Graph foundation models (GFMs) have emerged as a promising paradigm for learning transferable knowledge across diverse graph-structured data. The inherent heterogeneity in features and graph structures poses significant challenges for building scalable and generalizable GFMs. Existing research has employed mixture-of-experts (MoE) models to handle the challenges, assigning the most suitable expert to each graph. Despite this, the underlying mechanisms of MoE within the context of GFMs remain insufficiently explored. In this work, we conduct an in-depth experimental study on an MoE-based GFM and uncover an intriguing finding: the experts ranked second and third assigned by the router perform better than the top-ranked expert.

The growing ubiquity of relational data structured as graphs has underscored the need for graph learning models with exceptional generalization capabilities. However, current approaches often struggle to effectively extract generalizable insights, frequently requiring extensive fine-tuning and limiting their versatility. Graph foundation models offer a transformative solution, with the potential to learn robust, generalizable representations from graph data. This enables more effective and adaptable applications across a wide spectrum of tasks and domains. In this work, we investigate a unified graph model, AnyGraph, designed to handle key challenges: i) Structure Heterogenity. Addressing distribution shift in graph structural information; ii) Feature Heterogenity. Handling diverse feature representation spaces across graph datasets; iii) Fast Adaptation. Efficiently adapting the model to new graph domains; iv) Scaling Law Emergence. Enabling the model to exhibit scaling law behavior, where its performance scales favorably with the amount of data and parameter sizes. To tackle these critical challenges, we build the AnyGraph upon a Graph Mixture-of-Experts (MoE) architecture. This approach empowers the model to effectively manage both the in-domain and cross-domain distribution shift concerning structure-level and feature-level heterogeneity. Furthermore, a lightweight graph expert routing mechanism is proposed to facilitate AnyGraph's fast adaptability to new data and domains. Our extensive experiments on diverse 38 graph datasets have demonstrated the strong zero-shot learning performance of AnyGraph across diverse graph domains with significant distribution shift. Furthermore, we have validated the model's fast adaptation ability and scaling law emergence, showcasing its versatility.