Homophily principle, \ie{} nodes with the same labels or similar attributes are more likely to be connected, has been commonly believed to be the main reason for the superiority of Graph Neural Networks (GNNs) over traditional Neural Networks (NNs) on graph-structured data, especially on node-level tasks. However, recent work has identified a non-trivial set of datasets where GNN's performance compared to the NN's is not satisfactory. Heterophily, i.e. low homophily, has been considered the main cause of this empirical observation. People have begun to revisit and re-evaluate most existing graph models, including graph transformer and its variants, in the heterophily scenario across various kinds of graphs, e.g. heterogeneous graphs, temporal graphs and hypergraphs. Moreover, numerous graph-related applications are found to be closely related to the heterophily problem. In the past few years, considerable effort has been devoted to studying and addressing the heterophily issue. In this survey, we provide a comprehensive review of the latest progress on heterophilic graph learning, including an extensive summary of benchmark datasets and evaluation of homophily metrics on synthetic graphs, meticulous classification of the most updated supervised and unsupervised learning methods, thorough digestion of the theoretical analysis on homophily/heterophily, and broad exploration of the heterophily-related applications. Notably, through detailed experiments, we are the first to categorize benchmark heterophilic datasets into three sub-categories: malignant, benign and ambiguous heterophily. Malignant and ambiguous datasets are identified as the real challenging datasets to test the effectiveness of new models on the heterophily challenge. Finally, we propose several challenges and future directions for heterophilic graph representation learning.

同质性原则（Homophily principle）是图神经网络（Graph Neural Networks）在图结构数据中表现优越的主要原因，但低同质性（heterophily）却是导致某些情况下图神经网络表现不理想的主要原因。本综述调查了异质图学习的最新进展，包括标杆数据集的详细概述、合成图上同质性度量的评估、最新监督和非监督学习方法的分类、同质性/异质性的理论分析以及与异质性相关的广泛应用。同时，我们首次将标杆的异质性数据集分为恶性、良性和模糊三个子类，其中恶性和模糊数据集是用于测试新模型在异质性挑战上有效性的真正具有挑战性的数据集。最后，我们提出了几个关于异质图表示学习的挑战和未来方向。

异质图学习手册：基准、模型、理论分析、应用和挑战