The Superiority of the Minimal Spanning Tree in Percolation Analyses of Cosmological Datasets

In this work we demonstrate the ability of the Minimal Spanning Tree to duplicate the information contained within a percolation analysis for a point dataset. We show how to construct the percolation properties from the Minimal Spanning Tree, finding roughly an order of magnitude improvement in the computer time required. We apply these statistics to Particle-Mesh simulations of large-scale structure formation. We consider purely scale-free Gaussian initial conditions ($P(k)\propto k^n$, with $n=-2,-1,0\mathrm{\&}+1$) in a critical density universe. We find in general the mass of the percolating cluster is a much better quantity by which to judge the onset of percolation than the length of the percolating cluster.