  Node classification on graphs is an important research problem with many
applications. Real-world graph data sets may not be balanced and accurate as
assumed by most existing works. A challenging setting is positive-unlabeled
(PU) node classification, where labeled nodes are restricted to positive nodes.
It has diverse applications, e.g., pandemic prediction or network anomaly
detection. Existing works on PU node classification overlook information in the
graph structure, which can be critical. In this paper, we propose to better
utilize graph structure for PU node classification. We first propose a
distance-aware PU loss that uses homophily in graphs to introduce more accurate
supervision. We also propose a regularizer to align the model with graph
structure. Theoretical analysis shows that minimizing the proposed loss also
leads to minimizing the expected loss with both positive and negative labels.
Extensive empirical evaluation on diverse graph data sets demonstrates its
superior performance over existing state-of-the-art methods.
