When is Nontrivial Estimation Possible for Graphons and Stochastic Block Models?

in the δ2 metric with constant probability for at least some graphons. In particular, our bound rules out any nontrivial estimation (that is, with δ2 error substantially less than ρ) when k ≥ n√ρ. Combined with previous upper and lower bounds, our results characterize, up to logarithmic terms, the accuracy of graphon estimation in the δ2 metric. A similar lower bound to ours was obtained independently by Klopp, Tsybakov, and Verzelen [17].