  Graph self-training (GST), which selects and assigns pseudo-labels to
unlabeled nodes, is popular for tackling label sparsity in graphs. However,
recent study on homophily graphs show that GST methods could introduce and
amplify distribution shift between training and test nodes as they tend to
assign pseudo-labels to nodes they are good at. As GNNs typically perform
better on homophilic nodes, there could be potential shifts towards homophilic
pseudo-nodes, which is underexplored. Our preliminary experiments on
heterophilic graphs verify that these methods can cause shifts in homophily
ratio distributions, leading to \textit{training bias} that improves
performance on homophilic nodes while degrading it on heterophilic ones.
Therefore, we study a novel problem of reducing homophily ratio distribution
shifts during self-training on heterophilic graphs. A key challenge is the
accurate calculation of homophily ratios and their distributions without
extensive labeled data. To tackle them, we propose a novel Heterophily-aware
Distribution Consistency-based Graph Self-Training (HC-GST) framework, which
estimates homophily ratios using soft labels and optimizes a selection vector
to align pseudo-nodes with the global homophily ratio distribution. Extensive
experiments on both homophilic and heterophilic graphs show that HC-GST
effectively reduces training bias and enhances self-training performance.
