  A dynamical classification of the cosmic web is proposed. The large scale
environment is classified into four web types: voids, sheets, filaments and
knots. The classification is based on the evaluation of the deformation tensor,
i.e. the Hessian of the gravitational potential, on a grid. The classification
is based on counting the number of eigenvalues above a certain threshold,
lambda_th at each grid point, where the case of zero, one, two or three such
eigenvalues corresponds to void, sheet, filament or a knot grid point. The
collection of neighboring grid points, friends-of-friends, of the same web
attribute constitutes voids, sheets, filaments and knots as web objects.
  A simple dynamical consideration suggests that lambda_th should be
approximately unity, upon an appropriate scaling of the deformation tensor. The
algorithm has been applied and tested against a suite of (dark matter only)
cosmological N-body simulations. In particular, the dependence of the volume
and mass filling fractions on lambda_th and on the resolution has been
calculated for the four web types. Also, the percolation properties of voids
and filaments have been studied.
  Our main findings are: (a) Already at lambda_th = 0.1 the resulting web
classification reproduces the visual impression of the cosmic web. (b) Between
0.2 < lambda_th < 0.4, a system of percolated voids coexists with a net of
interconected filaments. This suggests a reasonable choice for lambda_th as the
parameter that defines the cosmic web. (c) The dynamical nature of the
suggested classification provides a robust framework for incorporating
environmental information into galaxy formation models, and in particular the
semi-analytical ones.
