There is robust evidence for sex differences in domain-specific cognitive performance in the general population, where females typically show an advantage for verbal memory (VM), while males tend to perform better on tasks of spatial memory (SM). Sex differences in brain structure and connectivity are also well-documented and may provide insight into sex differences in cognition. In this study, we examined sex differences in cognition and morphometric brain connectivity of a large healthy sample (N = 31,180) from the UK Biobank dataset. Using T1-weighted magnetic resonance imaging (MRI) scans and regional cortical thickness values, we applied jackknife bias estimation and graph theory to obtain subject-specific measures of morphometric brain connectivity, hypothesizing that sex-related differences in brain network global efficiency, or overall connectivity, would underlie observed cognitive differences. As predicted, females demonstrated better VM performance and males showed an advantage in SM. Females also demonstrated faster processing speed, with no observed sex difference in executive functioning. Males tended to have higher global efficiency, as well as higher regional connectivity (nodal strengths) in both the left and right hemispheres relative to females. Furthermore, higher global efficiency in males was found to mediate observed sex differences in cognition, predicting poorer verbal memory performance, better spatial memory, and slower processing speed in males. These findings contribute to an improved understanding of the way biological sex and differences in cognitive performance are related to morphometric brain connectivity as derived from graph-theoretic methods.