Discovery of the associations between brain structural connectivity and clinical and demographic variables can help to better understand the vulnerability and resilience of the brain architecture to neurodegenerative diseases and to discover biomarkers. We used four diffusion-MRI databases, three related to Alzheimer's disease (AD), to exploratorily correlate structural connections between 85 brain regions with non-MRI variables, while stringently correcting the significance values for multiple testing and ruling out spurious correlations via careful visual inspection. We repeated the analysis with brain connectivity augmented with multi-synaptic neural pathways. We found 85 and 101 significant relationships with direct and augmented connectivity, respectively, which were generally stronger for the latter. Age was consistently linked to decreased connectivity, and healthier clinical scores were generally linked to increased connectivity. Our findings help to elucidate which structural brain networks are affected in AD and aging and highlight the importance of including indirect connections.