  Graph Neural Networks (GNNs) have become pivotal tools for a range of
graph-based learning tasks. Notably, most current GNN architectures operate
under the assumption of homophily, whether explicitly or implicitly. While this
underlying assumption is frequently adopted, it is not universally applicable,
which can result in potential shortcomings in learning effectiveness. In this
paper, \textbf{for the first time}, we transfer the prevailing concept of ``one
node one receptive field" to the heterophilic graph. By constructing a proxy
label predictor, we enable each node to possess a latent prediction
distribution, which assists connected nodes in determining whether they should
aggregate their associated neighbors. Ultimately, every node can have its own
unique aggregation hop and pattern, much like each snowflake is unique and
possesses its own characteristics. Based on observations, we innovatively
introduce the Heterophily Snowflake Hypothesis and provide an effective
solution to guide and facilitate research on heterophilic graphs and beyond. We
conduct comprehensive experiments including (1) main results on 10 graphs with
varying heterophily ratios across 10 backbones; (2) scalability on various deep
GNN backbones (SGC, JKNet, etc.) across various large number of layers
(2,4,6,8,16,32 layers); (3) comparison with conventional snowflake hypothesis;
(4) efficiency comparison with existing graph pruning algorithms. Our
observations show that our framework acts as a versatile operator for diverse
tasks. It can be integrated into various GNN frameworks, boosting performance
in-depth and offering an explainable approach to choosing the optimal network
depth. The source code is available at
\url{https://github.com/bingreeky/HeteroSnoH}.
