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

The Skeleton: Connecting Large Scale Structures to Galaxy Formation