  Despite Graph Neural Networks (GNNs) have achieved remarkable accuracy,
whether the results are trustworthy is still unexplored. Previous studies
suggest that many modern neural networks are over-confident on the predictions,
however, surprisingly, we discover that GNNs are primarily in the opposite
direction, i.e., GNNs are under-confident. Therefore, the confidence
calibration for GNNs is highly desired. In this paper, we propose a novel
trustworthy GNN model by designing a topology-aware post-hoc calibration
function. Specifically, we first verify that the confidence distribution in a
graph has homophily property, and this finding inspires us to design a
calibration GNN model (CaGCN) to learn the calibration function. CaGCN is able
to obtain a unique transformation from logits of GNNs to the calibrated
confidence for each node, meanwhile, such transformation is able to preserve
the order between classes, satisfying the accuracy-preserving property.
Moreover, we apply the calibration GNN to self-training framework, showing that
more trustworthy pseudo labels can be obtained with the calibrated confidence
and further improve the performance. Extensive experiments demonstrate the
effectiveness of our proposed model in terms of both calibration and accuracy.
