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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-trivialdoi:10.1103/physrevlett.94.160202 pmid:15904198 fatcat:pca25s2cqzarhlk6twwqtccmaa