Out-of-distribution (OOD) detection has garnered increasing concern for identifying test samples that exhibit a distributional shift from the training dataset in practical deep learning applications. With the significant advancements in graph deep learning for graph representation, graph OOD detection has emerged as a research problem. Graph contrastive learning (GCL) is applied to graph OOD detection due to its capacity for learning discriminative representations in a self-supervised manner, thereby eliminating the need for time-consuming and labor-intensive label information. However, existing methods often neglect the explicit consideration of underlying semantics behind graph data distribution for OOD detection. We argue that simple data augmentations for GCL may risk disrupting the intrinsic graph structure while retaining redundant structural information, which hinders semantic discrimination between graphs. Additionally, Euclidean space embedding struggles to maintain hierarchical structural consistency, making it challenging to meaningfully capture the hierarchical semantic distribution of graph data. In response to these issues, we propose a novel framework termed HGOOD-D, which aims to explore latent semantic hierarchies in hyperbolic space for graph OOD detection. Specifically, we design a bottleneck graph extractor grounded in the information bottleneck (IB) principle, which captures the minimal sufficient information to distinguish graph patterns. Based on this, we introduce hierarchical contrastive learning to capture the hierarchical semantics within graph data distribution. These methods are based on hyperbolic space embedding that can preserve complex inter-relationships in graph hierarchies, thereby mitigating data distortion. Comprehensive evaluations on ten widely used benchmark datasets show that HGOOD-D consistently surpasses current state-of-the-art approaches in graph OOD detection.

Deep graph clustering, which aims to uncover the underlying structure within graphs and partition nodes into distinct groups, is a challenging research spot. However, the formation of the cluster in real-world graphs typically governed by the highly complex interaction of many underlying latent factors. Existing methods typically rely on the features and structure associated with the graph, and neglect the entanglement of these factors, resulting in sub-optimal clustering performance. In this paper, we propose a novel deep graph clustering framework named DisenCluster, which learns disentangled representations to simultaneously consider node separation results from diverse perspectives. Specifically, we introduce a disentangled graph encoder that iteratively identifies the latent factors of the input graph by modeling the distribution over different factors for each edge. Subsequently, we utilize a factor-wise contrastive loss to encourage clustering-friendly disentangled representations, allowing us to derive different clustering results based on the corresponding factor. These results are then structured as anchor graphs and seamlessly integrated into a unified graph. Finally, we formulate the framework as a continuous relaxation of the high-order graph cut problem and optimize the objective to obtain effective cluster assignments. Results from experiments on a variety of publicly available datasets further reveal the effectiveness and superiority of our DisenCluster compared with baselines.