Sleep deprivation (SD) has severe negative effects on health and is a widespread problem in society. However, how it affects cognition, and in particular, cognitive control and the brain, is less well understood. This study sought to elucidate the interplay of sleep duration, cognitive control and brain connectivity. In order to investigate this, 17 participants underwent diffusion weighted imaging (DWI), performed a stop-signal task (SST) and wore actigraphs for two weeks. The DWIs were analysed with atlas-based deterministic tractography, and the obtained connectivity matrices were then analysed with a graph theoretical approach to assess brain connectivity. While it was predicted that short sleep duration would be positively correlated with attention, performance monitoring and global efficiency, no such correlations were identified. However, higher global efficiency was found to be associated with longer reaction times on go trials. Results further indicated a positive relationship between stop signal reaction times (SSRTs) and local efficiencies of right inferior frontal gyrus pars opercularis and right supplementary motor area/pre-supplementary motor area. Lastly, as predicted, post-error slowing and post-stop slowing were both found to positively correlate with local efficiency of left anterior cingulate cortex. The somewhat unexpected results can be explained by the small, homogenous sample, although the latter results and the identified small-worldness implies that the analysis itself was successfully applied. Thus, this study provides useful insight into how a graph theoretical approach can be applied in order to assess sleep, cognitive control and brain connectivity in a healthy sample and encourages further research with a comparable approach.