Electroencephalogram (EEG) is widely used to predict performance degradation of human subjects due to mental or physical fatigue. Analysis of fatigue due to sleep deprivation using EEG synchronization is a promising field of research. The present paper analyses advancing levels of fatigue in human drivers in a sleep-deprivation experiment by studying the synchronization between EEG data recorded from various brain areas. The S-Estimator technique based on state-space analysis has been employed to quantify the synchronization between EEG channels, which has then been formulated in terms of a complex network. The change in the parameters of the network has been analyzed to find the variation of connectivity between brain areas and hence to trace the increase in fatigue levels of the subjects.