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Anomalous subgraph detection within networks is an important issue in many emerging applications. Existing algorithms, such as graph structure methods and spectral feature methods, usually focus on the special stochastic model (such as the Erdős-Rényi random graph) or may not efficiently extract the anomalous behaviors of the networks, which result in detection performance degradation. To mitigate the limitations, in this paper, we first present an anomalous subgraph detection framework associated with deep neural networks (DNN) for detecting anomalous behaviors within the networks. Furthermore, based on the developed framework, we propose a residual matrix-based convolutional neural network (RM-CNN) algorithm with respect to the given expected degree models, which are more general networks than the Erdős-Rényi random graphs. In particular, the trained RM-CNN can efficiently capture the anomalous changes of the network and then achieve the detection performance improvement. Simulation experiments display that the proposed RM-CNN algorithm is superior to the compared algorithms in both detection performance and detection speed.INDEX TERMS Anomalous subgraph detection, given expected degree models, deep learning, convolutional neural network.