EEG-based seizure detection models face challenges in terms of inference speed and memory efficiency, limiting their real-time implementation in clinical devices. This paper introduces a novel graph-based residual state update mechanism (REST) for real-time EEG signal analysis in applications such as epileptic seizure detection. By leveraging a combination of graph neural networks and recurrent structures, REST efficiently captures both non-Euclidean geometry and temporal dependencies within EEG data. Our model demonstrates high accuracy in both seizure detection and classification tasks. Notably, REST achieves a remarkable 9-fold acceleration in inference speed compared to state-of-the-art models, while simultaneously demanding substantially less memory than the smallest model employed for this task. These attributes position REST as a promising candidate for real-time implementation in clinical devices, such as Responsive Neurostimulation or seizure alert systems.