  Graph neural networks (GNNs) have exhibited impressive performance in
modeling graph data as exemplified in various applications. Recently, the GNN
calibration problem has attracted increasing attention, especially in
cost-sensitive scenarios. Previous work has gained empirical insights on the
issue, and devised effective approaches for it, but theoretical supports still
fall short. In this work, we shed light on the relationship between GNN
calibration and nodewise similarity via theoretical analysis. A novel
calibration framework, named SimCalib, is accordingly proposed to consider
similarity between nodes at global and local levels. At the global level, the
Mahalanobis distance between the current node and class prototypes is
integrated to implicitly consider similarity between the current node and all
nodes in the same class. At the local level, the similarity of node
representation movement dynamics, quantified by nodewise homophily and relative
degree, is considered. Informed about the application of nodewise movement
patterns in analyzing nodewise behavior on the over-smoothing problem, we
empirically present a possible relationship between over-smoothing and GNN
calibration problem. Experimentally, we discover a correlation between nodewise
similarity and model calibration improvement, in alignment with our theoretical
results. Additionally, we conduct extensive experiments investigating different
design factors and demonstrate the effectiveness of our proposed SimCalib
framework for GNN calibration by achieving state-of-the-art performance on 14
out of 16 benchmarks.
