Graph anomaly detection is a challenging task in graph data mining, aiming to recognize unconventional patterns within a network. Recently, there has been increasing attention on graph anomaly detection based on contrastive learning due to its high adaptability to the sample imbalance problem. However, most existing work typically focuses on the contrast of local views while neglecting global comparison information, leading to suboptimal performance. To address this issue, we introduce a new multiscale contrastive self-supervised learning framework for graph anomaly detection (GADMCLG). Our approach incorporates local-level contrasts involving node–node and node–subgraph contrast, and global-level subgraph–subgraph contrast. The former mines localized abnormal information, while the latter is intended to capture global anomalous patterns. Specifically, our proposed subgraph–subgraph contrast adopts theh-order neighbor subgraph sampling instead of augmented subgraphs through edge perturbation. This sampling strategy ensures a comprehensive observation of the neighborhood surrounding the target node, thereby mitigating the introduction of extraneous noise and providing interpretability for the detected results. Furthermore, we incorporate a subgraph centralization technique to reduce the bias caused by the absolute position of subgraphs in the attribute space, which enhances the model's ability to identify anomalies at different scales. Extensive experimental results on six real-world datasets demonstrate the effectiveness of our method and its superiority compared with state-of-the-art approaches.

The identification of important nodes (vertexes) in multilayer networks has aroused many scholars’ attention and various centrality methods have deen developed. However, the current centralities ignore the impact of community structure on node importance. In this article, we define a community-based centrality for finding key vertexes in multilayer networks, referred to as the CBCM. We first construct a multilayer network model with interlayer edges, which is represented by a fourth-order tensor. Based on the fourth-order tensor, we develop a centrality, called PR_BIS, to measure the importance of vertexes and network layers in multilayer networks, simultaneously. CBCM determines the importance of a vertex in each network layer by combining the following three factors: the PageRank centrality score of the vertex, the importance of the community where the vertex is located, and the ability of the vertex within a community to affect vertexes in other communities within two steps. Based on the importance of all the network layers measured by PR_BIS centrality, we perform weighted fusion for the importance of a vertex in all network layers to obtain the importance of the vertex in multilayer networks. Finally, numerical experiments are performed on several multilayer networks to verify the effectiveness and superiority of CBCM and PR_BIS.