  The notion of k-clique percolation in random graphs is introduced, where k is
the size of the complete subgraphs whose large scale organizations are
analytically and numerically investigated. For the Erdos-Renyi graph of N
vertices we obtain that the percolation transition of k-cliques takes place
when the probability of two vertices being connected by an edge reaches the
threshold pc(k)=[(k-1)N]^{-1/(k-1)}. At the transition point the scaling of the
giant component with N is highly non-trivial and depends on k. We discuss why
clique percolation is a novel and efficient approach to the identification of
overlapping communities in large real networks.
