The Large Scale Structure in the galaxy distribution is investigated using The First Data Release of the Sloan Digital Sky Survey .
Using the Minimal Spanning Tree technique we have extracted sets of filaments , of wall–like structures , of galaxy groups , and of rich clusters from this unique sample .
The physical properties of these structures were then measured and compared with the statistical expectations based on the Zel ’ dovich ’ theory .

The measured characteristics of galaxy walls were found to be consistent with those for a spatially flat \Lambda CDM cosmological model with \Omega _ { m } \approx 0.3 and \Omega _ { \Lambda } \approx 0.7 , and for Gaussian initial perturbations with a Harrison – Zel ’ dovich power spectrum .
Furthermore , we found that the mass functions of groups and of unrelaxed structure elements generally fit well with the expectations from Zel ’ dovich ’ theory .
We also note that both groups and rich clusters tend to prefer the environments of walls , which tend to be of higher density , rather than the environments of filaments , which tend to be of lower density .