Three new statistical methods and a smoothing procedure for objectively examining large-scale structure with minimal spanning trees are described. These statistics are then applied to three illustrative data sets: the Southern Sky Redshift Survey, a gravitationally evolved model for the galaxy distribution, and a Poisson distribution. The structures in each case are compared statistically. The observations are clearly different from the Poisson case, and are consistent with the gravitational model to within uncertainties of about 5 per cent; more extensive data will provide greater discrimination among models. Our velocity-edgelength correlation is particularly promising in this regard.