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Cosmological studies of large-scale structure have relied on two-pointstatistics, not fully exploiting the rich structure of the cosmic web. In thispaper we show how to capture some of this cosmic web information by using theminimum spanning tree (MST), for the first time using it to estimatecosmological parameters in simulations. Discrete tracers of dark matter such asgalaxies, $N$-body particles or haloes are used as nodes to construct a uniquegraph, the MST, that traces skeletal structure. We study the dependence of theMST on cosmological parameters using haloes from a suite of COLA simulationswith a box size of $250\ h^{-1}{\rm Mpc}$, varying the amplitude of scalarfluctuations $\left(A_{\rm s}\right)$, matter density $\left(\Omega_{\rmm}\right)$, and neutrino mass $\left(\sum m_{\nu}\right)$. The power spectrum$P$ and bispectrum $B$ are measured for wavenumbers between $0.125$ and $0.5$$h{\rm Mpc}^{-1}$, while a corresponding lower cut of $\sim12.6$ $h^{-1}{\rmMpc}$ is applied to the MST. The constraints from the individual methods arefairly similar but when combined we see improved $1\sigma$ constraints of $\sim17\%$ ($\sim 12\%$) on $\Omega_{\rm m}$ and $\sim 12\%$ ($\sim 10\%$) on$A_{\rm s}$ with respect to $P$ ($P+B$) thus showing the MST is providingadditional information. The MST can be applied to current and futurespectroscopic surveys (BOSS, DESI, Euclid, PSF, WFIRST, and 4MOST) in 3D andphotometric surveys (DES and LSST) in tomographic shells to constrainparameters and/or test systematics.

Beyond two-point statistics: using the minimum spanning tree as a tool for cosmology