In EEG based driving fatigue detection, the redundant EEG channels would increase the probability of introducing noise and heaving calculation burden. Aiming at this point, we built up an EEG dataset with thirty electrodes from every brain lobe, proposed a driving fatigue detection approach based on brain functional network. And provide a possible way for the key EEG electrode and rhythm investigation with these brain networks. First, a simulation driving experiment was set up to obtain EEG of multiple subjects during a long-term monotonous cognitive task. The feasibility of the collected data was verified with PSD. For brain functional network construction, partial directed coherence (PDC) is used to calculate the correlation between EEG channels. Then, four graph related features (i.e., node degree, clustering coefficient, characteristic path length and local efficiency) are extracted for fatigue detection with SVM as classifier. After that, we get the key electrodes with the feature of betweenness centrality. The results show that the low frequency rhythms are more distinguishable than that of high frequency. The best classification accuracy of 87.16% is achieved in delta, which is 18.9% higher than that of the baseline method with PSD. At last, we verified the effectiveness of the selected key electrodes, and drew the conclusion that the key EEG rhythm corresponding to different features may not be consistent.