Direction matters in complex networks: A theoretical and applied study for greedy modularity optimization

Many real-world systems can be modeled as directed networks, such as transportation, social, collaboration or vocabulary networks. However, direction is often neglected or even ignored in community detection algorithms. This is in particular the case on large networks, since there are only a few scalable algorithms at the time. One of the most used scalable algorithm, Louvain’s algorithm, is based on modularity maximization and commonly used for directed networks by forgetting direction. We show that this oversimplification in the modeling process may alter the quality of the results both theoretically and practically. Moreover, we introduced in a complementary version of this work the Directed Louvain algorithm based on directed modularity that found various successful applications that enlighten the importance of direction when detecting communities. We hence propose an overview of selected applications within some of the aforementioned fields. We hope that this study will encourage researchers to use directed modularity whenever it is relevant.