In nature, asymmetries are widely found in bilateral structures. Particularly in the brain, directional asymmetry (DA) has been of interest due to its association with functional lateralisation, although the asymmetry in the structural connectivity network has been scarcely explored. This study aims to investigate changes in the magnitude of DA in the structural connectivity of cortical and subcortical regions during adulthood. We analysed 151 3T T1 and DWI-DTI brain magnetic resonance images from healthy adult subjects (43.73 ± 16.25 years) residing in the Buenos Aires metropolitan area, as part of the GeNEDAR cohort. Topological parameters (i.e., local efficiency, strength, and clustering coefficient) of connectivity networks from 40 regions of interest were obtained in DSIstudio. In the analysis, the effects of sex and age on the AD of topological measures are examined. Changes in the asymmetrical organisation of the network tended to reveal a turning point around the transition from middle to late adulthood. In regions such as the putamen, frontal, and superior temporal, greater asymmetry was observed with age. Conversely, there was a tendency towards symmetry in the medial orbitofrontal, paracentral, and inferior parietal regions. These findings, largely novel, reinforce their potential as biomarkers of brain ageing.