latest/reference.html. 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. We typically reduce the dimensionality of the data first by running PCA, then construct a neighbor graph in the reduced space. For example, after four iterations, the Web UK network has 8% disconnected communities, but twice as many badly connected communities. We start by initialising a queue with all nodes in the network. Cite this article. All experiments were run on a computer with 64 Intel Xeon E5-4667v3 2GHz CPUs and 1TB internal memory. E 78, 046110, https://doi.org/10.1103/PhysRevE.78.046110 (2008). The quality improvement realised by the Leiden algorithm relative to the Louvain algorithm is larger for empirical networks than for benchmark networks. In the fast local move procedure in the Leiden algorithm, only nodes whose neighbourhood has changed are visited. The Leiden algorithm guarantees all communities to be connected, but it may yield badly connected communities. The algorithm is run iteratively, using the partition identified in one iteration as starting point for the next iteration. Use Git or checkout with SVN using the web URL. E 72, 027104, https://doi.org/10.1103/PhysRevE.72.027104 (2005). We provide the full definitions of the properties as well as the mathematical proofs in SectionD of the Supplementary Information. Eng. This is because Louvain only moves individual nodes at a time.