Graph neural networks (GNN) have achieved remarkable success in a wide range of tasks by encoding features combined with topology to create effective representations. However, the fundamental problem of understanding and analyzing how graph topology influences the performance of learning models on downstream tasks has not yet been well understood. In this paper, we propose a metric, TopoInf, which characterizes the influence of graph topology by measuring the level of compatibility between the topological information of graph data and downstream task objectives. We provide analysis based on the decoupled GNNs on the contextual stochastic block model to demonstrate the effectiveness of the metric. Through extensive experiments, we demonstrate that TopoInf is an effective metric for measuring topological influence on corresponding tasks and can be further leveraged to enhance graph learning.

翻译：图神经网络（GNN）通过将特征与拓扑结构编码以生成有效表征，已在广泛任务中取得显著成功。然而，理解并分析图拓扑如何影响下游任务中学习模型性能这一基础性问题仍未得到充分研究。本文提出一种名为TopoInf的度量指标，通过测量图数据的拓扑信息与下游任务目标之间的兼容性水平，来刻画图拓扑的影响。我们基于解耦GNN在情境随机块模型上的分析，论证了该指标的有效性。通过大量实验表明，TopoInf是衡量相应任务中拓扑影响的有效指标，并可进一步用于增强图学习。