Recently, many carefully crafted graph representation learning methods have
achieved impressive performance on either strong heterophilic or homophilic
graphs, but not both. Therefore, they are incapable of generalizing well across
real-world graphs with different levels of homophily. This is attributed to
their neglect of homophily in heterophilic graphs, and vice versa. In this
paper, we propose a two-fold filtering mechanism to extract homophily in
heterophilic graphs and vice versa. In particular, we extend the graph heat
equation to perform heterophilic aggregation of global information from a long
distance. The resultant filter can be exactly approximated by the
Possion-Charlier (PC) polynomials. To further exploit information at multiple
orders, we introduce a powerful graph convolution PC-Conv and its instantiation
PCNet for the node classification task. Compared with state-of-the-art GNNs,
PCNet shows competitive performance on well-known homophilic and heterophilic
graphs. Our implementation is available at this https URL

提出了一种两重过滤机制来提取异态图里的同质性和同态图里的不同质性，其中使用了扩展图热方程来进行异态聚合，并介绍了一个强大的 PCNet 图卷积方法，通过该方法在节点分类任务上展现出了有竞争力的性能。