  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 \url{https://github.com/zylMozart/Disentangle_GraphHom}.
