Epileptic seizure detection using EEG is critical for neurological diagnosis and management. While deep learning methods have shown promise, they often fail to capture the temporal dependencies within EEG signals. This study proposes a Graph Neural Network (GNN)-based approach tailored for single-channel EEG classification using the University of Bonn (BONN) dataset. Each EEG signal is divided into eight non-overlapping segments, from which features are extracted. These segments are represented as graph nodes, with edges formed based on feature similarity between segments. The resulting graph representation enables classification into five distinct EEG categories (Z, N, F, S, O). To ensure robust evaluation, we trained and validated the proposed Graph Convolutional Network (GCN) model using 10 different random seeds. The best performance was achieved with seed 4, yielding an accuracy of 91.00%, macro F1 score of 0.9105, and micro F1 score of 0.9100. Across all seeds, the model maintained high reliability, with an average accuracy of 0.87 ± 0.0147, macro F1 of 0.8681 ± 0.0157, and micro F1 of 0.87 ± 0.0147. This work demonstrates the effectiveness of GNNs for EEG-based seizure detection and highlights their potential for lightweight, portable, and real-time applications in clinical and wearable systems.