  Much data with graph structures satisfy the principle of homophily, meaning
that connected nodes tend to be similar with respect to a specific attribute.
As such, ubiquitous datasets for graph machine learning tasks have generally
been highly homophilous, rewarding methods that leverage homophily as an
inductive bias. Recent work has pointed out this particular focus, as new
non-homophilous datasets have been introduced and graph representation learning
models better suited for low-homophily settings have been developed. However,
these datasets are small and poorly suited to truly testing the effectiveness
of new methods in non-homophilous settings. We present a series of improved
graph datasets with node label relationships that do not satisfy the homophily
principle. Along with this, we introduce a new measure of the presence or
absence of homophily that is better suited than existing measures in different
regimes. We benchmark a range of simple methods and graph neural networks
across our proposed datasets, drawing new insights for further research. Data
and codes can be found at https://github.com/CUAI/Non-Homophily-Benchmarks.
