2-hop Neighbor Class Similarity (2NCS): A graph structural metric indicative of graph neural network performance

TL;DR

This paper introduces 2-hop Neighbor Class Similarity (2NCS), a new graph structural metric that better predicts GNN performance across various datasets, especially on heterophilous graphs, outperforming existing metrics.

Contribution

The paper proposes 2NCS, a novel structural property based on two-hop neighborhoods, which more accurately correlates with GNN performance than previous metrics like homophily ratio and CCNS.

Findings

2NCS correlates more strongly with GNN accuracy.

Experiments on synthetic and real datasets show improved estimation.

2NCS outperforms existing metrics in predicting GNN performance.

Abstract

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.