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Graph Convolutional Networks (GCNs) have been widely applied in variousfields due to their significant power on processing graph-structured data.Typical GCN and its variants work under a homophily assumption (i.e., nodeswith same class are prone to connect to each other), while ignoring theheterophily which exists in many real-world networks (i.e., nodes withdifferent classes tend to form edges). Existing methods deal with heterophilyby mainly aggregating higher-order neighborhoods or combing the immediaterepresentations, which leads to noise and irrelevant information in the result.But these methods did not change the propagation mechanism which works underhomophily assumption (that is a fundamental part of GCNs). This makes itdifficult to distinguish the representation of nodes from different classes. Toaddress this problem, in this paper we design a novel propagation mechanism,which can automatically change the propagation and aggregation processaccording to homophily or heterophily between node pairs. To adaptively learnthe propagation process, we introduce two measurements of homophily degreebetween node pairs, which is learned based on topological and attributeinformation, respectively. Then we incorporate the learnable homophily degreeinto the graph convolution framework, which is trained in an end-to-end schema,enabling it to go beyond the assumption of homophily. More importantly, wetheoretically prove that our model can constrain the similarity ofrepresentations between nodes according to their homophily degree. Experimentson seven real-world datasets demonstrate that this new approach outperforms thestate-of-the-art methods under heterophily or low homophily, and gainscompetitive performance under homophily.

Powerful Graph Convolutioal Networks with Adaptive Propagation Mechanism for Homophily and Heterophily