Graph Neural Networks (GNNs) achieve state-of-the-art performance on graph-structured data across numerous domains. Their underlying ability to represent nodes as summaries of their vicinities has proven effective for homophilous graphs in particular, in which same-type nodes tend to connect. On heterophilous graphs, in which different-type nodes are likely connected, GNNs perform less consistently, as neighborhood information might be less representative or even misleading. On the other hand, GNN performance is not inferior on all heterophilous graphs, and there is a lack of understanding of what other graph properties affect GNN performance. In this work, we highlight the limitations of the widely used homophily ratio and the recent Cross-Class Neighborhood Similarity (CCNS) metric in estimating GNN performance. To overcome these limitations, we introduce 2-hop Neighbor Class Similarity (2NCS), a new quantitative graph structural property that correlates with GNN performance more strongly and consistently than alternative metrics. 2NCS considers two-hop neighborhoods as a theoretically derived consequence of the two-step label propagation process governing GCN's training-inference process. Experiments on one synthetic and eight real-world graph datasets confirm consistent improvements over existing metrics in estimating the accuracy of GCN- and GAT-based architectures on the node classification task.

通过介绍2NCS方法，本文挖掘了同质网络比率和Cross-Class邻域相似性(CCNS)等指标的局限性，并在一个合成和8个真实图数据集上进行实验，结果表明2NCS可以更准确和一致地评估基于GCN和GAT的体系结构在节点分类任务上的准确性。

2-hop邻居类相似度（2NCS）：预示图神经网络性能的图结构度量