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The human right inferior frontal cortex (IFC) plays a critical role in response inhibition. It has also been demonstrated that the IFC is heterogeneous and that the ventral part of the IFC (vIFC) is more critical to inhibition of prepotent response tendency. Recent areal parcellation analyses based on resting-state functional connectivity have revealed that the right vIFC consists of multiple functional areas. In the present study, we characterized the parcellated areas (parcels) in the right vIFC using graph theory analysis, which characterizes local connectivity properties of a brain network by referring to its global structure of functional connectivity. Functional magnetic resonance imaging (MRI) scans were obtained during performance of a stop-signal task and during resting state. The cerebral cortex was parcellated into areas using resting-state functional connectivity. The parcels were then subjected to graph theory analysis to reveal central areas. Two parcels, ventral and dorsal, in the posterior part of the vIFC, exhibited significant brain activity during response inhibition. The ventral parcel exhibited a positive correlation between betweenness centrality and brain activity while the dorsal parcel did not. Correlations were significantly stronger in the ventral parcel. Moreover, the ventral parcel exhibited a negative correlation between brain activity during response inhibition and stop-signal reaction time (SSRT), a behavioral measure used to evaluate stopping performance. These dissociation results suggest that the ventral region in the vIFC plays a more central role in the brain network by increasing brain activity, which may further predict better performance of response inhibition.