  Let G be a Lie group and Q a quiver with relations. In this paper, we define
G-valued representations of Q which directly generalize G-valued
representations of finitely generated groups. Although as G-spaces, the
G-valued quiver representations are more general than G-valued representations
of finitely generated groups, we show by collapsing arrows that their quotient
spaces are equivalent. We then establish a general criterion for the moduli of
G-valued quiver representations with relations to admit a strong deformation
retraction to a compact quotient by pinching vertices on the quiver. This
provides two different generalizations of main results in our previous work.
Lastly, we establish quiver theoretic conditions for the moduli spaces of
GL(n,C) and SL(n,C)-valued quiver representations to embed into traditional
moduli spaces of quiver representations having constant dimension vector.
