In this work we present an important part of network analysis, the problem of community detection. Hidden community structure, which we aim to reconstruct using community detection methods, contains important information about the underlying graph structure. The main focus of this work is to analyze the consideration of edge direction, which is usually ignored because of its complicated nature. We offer an exhaustive review of the problem and corresponding methods on intuitive as well as on formal level.
An additional difficulty we face is the unclear definition of the problem. We explore various views of the problem definition with the detailed analysis including the presentation of the main approaches dealing with the problem. Additionally, we focus on four different methods, each dealing with directed and weighted networks on its own way. Methods we include are the well-known Louvain method, Leiden, Infomap and OSLOM. An important part of the work is the empirical comparative analysis of the presented methods based on a number of detected communities, accuracy, stability and value of modularity in synthetic as well as in real networks.