Over the past few years, there has been a surge in research attention towards tasks involving graph data, largely due to the impressive performance demonstrated by graph neural networks (GNNs) in handling such information. Currently, out-of-distribution (OOD) detection in graphs is a hot research topic. The goal of graph OOD detection is to identify nodes or new graphs that differ from the training data distribution, primarily in terms of attributes and structures. OOD detection is crucial for enhancing the stability, security, and robustness of models. In various applications, such as biological networks and financial fraud, graph OOD detection can help models identify anomalies or unforeseen situations, thereby enabling appropriate responses. In node-level OOD detection, existing models typically only consider first-order neighbors. This paper introduces graph diffusion to the OOD detection task for the first time, proposing the HOOD model, a graph diffusion-based OOD node detection algorithm. Specifically, the original graph is processed through graph diffusion to obtain a new graph that can directly capture high-order neighbor information, overcoming the limitation that message passing must go through first-order neighbors. The new graph is then sparsified using a top-k approach. Based on entropy information, regularization is employed to ensure the uncertainty of OOD nodes, thereby giving these nodes higher scores and enabling the model to effectively detect OOD nodes while ensuring the accuracy of in-distribution node classification. Experimental results demonstrate that the HOOD model outperforms existing methods in both node classification and OOD detection tasks on multiple benchmarks, highlighting its robustness and effectiveness.

Structural graph clustering is a data analysis technique that groups nodes within a graph based on their connectivity and structural similarity. The Structural graph clustering SCAN algorithm, a density-based clustering method, effectively identifies core points and their neighbors within areas of high density to form well-defined clusters. However, the clustering quality of SCAN heavily depends on the input parameters, $ϵ$ and $\mu$, making the clustering results highly sensitive to parameter selection. Different parameter settings can lead to significant differences in clustering results, potentially compromising the accuracy of the clusters. To address this issue, a novel structural graph clustering algorithm based on the adaptive selection of density peaks is proposed in this paper. Unlike traditional methods, our algorithm does not rely on external parameters and eliminates the need for manual selection of density peaks or cluster centers by users. Density peaks are adaptively identified using the generalized extreme value distribution, with consideration of the structural similarities and interdependencies among nodes, and clusters are expanded by incorporating neighboring nodes, enhancing the robustness of the clustering process. Additionally, a distance-based structural similarity method is proposed to re-cluster noise nodes to the correct clusters. Extensive experiments on real and synthetic graph datasets validate the effectiveness of our algorithm. The experiment results show that the ADPSCAN has a superior performance compared with several state-of-the-art (SOTA) graph clustering methods.