Steganographer detection aims to find guilty users who hide secret information in images or other multimedia data in the social network. In existing work, the distances between users are calculated based on the distributions of all images shared by the corresponding users, then users lying an abnormal distance from others are detected as guilty users. This flattened method is difficult to grasp the nuances of the guilty and innocent users. In this paper, we are the first to propose a graph-based deep learning framework for steganographer detection. The proposed Enhancement-aware Graph Convolutional Network (EGCN) represents each user as a weighted complete graph and learns to highlight the differences between guilty users and innocent users based on the structured graph. Compared with the state-of-the-art method and other representative graph-based models, the proposed framework demonstrates its effectiveness across image domains, and even under the context of large-scale social media scenario.