  The Large Scale Structure (LSS) found in galaxy redshift surveys and in
computer simulations of cosmic structure formation shows a very complex network
of galaxy clusters, filaments, and sheets around large voids. Here, we
introduce a new algorithm, based on a Minimal Spanning Tree, to find basic
structural elements of this network and their properties. We demonstrate how
the algorithm works using simple test cases and then apply it to haloes from
the Millennium Run simulation (Springel et al. 2005). We show that about 70% of
the total halo mass is contained in a structure composed of more than 74,000
individual elements, the vast majority of which are filamentary, with lengths
of up to 15 Mpc/h preferred. Spatially more extended structures do exist, as do
examples of what appear to be sheet-like configurations of matter. What is
more, LSS appears to be composed of a fixed set of basic building blocks. The
LSS formed by mass selected subsamples of haloes shows a clear correlation
between the threshold mass and the mean extent of major branches, with
cluster-size haloes forming structures whose branches can extend to almost 200
Mpc/h - the backbone of LSS to which smaller branches consisting of smaller
haloes are attached.
