In this article, we propose a sparse spectra graph convolutional network (SSGCNet) for epileptic electroencephalogram (EEG) signal classification. The goal is to develop a lightweighted deep learning model while retaining a high level of classification accuracy. To do so, we propose a weighted neighborhood field graph (WNFG) to represent EEG signals. The WNFG reduces redundant edges between graph nodes and has lower graph generation time and memory usage than the baseline solution. The sequential graph convolutional network is further developed from a WNFG by combining sparse weight pruning and the alternating direction method of multipliers (ADMM). Compared with the state-of-the-art method, our method has the same classification accuracy on the Bonn public dataset and the spikes and slow waves (SSW) clinical real dataset when the connection rate is ten times smaller.