针对图数据规模差异导致的深度敏感问题，提出自适应专家混合模型。

Graph neural networks (GNNs) are gaining popularity for processing graph-structured data. In real-world scenarios, graph data within the same dataset can vary significantly in scale. This variability leads to depth-sensitivity, where the optimal depth of GNN layers depends on the scale of the graph data. Empirically, fewer layers are sufficient for message passing in smaller graphs, while larger graphs typically require deeper networks to capture long-range dependencies and global features. However, existing methods generally use a fixed number of GNN layers to generate representations for all graphs, overlooking the depth-sensitivity issue in graph structure data. To address this challenge, we propose the depth adaptive mixture of expert (DA-MoE) method, which incorporates two main improvements to GNN backbone: \textbf{1)} DA-MoE employs different GNN layers, each considered an expert with its own parameters. Such a design allows the model to flexibly aggregate information at different scales, effectively addressing the depth-sensitivity issue in graph data. \textbf{2)} DA-MoE utilizes GNN to capture the structural information instead of the linear projections in the gating network. Thus, the gating network enables the model to capture complex patterns and dependencies within the data. By leveraging these improvements, each expert in DA-MoE specifically learns distinct graph patterns at different scales. Furthermore, comprehensive experiments on the TU dataset and open graph benchmark (OGB) have shown that DA-MoE consistently surpasses existing baselines on various tasks, including graph, node, and link-level analyses. The code are available at \url{https://github.com/Celin-Yao/DA-MoE}.