Higher-order graph neural networks (HOGNNs) are an important class of GNN models that harness polyadic relations between vertices beyond plain edges. They have been used to eliminate issues such as over-smoothing or over-squashing, to significantly enhance the accuracy of GNN predictions, to improve the expressiveness of GNN architectures, and for numerous other goals. A plethora of HOGNN models have been introduced, and they come with diverse neural architectures, and even with different notions of what the "higher-order" means. This richness makes it very challenging to appropriately analyze and compare HOGNN models, and to decide in what scenario to use specific ones. To alleviate this, we first design an in-depth taxonomy and a blueprint for HOGNNs. This facilitates designing models that maximize performance. Then, we use our taxonomy to analyze and compare the available HOGNN models. The outcomes of our analysis are synthesized in a set of insights that help to select the most beneficial GNN model in a given scenario, and a comprehensive list of challenges and opportunities for further research into more powerful HOGNNs.

高阶图神经网络（HOGNNs）是一类重要的GNN模型，能够利用顶点之间的多系关系来解决过度平滑或过度压缩等问题，显著提高GNN预测准确性，改进GNN架构，并能帮助选择最适合特定场景的GNN模型，提出了具有挑战与机遇的HOGNN进一步研究的全面列表。

高阶图神经网络揭秘