Distribution　shift　widely　exists　in　graph　representation　learning　and　often　reduces　model　performance.　This　work　investigates　how　to　improve　the　performance　of　a　graph　neural　network　(GNN)　in　a　single　graph　by　controlling　distribution　shift　between　embedding　spaces.　Specifically,　we　provide　an　upper　error　-bound　estimation,　which　quantitatively　analyzes　how　distribution　shift　affects　GNNs＇　performance　in　a　single　graph.　Considering　that　there　is　no　natural　domain　division　in　a　single　graph,　we　propose　PW-GNN　to　simultaneously　learn　discriminative　embedding　and　reduce　distribution　shift.　PW-GNN　measures　distribution　discrepancy　using　the　distance　between　test　embeddings　and　prototypes,　and　transfers　minimizing　distribution　shift　to　minimizing　the　power　of　Wasserstein　distance,　which　is　introduced　into　GNNs　as　a　regularizer.　A　series　of　theoretical　analyses　are　carried　out　to　demonstrate　the　effectiveness　of　PW-GNN.　Besides,　a　lowcomplexity　training　algorithm　is　designed　by　exploring　entropy　-regularized　strategy　and　block　coordinate　descent　method.　Extensive　numerical　experiments　are　conducted　on　different　datasets　with　both　biased　and　unbiased　splits.　We　empirically　test　our　model　equipped　with　four　backbone　models.　Results　show　that　PW-GNN　outperforms　state-of-the-art　baselines　and　mitigates　up　to　8%　of　negative　effects　off　distribution　shift　on　backbones.