Central brain network connections greatly contribute to overall network efficiency. Here we examined whether small vessel disease (SVD) related white matter alterations in central brain network connections have a greater impact on executive functioning than alterations in non-central brain network connections. Brain networks were reconstructed from diffusion-weighted MRI scans in 72 individuals (75 ± 8 years) with cognitive impairment and SVD on MRI. The centrality of white matter connections in the network was defined using graph theory. The association between the fractional anisotropy (FA) of central versus non-central connections, executive functioning, and markers of SVD was evaluated with linear regression and mediation analysis. Lower FA in central network connections was more strongly associated with impairment in executive functioning than FA in non-central network connections (r = 0.41 vs. r = 0.27; P < 0.05). Results were consistent across varying thresholds to define the central subnetwork (>50%–10% connections). Higher SVD burden was associated with lower FA in central as well as non-central network connections. However, only central network FA mediated the relationship between white matter hyperintensity volume and executive functioning [change in regression coefficient after mediation (95% CI): −0.15 (−0.35 to −0.02)]. The mediation effect was not observed for FA alterations in non-central network connections [−0.03 (−0.19 to 0.04)]. These findings suggest that the centrality of network connections, and thus their contribution to global network efficiency, appears to be relevant for understanding the relationship between SVD and cognitive impairment. Hum Brain Mapp 37:2446–2454, 2016. © 2016 Wiley Periodicals, Inc.