Models and average properties of scale-free directed networks

We extend the merging model for undirected networks by Kim [Eur. Phys. J. B 43, 369 (2004)] to directed networks and investigate the emerging scale-free networks. Two versions of the directed merging model, friendly and hostile merging, give rise to two distinct network types. We uncover that some nontrivial features of these two network types resemble two levels of a certain randomization/nonspecificity in the link reshuffling during network evolution. Furthermore, the same features show up, respectively, in metabolic networks and transcriptional networks. We introduce measures that single out the distinguishing features between the two prototype networks, as well as point out features that are beyond the prototypes.