  We show how the Turaev--Viro invariant can be understood within the framework
of Chern--Simons theory with gauge group SU(2). We also describe a new
invariant for certain class of graphs by interpreting the triangulation of a
manifold as a graph consisiting of crossings and vertices with three lines. We
further show, for $S^3$ and $RP^3$, that the Turaev-Viro invariant is the
square of the absolute value of their respective partition functions in SU(2)
Chern--Simons theory and give a method of evaluating the later in a closed form
for lens spaces $L_{p,1}$.
