Disclosed is system and method of connection information regularization, graph feature extraction and graph classification based on adjacency matrix. By concentrating the connection information elements in the adjacency matrix into a specific diagonal region of the adjacency matrix in order to reduce the non-connection information elements in advance. The subgraph structure of the graph is further extracted along the diagonal direction using the filter matrix. Then a stacked convolutional neural network is used to extract a larger subgraph structure. On the one hand, it greatly reduces the amount of computation and complexity, solving the limitations of the computational complexity and the limitations of window size. And on the other hand, it can capture large subgraph structure through a small window, as well as deep features from the implicit correlation structures at both vertex and edge level, which improves the accuracy and speed of the graph classification.