Abstract. A search technique locating network modules, i.e. , internally densely connected groups of nodes in directed networks is introduced by extending the Clique Percolation Method originally proposed for undirected networks. After giving a suitable definition for directed modules we investigate their percolation transition in the Erdős-Rényi graph both analytically and numerically. We also analyse four real-world directed networks, including Google's own webpages, an email network, a word association graph and the transcriptional regulatory network of the yeast Saccharomyces cerevisiae. The obtained directed modules are validated by additional information available for the nodes. We find that directed modules of real-world graphs inherently overlap and the investigated networks can be classified into two major groups in terms of the overlaps between the modules. Accordingly, in the word-association network and among Google's web pages the overlaps are likely to contain in-hubs, whereas the modules in the email and transcriptional regulatory networks tend to overlap via out-hubs.
REF proposed the Clique Percolation Method with weights (CPMw) for weighted networks.
Weighted network modules
New J. Phys. 9
Physics