  Understanding the magnetism and its possible correlations to the topological
properties has emerged as a forefront and difficult topic in studying magnetic
Weyl semimetals. Co$_{3}$Sn$_{2}$S$_{2}$ is a newly discovered magnetic Weyl
semimetal with a kagome lattice of cobalt ions and has triggered intense
interest for rich fantastic phenomena. Here, we report the magnetic exchange
couplings of Co$_{3}$Sn$_{2}$S$_{2}$ using inelastic neutron scattering and two
density functional theory (DFT) based methods: constrained magnetism and
multiple-scattering Green's function methods. Co$_{3}$Sn$_{2}$S$_{2}$ exhibits
highly anisotropic magnon dispersions and linewidths below $T_{C}$, and
paramagnetic excitations above $T_{C}$. The spin-wave spectra in the
ferromagnetic ground state is well described by the dominant third-neighbor
"across-hexagon" $J_{d}$ model. Our density functional theory calculations
reveal that both the symmetry-allowed 120$^\circ$ antiferromagnetic orders
support Weyl points in the intermediate temperature region, with distinct
numbers and the locations of Weyl points. Our study highlights the important
role Co$_{3}$Sn$_{2}$S$_{2}$ can play in advancing our understanding of kagome
physics and exploring the interplay between magnetism and band topology.
