Nonequilibrium phase transitions in directed small-world networks.
Many social, biological, and economic systems can be approached by complex networks of interacting units. In many of these systems relations are directed in the sense that links act only in one direction (outwards or inwards). We investigate the effect of directed links on the behavior of a simple spin-like model evolving on a small-world network. This model may describe for instance the dynamics of public opinion in social influence networks. We show that directed networks may lead to a highly nontrivial phase diagram including first- and second-order phase transitions out of equilibrium.