Community detection in complex networks via node similarity, graph representation learning, and hierarchical clustering

Community detection is a critical challenge in the analysis of real-world graphs and complex networks, including social, transportation, citation, cybersecurity networks, and food webs. Motivated by many similarities between community detection and clustering in Euclidean spaces, we propose three algorithm frameworks to apply hierarchical clustering methods for community detection in graphs. We show that using our methods, it is possible to apply various linkage-based (single-, complete-, average- linkage, Ward, Genie) clustering algorithms to find communities based on vertex similarity matrices, eigenvector matrices thereof, and Euclidean vector representations of nodes. We convey a comprehensive analysis of choices for each framework, including state-of-the-art graph representation learning algorithms, such as Deep Neural Graph Representation, and a vertex proximity matrix known to yield high-quality results in machine learning -- Positive Pointwise Mutual Information. Overall, we test over a hundred combinations of framework components and show that some -- including Wasserman-Faust and PPMI proximity, DNGR representation -- can compete with algorithms such as state-of-the-art Leiden and Louvain and easily outperform other known community detection algorithms. Notably, our algorithms remain hierarchical and allow the user to specify any number of clusters a priori.