  Graph neural networks (GNNs) hold the promise of learning efficient
representations of graph-structured data, and one of its most important
applications is semi-supervised node classification. However, in this
application, GNN frameworks tend to fail due to the following issues:
over-smoothing and heterophily. The most popular GNNs are known to be focused
on the message-passing framework, and recent research shows that these GNNs are
often bounded by low-pass filters from a signal processing perspective. We thus
incorporate high-frequency information into GNNs to alleviate this genetic
problem. In this paper, we argue that the complement of the original graph
incorporates a high-pass filter and propose Complement Laplacian Regularization
(CLAR) for an efficient enhancement of high-frequency components. The
experimental results demonstrate that CLAR helps GNNs tackle over-smoothing,
improving the expressiveness of heterophilic graphs, which adds up to 3.6%
improvement over popular baselines and ensures topological robustness.
