RouterGFM: Inductive Routing and Local Expertise Transfer for Graph Learning

Reusing pretrained *graph neural networks* (GNNs) requires deciding which experts suit a new application and how to combine their predictions across graph contexts. Application-level selection does not resolve instance-specific contributions, while learning a new local router can require more target supervision than is available. We propose GraphRouter, a graph mixture-of-experts framework that combines inductive expert selection with context-guided local integration. A shared application–expert scorer over a heterogeneous context graph selects experts from metadata and historical evaluations before executing candidate GNNs on target data. After fitting the selected task heads, expert-conditioned retrieval transfers historical local performance differences into instance-dependent prediction weights, while the pretrained GNNs and router parameters remain fixed. Our conditional analysis separates omitted local expertise, performance-estimation error, and mixture temperature, and characterizes the limits of metadata-only expert insertion. Experiments on nine datasets cover node classification, link prediction, graph classification, and graph regression. In the five-shot classification diagnosis with expert predictions fixed, local integration reduces average and worst-cell Brier loss by 11.7% and 17.3% relative to application-level weighting. Further analyses distinguish useful expert coverage from accurate integration and identify when unreliable historical evidence limits transfer.