Observations of the quiet Sun from the Solar Optical Telescope/Spectro-Polarimeter aboard the Hinode spacecraft reveal the magnetic characteristics of the solar photosphere. By making use of the deep-mode observations of three quiet regions, we have statistically studied the vector magnetic fields of solar granulation. More than 2000 normal granules are manually selected to form a sample. It is recognized that some granules are even darker than the mean photosphere in intensity, and there is a linear correlation between intensity and Doppler velocity in the granules. The distributions of longitudinal and transverse apparent magnetic flux densities, Doppler velocity, and continuum intensity of granules are obtained, and their unsigned magnetic flux measured. Two approaches are used in this study. First, we obtained the magnetic properties of granulation by averaging the measurements for all the sampling granules. Second, we reconstructed an average granular cell based on a subsample, and obtained the detailed distribution of apparent magnetic flux density within the model granular cell. All the results have been compared with those for intergranular lanes and a few typical abnormal granules. Our statistical analysis reveals the following results. (1) The unsigned magnetic flux of individual granules spans the range from 1.1 x 10(15) Mx to 3.3 x 10(18) Mx with a peak distribution at 1.6 x 10(16) Mx. (2) The unsigned longitudinal apparent flux density of granules ranges from almost 0 to 212 Mx cm(-2) with a mean longitudinal apparent flux density of 12 Mx cm(-2), while the transverse apparent flux density of granules ranges from 4 to 218 Mx cm(-2) with a mean transverse apparent flux density of 79 Mx cm-2. The longitudinal and transverse apparent magnetic flux densities of granules are positively correlated, and the longitudinal apparent flux density of granules is weaker than the corresponding transverse apparent flux density. (3) The magnetic inclination of granules with respect to the surface that is perpendicular to the line of sight falls in the range of 4.8-76.7 degrees with a peak distribution at 25 degrees. On average, the magnetic vectors in granules are more vertical than those in the intergranular lanes. (4) There is a strong preference that both the vertical and horizontal fields on the quiet Sun reside in the intergranular lanes. (5) The detailed distributions of apparent flux density, Doppler velocity, and continuum intensity within an average granular cell are presented. These distributions can be empirically formulated well.
