  Using percolation statistics we, for the first time, demonstrate the
universal character of a network pattern in the real space, mass distributions
resulting from nonlinear gravitational instability of initial Gaussian
fluctuations. Percolation analysis of five stages of the nonlinear evolution of
five power law models reveals that all models show a shift toward a network
topology if seen with high enough resolution. However, quantitatively, the
shift is significantly different in different models: the smaller the spectral
index ,n, the stronger the shift. On the contrary, the shift toward the
"bubble" topology is characteristic only for the n <= -1 models. We find that
the mean density of the percolating structures in the nonlinear density
distributions generally is very different from the density threshold used to
identify them and corresponds much better to a visual impression. We also find
that the maximum of the number of structures (connected regions above or below
a specified density threshold) in the evolved, nonlinear distributions is
always smaller than in Gaussian fields with the same spectrum, and is
determined by the effective slope at the cutoff frequency.
