In this work we propose a random graph model that can produce graphs at different levels of sparsity. We analyze how sparsity affects the graph spectra, and thus the performance of graph neural networks (GNNs) in node classification on dense and sparse graphs. We compare GNNs with spectral methods known to provide consistent estimators for community detection on dense graphs, a closely related task. We show that GNNs can outperform spectral methods on sparse graphs, and illustrate these results with numerical examples on both synthetic and real graphs.

翻译：本文提出了一种随机图模型，可生成不同稀疏程度的图。我们分析了稀疏性如何影响图谱特征，进而分析在图神经网络（GNN）对稠密图与稀疏图的节点分类任务上的性能表现。我们将GNN与已知在稠密图上能为社区检测（一项紧密相关的任务）提供一致估计量的谱方法进行比较。研究表明，GNN在稀疏图上的表现可优于谱方法，并通过在合成图与真实图上的数值实例验证了这些结果。