This study aims to investigate the effects of individual differences in trait coping on brain networks at rest using electroencephalography (EEG) data. EEG recordings were processed using graph theory analysis. Active and passive coping styles were determined according to the factor structure of the Brief Coping Orientation to Problems Experienced questionnaire. A structural equation modeling analysis indicated that the influence of coping strategies on quality of life varies in strength and direction. In particular, active coping strategies were positively correlated with the psychological dimension. Graph measures, at both global and nodal levels, were used to identify the brain network properties in accordance with passive versus active coping styles. Preliminary evidence showed that both the global and nodal graph metrics were affected by the coping strategy in the delta band. During resting state, passive coping strategy participants had network topology characterized by a high global efficiency, indicating an important level of integration between distant brain areas and a high local efficiency and transitivity, suggesting a high local communication between adjacent regions. Various regions, such as the paracentral lobule, posterior cingulate, and other frontal or parietal areas, seemed to play a key role, suggesting that processes such as emotional load are highly solicited in passive coping individuals. In active coping participants, the superior temporal gyrus seemed to be of importance when neurons oscillated in the theta and alpha frequencies.