Simplified Graph Convolution with Heterophily

TL;DR

This paper introduces Adaptive Simple Graph Convolution (ASGC), a fast, scalable method that effectively handles both homophilous and heterophilous graphs, outperforming traditional SGC on diverse datasets.

Contribution

We propose ASGC, an extension of SGC, with the ability to adapt to different graph structures, supported by theoretical guarantees and empirical validation.

Findings

ASGC outperforms SGC on heterophilous graphs.

ASGC is competitive with deep models on real-world datasets.

Theoretical performance guarantees are established for synthetic models.

Abstract

Recent work has shown that a simple, fast method called Simple Graph Convolution (SGC) (Wu et al., 2019), which eschews deep learning, is competitive with deep methods like graph convolutional networks (GCNs) (Kipf & Welling, 2017) in common graph machine learning benchmarks. The use of graph data in SGC implicitly assumes the common but not universal graph characteristic of homophily, wherein nodes link to nodes which are similar. Here we confirm that SGC is indeed ineffective for heterophilous (i.e., non-homophilous) graphs via experiments on synthetic and real-world datasets. We propose Adaptive Simple Graph Convolution (ASGC), which we show can adapt to both homophilous and heterophilous graph structure. Like SGC, ASGC is not a deep model, and hence is fast, scalable, and interpretable; further, we can prove performance guarantees on natural synthetic data models. Empirically, ASGC is often competitive with recent deep models at node classification on a benchmark of real-world datasets. The SGC paper questioned whether the complexity of graph neural networks is warranted for common graph problems involving homophilous networks; our results similarly suggest that, while deep learning often achieves the highest performance, heterophilous structure alone does not necessitate these more involved methods.