Diffusion weighted imaging (DWI) is widely used to study microstructural characteristics of the brain. High angular resolution diffusion imaging (HARDI) samples diffusivity at a large number of spherical angles, to better resolve neural fibers that mix or cross. Here, we implemented a framework for advanced mathematical analysis of mouse 5-shell HARDI (b=1000, 3000, 4000, 8000, 12000 s/mm2), also known as hybrid diffusion imaging (HYDI). Using q-ball imaging (QBI) at ultra-high field strength (7 Tesla), we computed diffusion and fiber orientation distribution functions (dODF, fODF) to better detect crossing fibers. We also computed a quantitative anisotropy (QA) index, and deterministic tractography, from the peak orientation of the fODFs. We found that the signal to noise ratio (SNR) of the QA was significantly higher in single and multi-shell reconstructed data at the lower b-values (b=1000, 3000, 4000 s/mm2) than at higher b-values (b=8000, 12000 s/mm2); the b=1000 s/mm2 shell increased the SNR of the QA in all multi-shell reconstructions, but when used alone or in <5-shell reconstruction, it led to higher angular error for the major fibers, compared to 5-shell HYDI. Multi-shell data reconstructed major fibers with less error than single-shell data, and was most successful at reducing the angular error when the lowest shell was excluded (b=1000 s/mm2). Overall, high-resolution connectivity mapping with 7T HYDI offers great potential for understanding unresolved changes in mouse models of brain disease.