Simplified Graph Convolution with Heterophily

Graph convolutional networks (GCNs) (Kipf & Welling, 2017) attempt to extend the success of deep learning in modeling image and text data to graphs. However, like other deep models, GCNs comprise repeated nonlinear transformations of inputs and are therefore time and memory intensive to train. Recent work has shown that a much simpler and faster model, Simple Graph Convolution (SGC) (Wu et al., 2019), is competitive with GCNs 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 show 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. We find that our non-deep method often outperforms state-of-the-art 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 suggest that this question is still open even for more complicated problems involving heterophilous networks.