The apparatus of correlation gamma function ( \Gamma ^ { * } ( r ) ) is used to analyze volume-limited samples from the DR4 Main Galaxy Sample of the SDSS survey with the aim of determining the characteristic scales of galaxy clustering .
Up to 20 h ^ { -1 }  Mpc ( H _ { 0 } = 65  km s ^ { -1 } Mpc ^ { -1 } ) , the distribution of galaxies is described by a power-law density-distance dependence , \Gamma ^ { * } ( r ) \propto r ^ { - \gamma } , with an index \gamma \approx 1.0 .
A change in the state of clustering ( a significant deviation from the power law ) was found on a scale of 20 - 25 h ^ { -1 } Â Mpc .
The distribution of SDSS galaxies becomes homogeneous ( \gamma \sim 0 ) from a scale of \sim 60 h ^ { -1 } Â 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 of sample galaxies M _ { abs } .
At M _ { abs } \sim - 21.4 , which corresponds to the characteristic value M ^ { * } _ { r } of the SDSS luminosity function , this dependence exhibits a break followed by a more rapid increase in \gamma .