  We introduce the NEXUS algorithm for the identification of Cosmic Web
environments: clusters, filaments, walls and voids. This is a multiscale and
automatic morphological analysis tool that identifies all the cosmic structures
in a scale free way, without preference for a certain size or shape. We develop
the NEXUS method to incorporate the density, tidal field, velocity divergence
and velocity shear as tracers of the Cosmic Web. We also present the NEXUS+
procedure which, taking advantage of a novel filtering of the density in
logarithmic space, is very successful at identifying the filament and wall
environments in a robust and natural way. To asses the algorithms we apply them
to an N-body simulation. We find that all methods correctly identify the most
prominent filaments and walls, while there are differences in the detection of
the more tenuous structures. In general, the structures traced by the density
and tidal fields are clumpier and more rugged than those present in the
velocity divergence and velocity shear fields. We find that the NEXUS+ method
captures much better the filamentary and wall networks and is successful in
detecting even the fainter structures. We also confirm the efficiency of our
methods by examining the dark matter particle and halo distributions.
