What are the best algorithms for community detection and partitioning?

1 Modularity-based methods

One of the most widely used criteria for evaluating the quality of a community partition is modularity, which measures how much the density of edges within communities differs from a random expectation. Modularity-based methods optimize modularity by moving nodes between communities or merging and splitting communities. Some examples of these methods are the Louvain algorithm, the Infomap algorithm, and the Girvan-Newman algorithm.

2 Spectral methods

Another approach to community detection is based on spectral graph theory, which uses the eigenvalues and eigenvectors of matrices associated with the graph, such as the adjacency matrix, the Laplacian matrix, or the modularity matrix. Spectral methods can identify communities by applying clustering techniques, such as k-means or hierarchical clustering, to the eigenvectors corresponding to the smallest or largest eigenvalues. Some examples of these methods are the Shi-Malik algorithm, the Newman algorithm, and the Leicht-Newman algorithm.

3 Generative models

A third approach to community detection is based on generative models, which assume that the graph is generated by a probabilistic process that depends on some hidden parameters, such as the number and size of communities, and the probabilities of connections between and within communities. Generative models can infer the most likely community structure by using statistical methods, such as maximum likelihood estimation or Bayesian inference. Some examples of these models are the stochastic block model, the degree-corrected block model, and the mixed-membership block model.

4 Optimization methods

A fourth approach to community detection is based on optimization methods, which formulate the problem as a combinatorial optimization problem that seeks to minimize or maximize some objective function that captures the notion of community. Optimization methods can solve the problem by using heuristic algorithms, such as simulated annealing, genetic algorithms, or ant colony optimization. Some examples of these methods are the Kernighan-Lin algorithm, the Markov clustering algorithm, and the label propagation algorithm.

5 Evaluation methods

Besides choosing an algorithm for community detection, it is also important to evaluate the results and compare them with other methods or with ground truth data. Evaluation methods can be divided into two categories: internal and external. Internal methods use only the graph structure and the community partition to assess the quality, such as modularity, conductance, or silhouette coefficient. External methods use some additional information, such as node attributes or labels, to measure the agreement, such as normalized mutual information, adjusted rand index, or F1 score.

6 Applications and challenges

Community detection and partitioning have many applications in various domains, such as social network analysis, bioinformatics, recommender systems, or image segmentation. However, there are also many challenges and open questions that remain to be solved, such as how to define and measure communities, how to deal with overlapping and hierarchical communities, how to handle dynamic and heterogeneous networks, or how to scale up to large and complex networks.

7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?