2007MNRAS.375..337C

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. We show that about 70 per cent of the total halo mass is contained in a structure composed of more than 74000 individual elements, the vast majority of which are filamentary, with lengths of up to 15h^–1Mpc 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 200h^–1Mpc - the backbone of LSS to which smaller branches consisting of smaller haloes are attached.