  In this paper, we provide the structure of Hopf graphs associated to pairs
$(G, \mathfrak{r})$ consisting of groups $G$ together with ramification datas
$\mathfrak{r}$ and their Leavitt path algebras. Consequently, we characterize
the Gelfand-Kirillov dimension, the stable rank, the purely infinite simplicity
and the existence of a nonzero finite dimensional representation of the Leavitt
path algebra of a Hopf graph via properties of ramification data $\mathfrak{r}$
and $G$.
