The success of foundation models in language and vision has motivated Graph Foundation Models (GFMs), which learn transferable knowledge through multi-domain graph pre-training. Existing methods advance GFMs through feature unification and structural learning, and in doing so they rely on the raw graph structure to organize node contexts. However, we observe that removing a large proportion of edges from source graphs during pre-training improves cross-domain transfer accuracy across four representative methods. Our theoretical analysis identifies the raw graph structure as a source of conflict in cross-graph model sharing. We therefore advocate defining node contexts using criteria consistent across graphs. Achieving this requires (1) constructing node contexts consistently across graphs without a shared positional structure, such as the token order of text or the pixel grid of images, and (2) retaining the structural and neighborhood information of the original graphs. To this end, we introduce Relative Contexts for Graphs (ReCoG) for multi-domain graph pre-training. Specifically, we first construct attribute contexts to provide a comparison rule independent of the raw graph structure. Furthermore, we construct structural contexts based on common neighbors and semantic contexts based on neighborhood attribute summaries to retain the topological and neighborhood information of the original graphs. Since all graphs share these construction rules, we pre-train a single graph encoder by reconstructing node attributes over these contexts, without domain-specific modules. We conduct extensive experiments on 18 target datasets, which demonstrate the effectiveness of ReCoG. In particular, ReCoG exceeds the strongest baseline by 7.61 percentage points in mean 1-shot cross-domain node classification accuracy and by 4.47 points in cross-type transfer to heterophilous graphs.

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