Demystifying Graph Convolution with a Simple Concatenation

TL;DR

This paper analyzes the representation power of graph convolution and introduces a simple concatenation method that outperforms traditional GConv, especially in heterophily cases, by better leveraging graph topology and node features.

Contribution

It provides a theoretical and empirical analysis showing that concatenating graph topology and node features is a more effective alternative to traditional graph convolution.

Findings

Concatenation outperforms traditional GConv in heterophily cases.

Graph concatenation is a flexible and simple alternative to GConv.

Theoretical analysis confirms the effectiveness of concatenation in node classification.

Abstract

Graph convolution (GConv) is a widely used technique that has been demonstrated to be extremely effective for graph learning applications, most notably node categorization. On the other hand, many GConv-based models do not quantify the effect of graph topology and node features on performance, and are even surpassed by some models that do not consider graph structure or node properties. We quantify the information overlap between graph topology, node features, and labels in order to determine graph convolution's representation power in the node classification task. In this work, we first determine the linear separability of graph convoluted features using analysis of variance. Mutual information is used to acquire a better understanding of the possible non-linear relationship between graph topology, node features, and labels. Our theoretical analysis demonstrates that a simple and efficient graph operation that concatenates only graph topology and node properties consistently outperforms conventional graph convolution, especially in the heterophily case. Extensive empirical research utilizing a synthetic dataset and real-world benchmarks demonstrates that graph concatenation is a simple but more flexible alternative to graph convolution.