Estimating vigilance has always been a non-trivial challenge in safety-critical domains such as surveillance, driving, security monitoring, and air traffic control. Traditional methods have been enhanced by machine learning and deep learning approaches to seek effective solutions. However, despite several notable approaches, the problem persists due to the binary nature of classification. To gain a comprehensive understanding of an operator’s mental state, it is crucial to categorize vigilance into multiple levels for deeper insights. Another challenge is handling variable-sized data, as human performance leads to fluctuating data sizes. While many researchers address this issue by data padding or truncation, which often results in introducing biases. In this research, we address both issues by proposing a Graph Convolution Network (GCN)-based approach to estimate vigilance from varying lengths of EEG signals. The use of GCNs is motivated by their flexibility and scalability, allowing them to manage datasets of varying lengths effectively and adapt to diverse data patterns by focusing on localized node relationships. Features extracted by the GCN are classified into six vigilance levels using a Multilayer Perceptron (MLP) and a Liquid Neural Network (LNN). Our results show that the MLP outperforms the LNN, achieving an accuracy of 93.23% in training and 91.45% in testing when combined with the GCN, while the GCN paired with the LNN achieves 81.94% in training and 82.16% in testing. These findings suggest that the GCN-MLP framework is a promising tool for real-time vigilance monitoring in high-stakes environments.