Predicting unobserved links in incompletely observed networks

In this paper we consider networks in which the links (edges) are imperfectly observed. This may be a result of sampling, or it may be caused by actors (vertices) who are actively attempting to hide their links (edges). Thus the network is incompletely observed, and we wish to predict which of the possible unobserved links are actually present in the network. To this end, we apply a constrained random dot product graph (CRDPG) to rank the potential edges according to the probability (under the model) that they are in fact present. This model is then extended to utilize covariates measured on the actors, to improve the link prediction. The method is illustrated on a data set of alliances between nations, in which a subset of the links (alliances) is assumed unobserved for the purposes of illustration.