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The apparatus of correlation gamma function (\Gamma*(r)) is used to analyzevolume-limited samples from the DR4 Main Galaxy Sample of the SDSS survey withthe aim of determining the characteristic scales of galaxy clustering. Up to 20h^{-1} Mpc (H_0 = 65 km s^{-1}Mpc^{-1}), the distribution of galaxies isdescribed by a power-law density-distance dependence, \Gamma*(r) proportionalto r^{-\gamma}, with an index \gamma approximately 1.0. A change in the stateof clustering (a significant deviation from the power law) was found on a scaleof 20-25 h^{-1}Mpc. The distribution of SDSS galaxies becomes homogeneous(\gamma approximately 0) from a scale of ~60 h^{-1}Mpc. The dependence of\gamma on the luminosity of galaxies in volume-limited samples was obtained.The power-law index \gamma increases with decreasing absolute magnitude ofsample galaxies M_abs. At M_abs ~ -21.4, which corresponds to thecharacteristic value Mr* of the SDSS luminosity function, this dependenceexhibits a break followed by a more rapid increase in \gamma.Comment: 11 pages, 5 figure

Correlation properties of galaxies from the Main Galaxy Sample of the SDSS survey