Fast unfolding of communities in large networks: 15 years later

The Louvain method was proposed 15 years ago as a heuristic method for the fast detection of communities in large networks. During this period, it has emerged as one of the most popular methods for community detection, the task of partitioning vertices of a network into dense groups, usually called communities or clusters. Here, after a short introduction to the method, we give an overview of the different generalizations and modifications that have been proposed in the literature, and also survey the quality functions, beyond modularity, for which it has been implemented.