Advances in magnetic resonance imaging, particularly diffusion imaging, have allowed researchers to analyze brain connectivity. Identification of structural connectivity differences between patients with normal cognition, cognitive impairment, and dementia could lead to new biomarker discoveries that could improve dementia diagnostics. In our study, we analyzed 22 patients (11 control group patients, 11 dementia group patients) that underwent 3T MRI diffusion tensor imaging (DTI) scans and the Montreal Cognitive Assessment (MoCA) test. We reconstructed DTI images and used the Desikan-Killiany-Tourville cortical parcellation atlas. The connectivity matrix was calculated, and graph theoretical analysis was conducted using DSI Studio. We found statistically significant differences between groups in the graph density, network characteristic path length, small-worldness, global efficiency, and rich club organization. We did not find statistically significant differences between groups in the average clustering coefficient and the assortativity coefficient. These statistically significant graph theory measures could potentially be used as quantitative biomarkers in cognitive impairment and dementia diagnostics.