Cosmological studies of large-scale structure have relied on two-point statistics, not fully exploiting the rich structure of the cosmic web. In this paper we show how to capture some of this cosmic web information by using the minimum spanning tree (MST), for the first time using it to estimate cosmological parameters in simulations. Discrete tracers of dark matter such as galaxies, N-body particles or haloes are used as nodes to construct a unique graph, the MST, that traces skeletal structure. We study the dependence of the MST on cosmological parameters using haloes from a suite of COmoving Lagrangian Acceleration (COLA) simulations with a box size of 250 h−1Mpc, varying the amplitude of scalar fluctuations (As), matter density (Ωm), and neutrino mass (∑mν). The power spectrum P and bispectrum B are measured for wavenumbers between 0.125 and 0.5 hMpc−1, while a corresponding lower cut of ∼12.6 h−1Mpc is applied to the MST. The constraints from the individual methods are fairly similar but when combined we see improved 1σ constraints of ∼17 per cent (∼12 per cent) on Ωm and ∼12 per cent (∼10 per cent) on As with respect to P (P + B) thus showing the MST is providing additional information. The MST can be applied to current and future spectroscopic surveys (BOSS, DESI, Euclid, PSF, WFIRST, and 4MOST) in 3D and photometric surveys (DES and LSST) in tomographic shells to constrain parameters and/or test systematics
