Graph homophily refers to the phenomenon that connected nodes tend to share
similar characteristics. Understanding this concept and its related metrics is
crucial for designing effective Graph Neural Networks (GNNs). The most widely
used homophily metrics, such as edge or node homophily, quantify such
"similarity" as label consistency across the graph topology. These metrics are
believed to be able to reflect the performance of GNNs, especially on
node-level tasks. However, many recent studies have empirically demonstrated
that the performance of GNNs does not always align with homophily metrics, and
how homophily influences GNNs still remains unclear and controversial. Then, a
crucial question arises: What is missing in our current understanding of
homophily? To figure out the missing part, in this paper, we disentangle the
graph homophily into $3$ aspects: label, structural, and feature homophily,
providing a more comprehensive understanding of GNN performance. To investigate
their synergy, we propose a Contextual Stochastic Block Model with $3$ types of
Homophily (CSBM-3H), where the topology and feature generation are controlled
by the $3$ metrics. Based on the theoretical analysis of CSBM-3H, we derive a
new composite metric, named Tri-Hom, that considers all $3$ aspects and
overcomes the limitations of conventional homophily metrics. The theoretical
conclusions and the effectiveness of Tri-Hom have been verified through
synthetic experiments on CSBM-3H. In addition, we conduct experiments on $31$
real-world benchmark datasets and calculate the correlations between homophily
metrics and model performance. Tri-Hom has significantly higher correlation
values than $17$ existing metrics that only focus on a single homophily aspect,
demonstrating its superiority and the importance of homophily synergy. Our code
is available at https://github.com/zylMozart/Disentangle_GraphHom.

本文将图同质性分解为标签、结构和特征三个方面，提出了考虑三个方面的新组合指标 Tri-Hom，并通过理论分析和合成实验验证了 Tri-Hom 的有效性和同质性协同的重要性。

同质性中缺失了什么？拆解图同质性用于图神经网络

What Is Missing In Homophily? Disentangling Graph Homophily For Graph  Neural Networks

We initiate an empirical investigation into differentially private graph
neural networks on population graphs from the medical domain by examining
privacy-utility trade-offs at different privacy levels on both real-world and
synthetic datasets and performing auditing through membership inference
attacks. Our findings highlight the potential and the challenges of this
specific DP application area. Moreover, we find evidence that the underlying
graph structure constitutes a potential factor for larger performance gaps by
showing a correlation between the degree of graph homophily and the accuracy of
the trained model.

通过在真实和合成数据集上不同隐私水平下进行隐私 - 效用权衡和通过成员推断攻击进行审计，从医疗领域的人口图中启动对不同 ially 静态图神经网络的经验调查。我们的发现强调了此特定 DP 应用领域的潜力和挑战。此外，我们通过显示图同质度的程度与训练模型准确度之间的相关性，发现底层图结构构成更大性能差距的潜在因素。