  The clustering property of complex networks indicates the abundance of small
dense subgraphs in otherwise sparse networks.
  For a community-affiliation network defined by a superposition of Bernoulli
random graphs, which has a nonvanishing global clustering coefficient and a
power-law degree distribution, we establish normal and $\alpha$--stable
approximations to the number of small cliques, cycles and more general
$2$-connected subgraphs.
