  We report on two quantitative, morphological estimators of the filamentary
structure of the Cosmic Web, the so-called global and local skeletons. The
first, based on a global study of the matter density gradient flow, allows us
to study the connectivity between a density peak and its surroundings, with
direct relevance to the anisotropic accretion via cold flows on galactic halos.
  From the second, based on a local constraint equation involving the
derivatives of the field, we can derive predictions for powerful statistics,
such as the differential length and the relative saddle to extrema counts of
the Cosmic web as a function of density threshold (with application to
percolation of structures and connectivity), as well as a theoretical framework
to study their cosmic evolution through the onset of gravity-induced
non-linearities.
