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 \& + 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 .