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

Graph Neural Networks (GNNs) extend basic Neural Networks (NNs) by using
graph structures based on the relational inductive bias (homophily assumption).
While GNNs have been commonly believed to outperform NNs in real-world tasks,
recent work has identified a non-trivial set of datasets where their
performance compared to NNs is not satisfactory. Heterophily has been
considered the main cause of this empirical observation and numerous works have
been put forward to address it. In this paper, we first revisit the widely used
homophily metrics and point out that their consideration of only graph-label
consistency is a shortcoming. Then, we study heterophily from the perspective
of post-aggregation node similarity and define new homophily metrics, which are
potentially advantageous compared to existing ones. Based on this
investigation, we prove that some harmful cases of heterophily can be
effectively addressed by local diversification operation. Then, we propose the
Adaptive Channel Mixing (ACM), a framework to adaptively exploit aggregation,
diversification and identity channels node-wisely to extract richer localized
information for diverse node heterophily situations. ACM is more powerful than
the commonly used uni-channel framework for node classification tasks on
heterophilic graphs and is easy to be implemented in baseline GNN layers. When
evaluated on 10 benchmark node classification tasks, ACM-augmented baselines
consistently achieve significant performance gain, exceeding state-of-the-art
GNNs on most tasks without incurring significant computational burden.

本文通过重新评估广泛使用的同质性度量，并从后集成节点相似性的角度研究了异质性。提出了一种新的度量方法，并证明了 local diversification operation 可以有效解决一些有害的异质性情况，然后提出了 Adaptive Channel Mixing（ACM）框架来自适应地利用聚合，多样性和标识通道，从而从多样化的节点异质性情况中提取更丰富的局部信息。经过 10 项基准节点分类任务的评估，ACM-augmented 基线始终实现了显着的性能提升，超过大多数任务上的最新 GNN，而不会带来显着的计算负担。