  Graph-based methods, pivotal for label inference over interconnected objects
in many real-world applications, often encounter generalization challenges, if
the graph used for model training differs significantly from the graph used for
testing. This work delves into Graph Domain Adaptation (GDA) to address the
unique complexities of distribution shifts over graph data, where
interconnected data points experience shifts in features, labels, and in
particular, connecting patterns. We propose a novel, theoretically principled
method, Pairwise Alignment (Pair-Align) to counter graph structure shift by
mitigating conditional structure shift (CSS) and label shift (LS). Pair-Align
uses edge weights to recalibrate the influence among neighboring nodes to
handle CSS and adjusts the classification loss with label weights to handle LS.
Our method demonstrates superior performance in real-world applications,
including node classification with region shift in social networks, and the
pileup mitigation task in particle colliding experiments. For the first
application, we also curate the largest dataset by far for GDA studies. Our
method shows strong performance in synthetic and other existing benchmark
datasets.
