The superiority of the minimal spanning tree in percolation analyses of cosmological data sets

In this work we demonstrate the ability of the minimal spanning tree (MST) to duplicate the information contained within a percolation analysis for a point data set. We show how to construct the percolation properties from the MST, 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)~k^n, with n=-2, -1, 0 and +1] in a critical-density universe. We find, in general, that 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.