  In this work we show that, using the eigen-decomposition of the adjacency
matrix, we can consistently estimate latent positions for random dot product
graphs provided the latent positions are i.i.d. from some distribution. If
class labels are observed for a number of vertices tending to infinity, then we
show that the remaining vertices can be classified with error converging to
Bayes optimal using the $k$-nearest-neighbors classification rule. We evaluate
the proposed methods on simulated data and a graph derived from Wikipedia.
