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We introduce a general (k,l) clique community, which consists of adjacent k-cliques sharing at least l vertices with k-1 > l > 1. The emergence of a giant (k,l) clique community indicates a (k,l) clique percolation, which is studied by the largest size gap Δ of the largest clique community during network evolution and the corresponding evolution step T_c. For a clique percolation, the averages of Δ and T_c and the root-mean-squares of their fluctuations have power law finite-size effects whosearXiv:1309.4535v1 fatcat:bgpqwjxjtjexvdpse56ekznt6a