  It is possible to visualize the Cosmic Web as an interconnected network of
one-dimensional filaments, two-dimensional sheets and three-dimensional
volume-filling structures which we refer to as clusters. We have used the Local
Dimension D, which takes values D = 1, 2 and 3 for filaments, sheets and
clusters, respectively, to analyse the Cosmic Web in a three-dimensional
volume-limited galaxy sample from the Sloan Digital Sky Survey Data Release 7.
The analysis was carried out separately using three different ranges of
length-scales: 0.5-5, 1-10 and 5-50 $h^{-1} {\rm Mpc}$. We find that there is a
progressive increase in the D values as we move to larger length-scales. At the
smallest length-scale, the galaxies predominantly reside in filaments and
sheets. There is a shift from filaments to sheets and clusters at larger
scales. Filaments are completely absent at the largest length-scale (5-50
$h^{-1} {\rm Mpc}$). Considering the effect of the density environment on the
Cosmic Web, we find that the filaments preferentially inhabit regions with a
lower density environment as compared to sheets and clusters which prefer
relatively higher density environments. A similar length-scale dependence and
environment dependence was also found in a galaxy sample drawn from the
Millennium Simulation which was analysed in exactly the same way as the actual
data.
