Title: Deep Graph-Level Orthogonal Hypersphere Compression for Anomaly Detection. Abstract: Graph-level anomaly detection aims to identify abnormal samples of a set of graphs in an unsupervised manner. It is non-trivial to find a reasonable decision boundary between normal data and anomalous data without using any anomalous data in the training stage, especially for data in graphs. This paper first proposes a novel deep graph-level anomaly detection model, which learns the graph representation with maximum mutual information between substructure features and global structure features while exploring a hypersphere anomaly decision boundary. The deep orthogonal projection layer is adopted to keep the training data distribution consistent with the decision hypersphere thus avoiding erroneous evaluations. We further propose projecting the normal data into the interval region between two co-centered hyperspheres, which makes the normal data distribution more compact and effectively overcomes the issue of outliers falling close to the center of the hypersphere. The numerical and visualization results on a few graph datasets demonstrate the effectiveness and superiority of our methods in comparison to many baselines and state-of-the-art.