Title: Towards graph-level anomaly detection via deep evolutionary mapping. Abstract: Graph-level anomaly detection aims at depicting anomalous individual graphs in a graph set. Due to its significance in various real-world application fields, such as identifying rare molecules in chemistry and detecting potential frauds in online social networks, graph-level anomaly detection has received great attention. In distinction from node- and edge-level anomaly detection that is devoted to identifying anomalies on a single graph, graph-level anomaly detection faces more significant challenges because both the intra- and inter-graph structural and attribute patterns need to be taken into account to distinguish anomalies that exhibit deviating structures, rare attributes or the both. Although deep graph representation learning shows effectiveness in fusing high-level representations and capturing characters of individual graphs, most of the existing works are defective in graph-level anomaly detection because of their limited capability in exploring information across graphs, the imbalanced data distribution of anomalies, and low interpretability of the black-box graph neural networks (GNNs). To bridge these gaps, we propose a novel deep evolutionary graph mapping framework named GmapAD, which can adaptively map each graph into a new feature space based on its similarity to a set of representative nodes chosen from the graph set. By automatically adjusting the candidate nodes using a specially designed evolutionary algorithm, anomalies and normal graphs are mapped to separate areas in the new feature space where a clear boundary between them can be learned. The selected candidate nodes can therefore be regarded as a benchmark for explaining anomalies because anomalies are more dissimilar/similar to the benchmark than normal graphs. Through our extensive experiments on nine real-world datasets, we demonstrate that exploring both intra- and inter-graph structural and attribute information are critical to spot anomalous graphs, and our framework outperforms the state of the art on all datasets used in the experiments.