Tracing the cosmic web
  The cosmic web is one of the most striking features of the distribution of
galaxies and dark matter on the largest scales in the Universe. It is composed
of dense regions packed full of galaxies, long filamentary bridges, flattened
sheets and vast low density voids. The study of the cosmic web has focused
primarily on the identification of such features, and on understanding the
environmental effects on galaxy formation and halo assembly. As such, a variety
of different methods have been devised to classify the cosmic web -- depending
on the data at hand, be it numerical simulations, large sky surveys or other.
In this paper we bring twelve of these methods together and apply them to the
same data set in order to understand how they compare. In general these cosmic
web classifiers have been designed with different cosmological goals in mind,
and to study different questions. Therefore one would not {\it a priori} expect
agreement between different techniques however, many of these methods do
converge on the identification of specific features. In this paper we study the
agreements and disparities of the different methods. For example, each method
finds that knots inhabit higher density regions than filaments, etc. and that
voids have the lowest densities. For a given web environment, we find
substantial overlap in the density range assigned by each web classification
scheme. We also compare classifications on a halo-by-halo basis; for example,
we find that 9 of 12 methods classify around a third of group-mass haloes (i.e.
$M_{\rm halo}\sim10^{13.5}h^{-1}M_{\odot}$) as being in filaments. Lastly, so
that any future cosmic web classification scheme can be compared to the 12
methods used here, we have made all the data used in this paper public.
