The properties of functional brain networks during rest are known to be related to individual differences in cognitive processing or psychopathology. Here, we ask if a personality trait, the behavioral approach system (BAS), is based on individual differences in neurobiological substrates, namely those of the resting-state functional brain network. Resting-state fMRI data were acquired for 30 healthy, normal participants during rest, and brain networks were analyzed using a graph-theoretical approach in which the brain is viewed as a network composed of connections (edges) between brain regions (nodes). The influence of the left nucleus accumbens on other brain regions (quantified by the metric ‘betweenness’), was found to greater tendency in those individuals with higher BAS sensitivity. High BAS sensitivity was also related to a higher tendency for global information processing in the network, rather than local information processing in the right visual cortex, as indicated by increased betweenness and decreased clustering and local efficiency. Finally, Higher BAS-sensitivity individuals also showed tendency of decreased connectivity (‘degree’) and information processing efficiency (‘global efficiency’) in the right superior frontal gyrus. These findings suggest that the differences in brain network properties in the nucleus accumbens, visual cortex, and frontal cortex are related to the greater reward sensitivity, high novelty seeking, and greater impulsivity in high-BAS individuals.