  In many real-world applications, graph-structured data used for training and
testing have differences in distribution, such as in high energy physics (HEP)
where simulation data used for training may not match real experiments. Graph
domain adaptation (GDA) is a method used to address these differences. However,
current GDA primarily works by aligning the distributions of node
representations output by a single graph neural network encoder shared across
the training and testing domains, which may often yield sub-optimal solutions.
This work examines different impacts of distribution shifts caused by either
graph structure or node attributes and identifies a new type of shift, named
conditional structure shift (CSS), which current GDA approaches are provably
sub-optimal to deal with. A novel approach, called structural reweighting
(StruRW), is proposed to address this issue and is tested on synthetic graphs,
four benchmark datasets, and a new application in HEP. StruRW has shown
significant performance improvement over the baselines in the settings with
large graph structure shifts, and reasonable performance improvement when node
attribute shift dominates.
