  We consider the Wilson line networks of the Chern-Simons $3d$ gravity theory
with toroidal boundary conditions which calculate global conformal blocks of
degenerate quasi-primary operators in torus $2d$ CFT. After general discussion
that summarizes and further extends results known in the literature we
explicitly obtain the one-point torus block and two-point torus blocks through
particular matrix elements of toroidal Wilson network operators in irreducible
finite-dimensional representations of $sl(2,\mathbb{R})$ algebra. The resulting
expressions are given in two alternative forms using different ways to treat
multiple tensor products of $sl(2,\mathbb{R})$ representations: (1) $3mj$
Wigner symbols and intertwiners of higher valence, (2) totally symmetric tensor
products of the fundamental $sl(2,\mathbb{R})$ representation.
