Extracting weights from edge directions to find communities in directed networks

Community structures are found to exist ubiquitously in real-world complex networks. We address here the problem of community detection in directed networks. Most of the previous literature ignores edge directions and applies methods designed for community detection in undirected networks, which discards valuable information and often fails when different communities are defined on the basis of incoming and outgoing edges. We suggest extracting information about edge directions using a PageRank random walk and translating such information into edge weights. After extraction we obtain a new weighted directed network in which edge directions can then be safely ignored. We thus transform community detection in directed networks into community detection in reweighted undirected networks. Such an approach can benefit directly from the large volume of algorithms for the detection of communities in undirected networks already developed, since it is not obvious how to extend these algorithms to account for directed networks and the procedure is often difficult. Validations on synthetic and real-world networks demonstrate that the proposed framework can effectively detect communities in directed networks.