The Minimal Spanning Tree technique allows us to reveal set of structure elements of the Large Scale Structure and to characterize statistically the large scale matter distributions in observed and simulated catalogs. With this approach we can identify the influence of different factors on the measured characteristics of strucutre elements. In particular, we
can reveal the influence of such factors as (1) the galaxy identification procedure in numerical simulations, (2) the geometry of the survey volume, (3) the selection effects within a catalogue, and (4) the random velocities in the redshift space. All of these factors lead to a significant bias between the statistical characteristics of the basic DM and `observed' galaxy distributions.
It is found that in real space the filamentary character of the matter distribution dominates in simulated catalogues and a moderate two-dimensional sheet-like component appears mainly within high density regions. In redshift space for the same catalogues the sheet-like structures dominate and contain up to 50\% of all objects. This means that the high density walls are formed by the successive compression and relaxation of earlier formed filaments, clouds and other structure
elements. Even the moderate random re-positioning of galaxies owing to random radial velocities results strongly affect the {\em observed\/} internal characteristics of structure elements.
In spite of this, the correspondence between the physical quantities of the theory and observational measures obtained through statistical analyses is demonstrated. It provides the direct physical interpretation of observations and complements the correlation function and power spectrum analyses. The agreement of measured statistical parameters
with the theoretical expectations is shown for actual mean physical measures of the walls such as their separation, sizes, galaxy surface density and internal velocity dispersion. The estimated parameters also provide the present amplitude of perturbations which characterizes the present epoch of evolution. Physically, our results show that walls represent high density, partially relaxed, quasi-stationary Zel'dovich'pancakes.
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