Scaling Community Detection with the Leiden Algorithm in C++

Scaling Community Detection with the Leiden Algorithm in C++

Community detection, a fundamental task in network analysis, aims to identify groups of vertices that are more densely connected to each other than to the rest of the network. The Leiden algorithm, implemented in C++, offers a powerful approach to community detection. In this article, we will explore the features, installation steps, and usage of the Leiden algorithm, highlighting its significance in network analysis.

Features and Functionalities

The Leiden algorithm, built upon the Louvain algorithm, provides several methods for community detection. These methods include:

1. Modularity: Measures the quality of a partition based on the difference between the observed number of edges within communities and the expected number of edges in a random network.
2. Reichardt and Bornholdt’s model: Uses the configuration null model and the Erdös-Rényi null model to detect communities.
3. Constant Potts model (CPM): Assigns weights to links to improve the resolution of the detected communities.
4. Significance: Identifies communities by evaluating the statistical significance of the observed community structure.
5. Surprise: Detects communities based on the unexpectedness of the community structure.

The Leiden algorithm also supports multiplex partition optimization, allowing community detection in scenarios such as negative links or multiple time slices. Additionally, it offers the flexibility to partially optimize a partition, enabling the preservation of fixed community assignments.

Installation

To use the Leiden algorithm in your project, follow these installation steps:

1. Get the source code: Download the source code from the latest release on the Leiden algorithm GitHub repository or clone the repository using git.

2. Create a build directory: Create a build directory, such as mkdir build, and navigate to it.

3. Configure the build system: Run cmake .. to configure the build system. Ensure that the build directory is the current working directory.

4. Build the library: Execute cmake --build . to build the library.

5. Install the library: Use cmake --build . --target install to install the library. You can change the installation location using CMAKE_INSTALL_PREFIX.

Please note that the Leiden algorithm depends on the igraph library, which you should install prior to building the Leiden algorithm. Refer to the igraph installation documentation for more details. If igraph is installed in a non-standard location, you can specify it using CMAKE_PREFIX_PATH when configuring libleidenalg.

Usage

The Optimiser class is the core component of the Leiden algorithm. It optimizes a MutableVertexPartition to find the optimal partition based on a specific quality function. The MutableVertexPartition represents the community assignments of the vertices and should be implemented with an explicit quality function.

To use the Leiden algorithm, instantiate an igraph_t object from the igraph library and construct a Graph object based on it. Then, create a specific MutableVertexPartition class based on the desired quality function. Finally, use the Optimiser class to optimize the partition. Here’s an example:

“`C
igraph_t g;
igraph_famous(&g, “Zachary”);

Graph graph(&g);

CPMVertexPartition part(&graph,
                        0.05 /* resolution */ );

Optimiser o;

o.optimise_partition(&part);

“`

Consider exploring the example directory in the Leiden algorithm repository for a complete example, including CMake build files.

References

When using the Leiden algorithm, it is essential to cite the relevant references. Here are the references associated with the algorithm’s development:

[^1]: Traag, V.A., Waltman. L., Van Eck, N.-J. (2018). From Louvain to Leiden: guaranteeing well-connected communities. Scientific Reports, 9(1), 5233. 10.1038/s41598-019-41695-z

[^2]: Blondel, V. D., Guillaume, J.-L., Lambiotte, R., & Lefebvre, E. (2008). Fast unfolding of communities in large networks. Journal of Statistical Mechanics: Theory and Experiment, 10008(10), 6. 10.1088/1742-5468/2008/10/P10008

[^3]: Newman, M. E. J., & Girvan, M. (2004). Finding and evaluating community structure in networks. Physical Review E, 69(2), 026113. 10.1103/PhysRevE.69.026113

[^4]: Reichardt, J., & Bornholdt, S. (2006). Statistical mechanics of community detection. Physical Review E, 74(1), 016110. 10.1103/PhysRevE.74.016110

[^5]: Traag, V. A., Van Dooren, P., & Nesterov, Y. (2011). Narrow scope for resolution-limit-free community detection. Physical Review E, 84(1), 1. 10.1103/PhysRevE.84.016114

[^6]: Traag, V. A., Krings, G., & Van Dooren, P. (2013). Significant scales in community structure. Scientific Reports, 3, 2930. 10.1038/srep02930

[^7]: Traag, V. A., Aldecoa, R., & Delvenne, J.-C. (2015). Detecting communities using asymptotical surprise. Physical Review E, 92(2), 1. 10.1103/PhysRevE.92.022816

[^8]: Traag, V. A., & Bruggeman, J. (2009). Community detection in networks with positive and negative links. Physical Review E, 80(3), 036115. 10.1103/PhysRevE.80.036115

[^9]: Mucha, P. J., Richardson, T., Macon, K., Porter, M. A., & Onnela, J.-P. (2010). Community structure in time-dependent, multiscale, and multiplex networks. Science, 328(5980), 876–8. 10.1126/science.1184819

[^10]: Zanini, F., Berghuis, B. A., Jones, R. C., Robilant, B. N. di, Nong, R. Y., Norton, J., Clarke, Michael F., Quake, S. R. (2019). northstar: leveraging cell atlases to identify healthy and neoplastic cells in transcriptomes from human tumors. BioRxiv, 820928. 10.1101/820928

Conclusion

The Leiden algorithm in C++ offers a scalable and flexible solution for community detection in large networks. With its various methods, multiplex partition optimization, and partial optimization capabilities, the Leiden algorithm provides a powerful tool for analyzing network structures. By integrating the Leiden algorithm into your projects, you can identify meaningful communities and gain valuable insights into complex networks.