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tokens: snapshots (see Table 3 ) – this is different from dark matter particles whose number count is constant across redshift and simulations. Figure 9. The MST constructed on halo catalogues derived from the HZ (blue), LZ (orange), and LN (green) N -body simulations. From left to right are the MST statistics: degree ( d ), edge length ( l ), branch length ( b ), and branch shape ( s ). They are plotted from top to bottom according to snapshots at redshift 1, 0.5, and 0. Corresponding shaded areas show the jackknife uncertainties in the measurements. The distribution of the MST statistics are indistinguishable from each other at all redshifts, demonstrating that we should expect to see similar lines of degeneracy as power spectrum. Note . To mitigate this issue, for each redshift we match the number of haloes to the lowest number found in the simulations (thus always matching the number of haloes found in the LZ simulations). For those with more haloes, we simply select the most massive haloes. In Fig. 9 , we find no real noticeable difference in the statistics suggesting the degeneracies of the MST may be similar to that found for P ( k ). 6 COMPARING THE SENSITIVITY TO COSMOLOGY OF POWER SPECTRUM, BISPECTRUM, AND THE MINIMUM SPANNING TREE In this section, we compare the sensitivities to cosmological parameters of power spectrum P ( k ), bispectrum B ( k 1 , k 2 , k 3 ), and MST, measured on the same halo catalogues, to establish whether the MST can improve parameter constraints. Specifically, we compare the constraints on A s , Ω m , and ∑ m ν for 10 sets of mock simulations. To obtain reliable posterior distributions for the three methods and their joint constraints, we would normally run a Markov Chain Monte Carlo (MCMC) using an analytic expression for the data vector. However, the MST statistics cannot be obtained analytically and hence have to be obtained from simulations. P ( k ), B ( k 1 , k 2 , k 3 ), and MST are therefore estimated from a grid of simulations in parameter space. To limit the noise in the estimates of the theory we take the mean of five simulations rather than just one at each point in parameter space. Additionally, since our simulation grid is rather sparse we use Gaussian process (GP) regression to interpolate the data vector. Finally, we use a corrected likelihood function (see Sellentin Heavens 2016 ; Jeffrey Abdalla 2018 ) which accounts for the use of an estimated covariance matrix. 6.1 COLA simulation suites A suite of COLA (Tassev, Zaldarriaga Eisenstein 2013 ) simulations were constructed using the mg-picola software (Winther et al. 2017 , an extension to l-picola by Howlett, Manera Percival 2015 ) which, among other things, can model the effects of massive neutrinos (Wright, Winther Koyama 2017 ). This allowed us to generate N -body-like simulations relatively cheaply (in terms of computation time), albeit by sacrificing accuracy at small scales. All simulations are run in boxes of lengths 250 , with 256 3