%0 Journal Article %T Loop-based Module Detection in Directed Networks %A Ralf Banisch %A Christof Sch¨ątte %A NataŁża Djurdjevac Conrad %J Computer Science %D 2014 %I arXiv %R 10.1209/0295-5075/108/68008 %X We investigate the problem of finding modules (or clusters, communities) in directed networks. Until now, most articles on this topic have been oriented towards finding full network partitions, where every node belongs to exactly one module. In this paper, we will present a novel random walk based approach for fuzzy partitions of the directed network into modules, such that some nodes do not belong to only one of the modules but to several or to none at all. Despite the fact that the new random walk process is reversible, we will show that it inherits all necessary information about directions and structure of the original network. We accompany our theoretical considerations with numerical examples. %U http://arxiv.org/abs/1404.2813v1