  Magnetic skyrmion crystals are traditionally associated with
non-centrosymmetric crystal structures; however, it has been demonstrated that
skyrmion crystals can be stabilized by competing interactions in
centrosymmetric crystals. To understand and optimize the physical responses
associated with topologically-nontrivial skyrmion textures, it is important to
quantify their magnetic interactions by comparing theoretical predictions with
spectroscopic data. Here, we present neutron diffraction and spectroscopy data
on the centrosymmetric skyrmion material GdRu$_2$Si$_2$, and show that the key
spectroscopic features can be explained by the magnetic interactions calculated
using density-functional theory calculations. We further show that the
recently-proposed 2-$\mathbf{q}$ "topological spin stripe" structure yields
better agreement with our data than a 1-$\mathbf{q}$ helical structure, and
identify how the magnetic structure evolves with temperature.
