Semi-supervised　graph　domain　adaptation,　as　a　subfield　of　graph　transfer　learning,　seeks　to　precisely　annotate　unlabeled　target　graph　nodes　by　leveraging　transferable　features　acquired　from　the　limited　labeled　source　nodes.　However,　most　existing　studies　often　directly　utilize　graph　convolutional　networks　(GCNs)-based　feature　extractors　to　capture　domain-invariant　node　features,　while　neglecting　the　issue　that　GCNs　are　insufficient　in　collecting　complex　structure　information　in　graph.　Considering　the　importance　of　graph　structure　information　in　encoding　the　complex　relationship　among　nodes　and　edges,　this　paper　aims　to　utilize　such　powerful　information　to　assist　graph　transfer　learning.　To　achieve　this　goal,　we　develop　a　novel　framework　called　HOGDA.　Concretely,　HOGDA　introduces　a　high-order　structure　information　mixing　(HSIM)　module　to　effectively　capture　abundant　structure　information　in　graph,　greatly　enhancing　the　feature　extractor＇s　ability　to　adapt　across　different　domains.　Moreover,　to　achieve　fine-grained　feature　distributions　alignment,　a　novel　strategy　called　adaptive　weighted　domain　alignment　(AWDA)　is　proposed　to　dynamically　adjust　the　node　weight　during　adversarial　domain　adaptation　process,　effectively　boosting　the　model＇s　transfer　ability.　Furthermore,　to　mitigate　the　overfitting　phenomenon　caused　by　limited　source　labeled　nodes,　we　also　design　a　trust-aware　node　clustering　(TNC)　strategy　to　guide　the　unlabeled　nodes　to　achieve　discriminative　clustering.　Extensive　experimental　results　show　that　our　HOGDA　outperforms　the　state-of-the-art　methods　on　various　transfer　tasks.　©　2024　ACM.