  We define invariants for colored oriented spatial graphs by generalizing CM
invariants, which were defined via non-integral highest weight representations
of $U_q(sl_2)$. We apply the same method to define Yokota's invariants, and we
call these invariants Yokota type invariants. Then we propose a volume
conjecture of the Yokota type invariants of plane graphs which relates to
volumes of hyperbolic polyhedra corresponding to the graphs, and check it
numerically for some square pyramids and pentagonal pyramids.
