Objective: The aim of the study was to assess the geometric characteristics of rat pial microcirculation and describe the vessel bifurcation patterns by ‘connectivity matrix’. Methods: Male Wistar rats were used to visualize pial microcirculation by a fluorescent microscopy technique through an open cranial window, using fluorescein isothiocyanate bound to dextran (molecular weight 70 kDa). The arteriolar network was mapped by stop-frame images. Diameters and lengths of arterioles were measured with a computer-assisted method. Pial arterioles were classified according to a centripetal ordering scheme (Strahler method modified according to diameter) from the smallest order 1 to the largest order 5 arterioles in the preparation. A distinction between arteriolar segments and elements was used to express the series-parallel features of the pial arteriolar networks. A connectivity matrix was used to describe the connection of blood vessels from one order to another. Results: The arterioles were assigned 5 orders of branching by Strahler’s ordering scheme, from order 1 (diameter: 16.0 ± 2.5 µm) to order 5 (62 ± 5.0 µm). Order 1 arterioles gave origin to capillaries, assigned order 0. The diameter, length and branching of the 5 arteriolar orders grew as a geometric sequence with the order number in accordance with Horton’s law. The segments/elements ratio was the highest in order 4 and 3 arterioles, indicating the greatest asymmetry of ramifications. Finally, the branching vessels in the networks were described in details by the connectivity matrix. Fractal dimensions of arteriolar length and diameter were 1.75 and 1.78, respectively. Conclusions: The geometric characteristics of rat pial microcirculation indicate that distribution of vessels is fractal. The connectivity matrix allowed us to describe the number of daughter vessels spreading from parent vessels. This ordering scheme may be useful to describe vessel function, according to diameter, length and branching.