In this talk, we will analyze the convergence to equilibrium of a simple random walk on a directed version of the classical Stochastic Block Model with $m$ communities. We show that the mixing behavior of the walk exhibits a trichotomy governed by the parameter $\alpha$, which controls the strength of inter-community interactions. In the subcritical regime (large $\alpha$) the dynamics displays cutoff at at the entropic timescale $T^* \sim \log(n)/\log\log(n)$. In the supercritical regime (small $\alpha$) the mixing is driven by rare inter-community transitions, leading to a metastable behavior. After an abrupt jump at timescale $T^*$, the distance to equilibrium decays smoothly at an exponential rate on the timescale $1/\alpha$. At criticality (when $1/\alpha\sim T^*$), an intermediate behavior emerges, characterized by an interplay between entropic mixing and inter-community transitions. Joint work with G. Passuello and M. Quattropani.