Graph Neural Networks (GNNs) have achieved remarkable success in various
applications, but their performance can be sensitive to specific data
properties of the graph datasets they operate on. Current literature on
understanding the limitations of GNNs has primarily employed a
$\textit{model-driven}$ approach that leverage heuristics and domain knowledge
from network science or graph theory to model the GNN behaviors, which is
time-consuming and highly subjective. In this work, we propose a
$\textit{metadata-driven}$ approach to analyze the sensitivity of GNNs to graph
data properties, motivated by the increasing availability of graph learning
benchmarks. We perform a multivariate sparse regression analysis on the
metadata derived from benchmarking GNN performance across diverse datasets,
yielding a set of salient data properties. To validate the effectiveness of our
data-driven approach, we focus on one identified data property, the degree
distribution, and investigate how this property influences GNN performance
through theoretical analysis and controlled experiments. Our theoretical
findings reveal that datasets with more balanced degree distribution exhibit
better linear separability of node representations, thus leading to better GNN
performance. We also conduct controlled experiments using synthetic datasets
with varying degree distributions, and the results align well with our
theoretical findings. Collectively, both the theoretical analysis and
controlled experiments verify that the proposed metadata-driven approach is
effective in identifying critical data properties for GNNs.

通过对多元稀疏回归分析来从元数据中派生得到一系列显著的数据属性，本文提出了一种基于元数据的方法，分析了图神经网络对图数据属性的敏感性，并通过理论分析和控制实验验证了平衡度分布与 GNN 性能之间的关系，从而验证了该基于元数据的方法在识别 GNN 关键数据属性方面的有效性。