The cerebral vasculature supplies blood to the brain and plays a crucial role in the function and survival of the brain tissue. Unfortunately, there are several diseases that affect the cerebral vasculature and hence the brain. The diagnosis of these diseases and the study of their underlying mechanisms is greatly benefited by the ability to image in vivo the anatomy and function of the vasculature. However, the objective and quantitative analysis of these images is challenging. In this thesis we present two novel methods to analyze images of the cerebral vasculature. In particular, we are interested in the connectivity of the vasculature, both on a macro- and microscopic level. The goal is to provide the medical community with tools that allow to increase their pace of research and to ultimately improve patient wellbeing. The first method segments and anatomically labels the large cerebral arteries. It performs these tasks simultaneously, which results in improved segmentations compared to earlier methods, as we demonstrate on a dataset of magnetic resonance angiography images. In clinical practice, it can be used to detect abnormalities such as stenoses and aneurysms by comparing the actual morphology of a named segment with its expected morphology. In research, it can be used to analyze large quantities of scans enabling research on the relation between vascular morphology and the prevalence of certain diseases or the underlying genetics. The second method infers from computed tomography perfusion images the connectivity of the cerebral arteries, even if the individual arteries are too small to be distinguished. Hereto, the method tracks the contrast agent bolus when it flows through the brain. This information was previously not measurable in vivo and provides researchers with a tool to investigate the role of collateral flow in stroke. We demonstrate the feasibility of the method on both healthy and diseased subjects and begin to validate the method clinically.