Title: Vertex Nomination Schemes for Membership Prediction

Abstract: Suppose that a graph is realized from a stochastic block model where one of the blocks is of interest, but many or all of the graph vertices' block labels are unobserved. The task is to order the vertices with unobserved block labels into a "nomination list" such that, with high probability, vertices from the interesting block are concentrated near the list's beginning. We propose several vertex nomination schemes which include the utilization of recent graph matching and spectral partitioning machinery.
Our basic---but principled---setting and development yields a best nomination scheme (which is a Bayes-Optimal analogue), and a likelihood maximization nomination scheme that is practical to implement when there are a thousand vertices, and which is empirically near-optimal when the number of vertices is small enough to allow the comparison. We then illustrate the robustness of likelihood maximization to the modeling challenges inherent in real data, using examples which include the Enron Graph, a worm brain connectome, and a political blog network.