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As the Internet of Things system becomes more popular and ubiquitous, it has also gradually entered the consumer electronics field. For example, smart home systems have numerous sensors that monitor the environment and interact with the Internet to provide smart services. A large amount of multivariate time series data generated using sensors can provide services for consumers and identify faulty systems through multivariate time series anomaly detection (MTSAD), which is crucial for maintaining system stability. However, representing the complex relationships among multivariate time series is challenging. Recently, graph neural networks and graph structure learning, which can excellently learn complex time series relationships, have been applied to multivariate time series. However, existing research on graph structure learning only constructs k-Nearest Neighbor (kNN) graphs based on the pair-wise …