Revisiting Homophily Ratio: A Relation-Aware Graph Neural Network for Homophily and Heterophily

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The graph neural network (GNN) is a type of powerful deep learning model used to process graph data consisting of nodes and edges. Many studies of GNNs have modeled the relationships between the edges and labels of nodes only by homophily/heterophily, where most/few nodes with the same label tend to have an edge between each other. However, this modeling method cannot describe the multiconnection mode on graphs where homophily can coexist with heterophily. In this work, we propose a transition matrix to describe the relationships between edges and labels at the class level. Through this transition matrix, we constructed a more interpretable GNN in a neighbor-predicting manner, measured the information that the edges can provide for the node classification task, and proposed a method to test whether the labels match the edges. The results show the improvement of the proposed method against state-of-the-art (SOTA) GNNs. We also obtain the following two results: (1) the poor performance of GNNs is highly relevant to the information of edges instead of heterophily, which is always considered the main factor resulting in the decline in performance; and (2) most benchmark heterophilic datasets exhibit the label-edge mismatch problem, leading them to become intractable