  We analyze the bootstrap percolation process on the stochastic block model
(SBM), a natural extension of the Erd\H{o}s--R\'{e}nyi random graph that
incorporates the community structure observed in many real systems. In the SBM,
nodes are partitioned into two subsets, which represent different communities,
and pairs of nodes are independently connected with a probability that depends
on the communities they belong to. Under mild assumptions on the system
parameters, we prove the existence of a sharp phase transition for the final
number of active nodes and characterize the sub-critical and the super-critical
regimes in terms of the number of initially active nodes, which are selected
uniformly at random in each community.
