The increasing integration of Inverter Interfaced Distributed Generators (IIDGs) into distribution networks has led to a more active nature of the grid. However, the accuracy-speed trade-off caused by iterative algorithms and simplified models in the short-circuit current calculation method for active distribution networks (ADNs) is becoming more prominent. To address this issue, we propose a novel approach that utilizes Graph Convolutional Neural Networks (GCNs) for short-circuit current calculation in ADNs. Our study explores the characteristics of short-circuit current in different network structures and evaluates the feasibility of representing electrical quantities using a graph data format. The proposed method employs the GCN model to calculate multi-output ADN short-circuit current and investigates the block construction of the GCN model. Algorithm analysis demonstrates that our method effectively calculates network-wide short-circuit current under various network structures, IIDG penetration rates, and fault conditions, meeting both accuracy and computational speed requirements. The proposed method offers several advantages, including superior precision, rapid computation, minimal hardware resource utilization, and robust resistance to interference.