Graph theory analysis, a mathematical approach, has been applied in brain connectivity studies to explore the organization of network patterns. The computation of graph theory metrics enables the characterization of the stationary behavior of electroencephalogram (EEG) signals that cannot be explained by simple linear methods. The main purpose of this study was to systematically review the graph theory applications for mapping the functional connectivity of the EEG data in neuroergonomics. Moreover, this article proposes a pipeline for constructing an unweighted functional brain network from EEG data using both source and sensor methods. Out of 57 articles, our results show that graph theory metrics used to characterize EEG data have attracted increasing attention since 2006, with the highest frequency of publications in 2018. Most studies have focused on cognitive tasks in comparison with motor tasks. The mean phase coherence method, based on the "phase-locking value," was the most frequently used functional estimation technique in the reviewed studies. Furthermore, the unweighted functional brain network has received substantially more attention in the literature than the weighted network. The global clustering coefficient and characteristic path length were the most prevalent metrics for differentiating between global integration and local segregation, and the small-worldness property emerged as a compelling metric for the characterization of information processing. This review provides insight into the use of graph theory metrics to model functional brain connectivity in the context of neuroergonomics research.