Transferable Structural Concordance for Graph Foundation Models

*Graph foundation models* (*GFMs*) aim to transfer knowledge across heterogeneous graph domains. Existing approaches largely organize cross-domain transfer at the graph level, treating each graph as a domain-specific structural unit and thereby overlooking substantial node-level structural heterogeneity. We characterize this heterogeneity through *structural concordance*, which measures the local agreement between a node's topological and feature-induced neighborhoods and reveals complementary high- and low-concordance regimes across graph domains. Building on this observation, we propose a *concordance-aware hierarchical coordination* framework for multi-domain GFM pre-training. Within each graph, two complementary coordinators specialize in high- and low-concordance regimes, while node-wise soft routing adapts their influence to each node's concordance level. Graph-specific meta coordinators further integrate concordance-conditioned information and mediate communication across source domains. This hierarchy enables node-adaptive cross-domain coordination while preserving the original graph topologies, following the principle of *coordinate without homogenizing*. We theoretically establish the informativeness, estimability, and representation stability of concordance-aware coordination. Experiments across diverse graph benchmarks consistently demonstrate improved unseen-domain transfer over existing GFMs.