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The KPFM random graph model is as defined in lines 66-69 where ([n], S) is a weighted graph that admits a pref. What we **should have** said at the bottom of p.2 is that we use independent sampling of edges only to prove concentration of hat{L}. The result extends to other graph models with dependent edges (e.g graph lifts) if one can prove concentration. "Misclustered" is defined the usual way: p_err (1/n)*(min over all permutations of cluster labels of the Hamming distance between label vectors). Alg 1 is almost that of [13,21] (there, columns are normalized after step 3 not before).