  Paper proposes a model of large networks based on a random preferential
attachment graph with addition of complete subgraphs (cliques). The proposed
model refers to models of random graphs following the nonlinear preferential
attachment rule and takes into account the possibility of
{\guillemotleft}adding{\guillemotright} entire communities of nodes to the
network. In the derivation of the relations that determine the vertex degree
distribution, the technique of finite-difference equations describing
stationary states of a graph is used. The obtained results are tested
empirically (by generating large graphs), special cases correspond to known
mathematical relations.
