Graph Neural Networks (GNNs) are emerging machine learning models on graphs. Although sufficiently deep GNNs are shown theoretically capable of fully preserving graph structures, most existing GNN models in practice are shallow and essentially feature-centric. We show empirically and analytically that the existing shallow GNNs cannot preserve graph structures well. To overcome this fundamental challenge, we propose Eigen-GNN, a simple yet effective and general plug-in module to boost GNNs ability in preserving graph structures. Specifically, we integrate the eigenspace of graph structures with GNNs by treating GNNs as a type of dimensionality reduction and expanding the initial dimensionality reduction bases. Without needing to increase depths, Eigen-GNN possesses more flexibilities in handling both feature-driven and structure-driven tasks since the initial bases contain both node features and graph structures. We present extensive experimental results to demonstrate the effectiveness of Eigen-GNN for tasks including node classification, link prediction, and graph isomorphism tests.

Eigen-GNN是一种简单而有效的插件模块，通过将GNN视为一种降维类型并扩展初始降维基础，将图结构的特征空间与GNN相集成，从而提高了GNN在保留图结构方面的能力，并在节点分类、链接预测和图同构测试等任务中表现出良好的灵活性和有效性。

Eigen-GNN: 一种用于保留图结构的插件的GNN插件