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We establish asymptotic normality results for estimation of the block probability matrix B in stochastic blockmodel graphs using spectral embedding when the average degrees grows at the rate of ω(√(n)) in n, the number of vertices. As a corollary, we show that when B is of full-rank, estimates of B obtained from spectral embedding are asymptotically efficient. When B is singular the estimates obtained from spectral embedding can have smaller mean square error than those obtained from maximizingarXiv:1710.10936v1 fatcat:jq7rq5ghubhy5a4liqvno2gkwm