  Classical blockmodel is known as the simplest among models of networks with
community structure. The model can be also seen as an extremely simply example
of interconnected networks. For this reason, it is surprising that the
percolation transition in the classical blockmodel has not been examined so
far, although the phenomenon has been studied in a variety of much more
complicated models of interconnected and multiplex networks. In this paper we
derive the self-consistent equation for the size the global percolation cluster
in the classical blockmodel. We also find the condition for percolation
threshold which characterizes the emergence of the giant component. We show
that the discussed percolation phenomenon may cause unexpected problems in a
simple optimization process of the multilevel network construction. Numerical
simulations confirm the correctness of our theoretical derivations.
