  The length of the three-dimensional filaments observed in the fourth public
data-release of the SDSS is measured using the {\em local skeleton} method. It
consists in defining the set of points where the gradient of the smoothed
density field is extremal along its isocontours, with some additional
constraints on local curvature to probe actual ridges in the galaxy
distribution. A good fit to the mean filament length per unit volume,
$\cal{L}$, in the SDSS survey is found to be ${\cal{L}}=(52500\pm6500) (L/{\rm
Mpc})^{-1.75\pm0.06}\rm{Mpc}/(100 \rm{Mpc})^{3}$ for $8.2 \leq L \leq 16.4$
Mpc, where $L$ is the smoothing length in Mpc. This result, which deviates only
slightly, as expected, from the trivial behavior ${\cal{L}} \propto L^{-2}$, is
in excellent agreement with a $\Lambda$CDM cosmology, as long as the matter
density parameter remains in the range $0.25 < \Omega_{\rm matter} < 0.4$ at
one sigma confidence level, considering the universe is flat. These
measurements, which are in fact dominated by linear dynamics, are not
significantly sensitive to observational biases such as redshift distortion,
edge effects, incompleteness, and biasing between the galaxy distribution and
the dark matter distribution. Hence it is argued that the local skeleton is a
rather promising and discriminating tool for the analysis of filamentary
structures in three-dimensional galaxy surveys.
