Visual information accounts for approximately 80 to 85 percent of the information available daily in modern cities. As such, person re-identification, an instance-level image retrieval task, has become an important research topic in computer vision, machine learning, and other fields in recent years. Traditional person re-identification methods based on convolutional neural networks only extract the global feature information of people. Thus, when external factors such as changes in occlusion and illumination disturb people, the recognition performance of these methods substantially decreases. We therefore develop body correlation network (BC-Net), which takes full advantage of images of body parts and the correlations between them. Specifically, BC-Net uses body part feature information and correlation feature information as nodes and edges, respectively, and then uses graph convolutions to learn the overall topology of people. To improve use of crucial feature information, we also design a unique method of propagation between nodes and edges. We conduct extensive comparative experiments on the Market-1501 and DukeMTMC-reID datasets, and the results demonstrate that BC-Net outperforms other state-of-the-art techniques.