  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.
