Eigen-GNN: A Graph Structure Preserving Plug-in for GNNs

TL;DR

Eigen-GNN is a plug-in module that enhances GNNs' ability to preserve graph structures by integrating eigenspaces, improving performance on various graph tasks without increasing network depth.

Contribution

The paper introduces Eigen-GNN, a novel plug-in that incorporates graph eigenspaces into GNNs, enabling better structure preservation without deeper networks.

Findings

Eigen-GNN improves structure preservation in GNNs.

Enhanced performance on node classification and link prediction.

Effective for graph isomorphism tests.

Abstract

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.