Epilepsy is a chronic brain disease that causes persistent and severe damage to the physical and mental health of patients. Daily effective prediction of epileptic seizures is crucial for epilepsy patients especially those with refractory epilepsy. At present, a large number of deep learning algorithms such as Convolutional Neural Networks and Recurrent Neural Networks have been used to predict epileptic seizures and have obtained better performance than traditional machine learning methods. However, these methods usually transform the Electroencephalogram (EEG) signal into a Euclidean grid structure. The conversion suffers from loss of adjacent spatial information, which results in deep learning models requiring more storage and computational consumption in the process of information fusion after information extraction. This study proposes a general Graph Convolutional Networks (GCN) model architecture for predicting seizures to solve the problem of oversized seizure prediction models based on exploring the graph structure of EEG signals. As a graph classification task, the network architecture includes graph convolution layers that extract node features with one-hop neighbors, pooling layers that summarize abstract node features; and fully connected layers that implement classification, resulting in superior prediction performance and smaller network size. The experiment shows that the model has an average sensitivity of 96.51%, an average AUC of 0.92, and a model size of 15.5 k on 18 patients in the CHB-MIT scalp EEG dataset. Compared with traditional deep learning methods, which require a large number of parameters and computational effort and are demanding in terms of storage space and energy consumption, this method is more suitable for implementation on compact, low-power wearable devices as a standard process for building a generic low-consumption graph network model on similar biomedical signals. Furthermore, the edge features of graphs can be used to make a preliminary determination of locations and types of discharge, making it more clinically interpretable.