  Estimating the probabilities of linkages in a network has gained increasing
interest in recent years. One popular model for network analysis is the
exchangeable graph model (ExGM) characterized by a two-dimensional function
known as a graphon. Estimating an underlying graphon becomes the key of such
analysis. Several nonparametric estimation methods have been proposed, and some
are provably consistent. However, if certain useful features of the nodes
(e.g., age and schools in social network context) are available, none of these
methods was designed to incorporate this source of information to help with the
estimation. This paper develops a consistent graphon estimation method that
integrates the information from both the adjacency matrix itself and node
features. We show that properly leveraging the features can improve the
estimation. A cross-validation method is proposed to automatically select the
tuning parameter of the method.
