Epileptic seizure is a neurological disorder characterized by recurrent, abrupt behavioral changes attributed to transient shifts in excessive electrical discharges within specific brain cell groups. Electroencephalogram (EEG) signals are the primary modality for capturing seizure activity, offering real-time, computer-assisted detection through long-term monitoring. Over the last decade, extensive experiments through deep learning techniques on EEG signal analysis, and automatic seizure detection. Nevertheless, realizing the full potential of deep neural networks in seizure detection remains a challenge, primarily due to limitations in model architecture design and their capacity to handle time series brain data. The fundamental drawback of current deep learning methods is their struggle to effectively represent physiological EEG recordings; as it is irregular and unstructured in nature, which is difficult to fit into matrix format in traditional methods. Because of this constraint, a significant research gap remains in this research field.  In this context, we propose a novel approach to bridge this gap, leveraging the inherent relationships within EEG data. Graph neural networks (GNNs) offer a potential solution, capitalizing on their ability to naturally encapsulate relational data between variables. By representing interacting nodes as entities connected by edges with weights determined by either temporal associations or anatomical connections, GNNs have garnered substantial attention for their potential in configuring brain anatomical systems. In this paper, we introduce a hybrid framework for epileptic seizure detection, combining the Graph Attention Network (GAT) with the Radial Basis Function Neural Network (RBFN) to address the limitations of existing approaches. Unlike traditional graph-based networks, GAT automatically assigns weights to neighbouring nodes, capturing the significance of connections between nodes within the graph. The RBFN supports this by employing linear optimization techniques to provide a globally optimal solution for adjustable weights, optimizing the model in terms of the minimum mean square error (MSE). Power spectral density is used in the proposed method to analyze and extract features from electroencephalogram (EEG) signals because it is naturally simple to analyze, synthesize, and fit into the graph attention network (GAT), which aids in RBFN optimization. The proposed hybrid framework outperforms the state-of-the-art in seizure detection tasks, obtaining an accuracy of 98.74%, F1-score of 96.2%, and Area Under Curve (AUC) of 97.3% in a comprehensive experiment on the publicly available CHB-MIT EEG dataset.