Recently, carriers of a common variant in the autism risk gene, CNTNAP2, were found to have altered functional brain connectivity using functional MRI. Here, we scanned 328 young adults with high-field (4-Tesla) diffusion imaging, to test the hypothesis that carriers of this gene variant would have altered structural brain connectivity. All participants (209 women, 119 men, age: 23.4±2.17 SD years) were scanned with 105-gradient high-angular-resolution diffusion imaging (HARDI) at 4 Tesla. After performing a whole-brain fiber tractography using the full angular resolution of the diffusion scans, 70 cortical surface-based regions of interest were created from each individual's co-registered anatomical data to compute graph metrics for all pairs of cortical regions. In graph theory analyses, subjects homozygous for the risk allele (CC) had lower characteristic path length, greater small-worldness and global efficiency in whole-brain analyses, and lower [corrected] eccentricity (maximum path length) in 60 of the 70 nodes in regional analyses. These results were not reducible to differences in more commonly studied traits such as fiber density or fractional anisotropy. This is the first study that links graph theory metrics of brain structural connectivity to a common genetic variant linked with autism and will help us understand the neurobiology of the circuits implicated in the risk for autism.