  We study the problem of identifying macroscopic structures in networks,
characterizing the impact of introducing link directions on the detectability
phase transition. To this end, building on the stochastic block model, we
construct a class of hardly detectable directed networks. We find closed form
solutions by using belief propagation method showing how the transition line
depends on the assortativity and the asymmetry of the network. Finally, we
numerically identify the existence of a hard phase for detection close to the
transition point.
