Beyond two-point statistics: using the minimum spanning tree as a tool
  for cosmology
  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 COLA simulations
with a box size of $250\ h^{-1}{\rm Mpc}$, varying the amplitude of scalar
fluctuations $\left(A_{\rm s}\right)$, matter density $\left(\Omega_{\rm
m}\right)$, 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 $\sim12.6$ $h^{-1}{\rm
Mpc}$ is applied to the MST. The constraints from the individual methods are
fairly similar but when combined we see improved $1\sigma$ constraints of $\sim
17\%$ ($\sim 12\%$) on $\Omega_{\rm m}$ and $\sim 12\%$ ($\sim 10\%$) on
$A_{\rm s}$ with respect to $P$ ($P+B$) thus showing the MST is 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.
