Graph neural networks (GNNs) have demonstrated significant efficacy in addressing graph learning tasks by leveraging both node features and graph topology. Prevalent GNN architectures often implicitly or explicitly rely on the homophily assumption, which presupposes that neighboring nodes tend to share similar features. Despite their efficacy, GNNs may prove inadequate in modeling graphs characterized by heterophily, wherein nodes with disparate labels frequently interconnect. To mitigate this limitation, we propose DCGNN, a novel GNN framework capable of accommodating heterophily while retaining effectiveness in homophily scenarios. Initially, we elucidate that prevailing message-passing neural networks (MPNNs) struggle to discern circular substructures, prevalent in graphs demonstrating heterophily. Consequently, we propose an adaptive deep graph convolution technique, which integrates adaptive aggregation of local high-order neighborhoods, replacing the conventional stacking of single-order convolutional layers in the message-passing paradigm. Theoretical analysis confirms that DCGNN demonstrates significantly enhanced expressive capacity compared to existing MPNNs. Empirical evaluations conducted on real-world datasets validate that DCGNN outperforms several state-of-the-art GNNs tailored for graphs exhibiting heterophily.

中文翻译：

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DCGNN：异质图的自适应深度图卷积

图神经网络（GNN）通过利用节点特征和图拓扑，在解决图学习任务方面表现出了显着的功效。流行的 GNN 架构通常隐式或显式依赖于同质性假设，该假设假设相邻节点倾向于共享相似的特征。尽管 GNN 很有效，但它可能不足以对具有异质特征的图进行建模，其中具有不同标签的节点经常互连。为了缓解这一限制，我们提出了 DCGNN，这是一种新颖的 GNN 框架，能够适应异质性，同时保留同质场景中的有效性。首先，我们阐明了流行的消息传递神经网络（MPNN）难以识别圆形子结构，这在展示异质性的图中普遍存在。因此，我们提出了一种自适应深度图卷积技术，该技术集成了局部高阶邻域的自适应聚合，取代了消息传递范式中单阶卷积层的传统堆叠。理论分析证实，与现有 MPNN 相比，DCGNN 表现出显着增强的表达能力。对现实世界数据集进行的实证评估证实，DCGNN 的性能优于几种针对表现出异质性的图量身定制的最先进的 GNN。