Accumulating evidences showed that the optimal brain network topology was altered with the progression of fatigue during car driving. However, the extent of the discriminative power of functional connectivity that contributes to driving fatigue detection is still unclear. In this article, we extracted two types of features (network properties and critical connections) to explore their usefulness in driving fatigue detection. EEG data were recorded twice from twenty healthy subjects during a simulated driving experiment. Multiband functional connectivity matrices were established using the phase lag index, which serve as input for the following graph theoretical analysis and critical connections determination between the most vigilant and fatigued states. We found a reorganization of a brain network toward less efficient architecture in fatigue state across all frequency bands. Further interrogations showed that the discriminative connections were mainly connected to frontal areas, i.e., most of the increased connections are from frontal pole to parietal or occipital regions. Moreover, we achieved a satisfactory classification accuracy (96.76%) using the discriminative connection features in beta band. This article demonstrated that graph theoretical properties and critical connections are of discriminative power for manifesting fatigue alterations and the critical connection is an efficient feature for driving fatigue detection.