  For graphs generated from stochastic blockmodels, adjacency spectral
embedding is asymptotically consistent. Further, adjacency spectral embedding
composed with universally consistent classifiers is universally consistent to
achieve the Bayes error. However when the graph contains private or sensitive
information, treating the data as non-private can potentially leak privacy and
incur disclosure risks. In this paper, we propose a differentially private
adjacency spectral embedding algorithm for stochastic blockmodels. We
demonstrate that our proposed methodology can estimate the latent positions
close to, in Frobenius norm, the latent positions by adjacency spectral
embedding and achieve comparable accuracy at desired privacy parameters in
simulated and real world networks.
