Summary: Accurately analyzing the flow and transport behavior in a large discrete fracture network is computationally expensive. Fortunately, recent research shows that most of the flow and transport occurs within a small backbone in the network, and identifying the backbone to replace the original network can greatly reduce computational consumption. However, the existing machine learning based methods mainly focus on the features of the fracture itself to evaluate the importance of the fracture, the local structural information of the fracture network is not fully utilized. More importantly, these machine learning methods can neither control the identified backbone’s size nor ensure the backbone’s connectivity. To solve these problems, a deep learning model named multi-aggregator graph neural network (MA-GNN) is proposed for identifying the backbone of discrete fracture networks. Briefly, MA-GNN uses multiple aggregators to aggregate neighbors’ structural features and thus generates an inductive embedding to evaluate the criticality score of each node in the entire fracture network. Then, a greedy algorithm, which can control the backbone’s size and connectivity, is proposed to identify the backbone based on the criticality score. Experimental results demonstrate that the backbone identified by MA-GNN can recover the transport characteristics of the original network, outperforming state-of-the-art baselines. In addition, MA-GNN can identify influential fractures with higher Kendall’s \(\tau\) correlation coefficient and Jaccard similarity coefficient. With the ability of size control, our proposed MA-GNN can provide an effective balance between accuracy and computational efficiency by choosing a suitable backbone size.