  The estimation of probabilities of network edges from the observed adjacency
matrix has important applications to predicting missing links and network
denoising. It has usually been addressed by estimating the graphon, a function
that determines the matrix of edge probabilities, but this is ill-defined
without strong assumptions on the network structure. Here we propose a novel
computationally efficient method, based on neighborhood smoothing to estimate
the expectation of the adjacency matrix directly, without making the structural
assumptions that graphon estimation requires. The neighborhood smoothing method
requires little tuning, has a competitive mean-squared error rate, and
outperforms many benchmark methods on link prediction in simulated and real
networks.
