  The information content of the minimum spanning tree (MST), used to capture
higher-order statistics and information from the cosmic web, is compared to
that of the power spectrum for a $\nu\Lambda$CDM model. The measurements are
made in redshift space using haloes from the Quijote simulation of mass $\geq
3.2\times 10^{13}\,h^{-1}{\rm M}_{\odot}$ in a box of length $L_{\rm
box}=1\,h^{-1}{\rm Gpc}$. The power spectrum multipoles (monopole and
quadrupole) are computed for Fourier modes in the range $0.006 < k < 0.5\,
h{\rm Mpc}^{-1}$. For comparison the MST is measured with a minimum length
scale of $l_{\min}\simeq13\,h^{-1}{\rm Mpc}$. Combining the MST and power
spectrum allows for many of the individual degeneracies to be broken; on its
own the MST provides tighter constraints on the sum of neutrino masses
$M_{\nu}$ and cosmological parameters $h$, $n_{\rm s}$, and $\Omega_{\rm b}$
but the power spectrum alone provides tighter constraints on $\Omega_{\rm m}$
and $\sigma_{8}$. Combined we find constraints that are a factor of two (or
greater) on all parameters with respect to the power spectrum (for $M_{\nu}$
there is a factor of four improvement). These improvements appear to be driven
by the MST's sensitivity to small scale clustering, where the effect of
neutrino free-streaming becomes relevant, and high-order statistical
information in the cosmic web. The MST is shown to be a powerful tool for
cosmology and neutrino mass studies, and therefore could play a pivotal role in
ongoing and future galaxy redshift surveys (such as DES, DESI, \emph{Euclid},
and Rubin-LSST).
