The results are presented of a statistical analysis of the variability of the circle of Willis using univariate and bivariate methods. For this purpose 100 circles of Willis were available. From each circle 19 indexes of arterial size were determined, the basilar artery was measured in two places. Half the circumference was measured. This data yielded no evidence of differences between left- and right-sided vessels in the sample. An important source of variation is the general size of all vessels considered. When the data are cleared from this general size variation, correlation coefficients reveal interesting relations between the vessels. The posterior communicating arteries are strongly related to the ipsilateral carotid artery, whereas a strong inverse relationship exists with the basilar artery and the precommunicating part of the ipsilateral posterior cerebral artery. These relationships can be understood from the expected patterns of the blood flow in these vessels. Similar relationships can be found in the anterior part of the circle of Willis and in the vertebro-basilar junction. In a different manner, based on previous haemodynamic studies, the relation between blood flow and vessel size within the circle of Willis can be demonstrated by relating the ratios of the sizes of afferent and efferent arteries to the sizes of the posterior communicating arteries, an "intuitive" model. The supposed correlations of the outcome of this "intuitive" model with the size of the communicating arteries appeared to by highly significant. It is concluded that the variations of the circle of Willis are related to the individual variations of the blood flow in this arterial network.