The importance of understanding mental fatigue can be seen from many studies that started back in past decades. It is only until recent years has mental fatigue been explored through connectivity network analysis using graph theory. Although previous studies have revealed certain properties of the mental fatigue network via graph theory, some of these findings seemingly conflict with one another. The differences in findings could be due to mental fatigue being caused by various factors or being analyzed using different methods. So, in this study, to further understand the functional connectivity of driving fatigue, a weighted and undirected connectivity matrix would be constructed before applying graph theory to identify the biomarker from the network property. To obtain data for analysis, a 64-channel EEG cap was used to record the brain signals of subjects undergoing a one-hour driving simulation. Using the recorded EEG signal, a connectivity matrix was constructed using a synchronous method known as phase lag index (PLI) for the graph theory analysis. Results from this graph theory analysis showed that the synchronous network had increased clustering coefficient and decreased path length with the accumulation of mental fatigue. Furthermore, by calculating clustering coefficient regionally, its results revealed that the significant increase occurred mainly in the parietal and occipital regions of the brain.