Long-range dependencies are critical for effective graph representation learning, yet most existing datasets focus on small graphs tailored to inductive tasks, offering limited insight into long-range interactions. Current evaluations primarily compare models employing global attention (e.g., graph transformers) with those using local neighborhood aggregation (e.g., message-passing neural networks) without a direct measurement of long-range dependency. In this work, we introduce City-Networks, a novel large-scale transductive learning dataset derived from real-world city roads. This dataset features graphs with over $10^5$ nodes and significantly larger diameters than those in existing benchmarks, naturally embodying long-range information. We annotate the graphs using an eccentricity-based approach, ensuring that the classification task inherently requires information from distant nodes. Furthermore, we propose a model-agnostic measurement based on the Jacobians of neighbors from distant hops, offering a principled quantification of long-range dependencies. Finally, we provide theoretical justifications for both our dataset design and the proposed measurement - particularly by focusing on over-smoothing and influence score dilution - which establishes a robust foundation for further exploration of long-range interactions in graph neural networks.

本研究针对现有数据集中长程依赖不足的问题，提出了名为City-Networks的大规模数据集，该数据集源自真实城市道路，包含超过$10^5$个节点，且具备显著更大的直径。我们还提出了一种基于雅可比矩阵的模型无关的长程依赖度量方法，为图神经网络中的长程交互研究奠定了坚实基础。

定量化图机器学习中的长程交互：一个大型图数据集及其度量