  Random intersection graphs containing an underlying community structure are a
popular choice for modelling real-world networks. Given the group memberships,
the classical random intersection graph is obtained by connecting individuals
when they share at least one group. We extend this approach and make the
communities dynamic by letting them alternate between an active and inactive
phase. We analyse the new model, delivering results on degree distribution,
local convergence, giant component, and maximum group size, paying particular
attention to the dynamic description of these properties. We also describe the
connection between our model and the bipartite configuration model, which is of
independent interest.
