  Andrei et al. have shown in 2000 that the graph $\boldsymbol{\mathrm{C}}$ of
the Collatz function starting with root $8$ after the initial loop is an
infinite binary tree $\boldsymbol{A}(8)$. According to their result they gave a
reformulated version of the Collatz conjecture: the vertex set
$V(\boldsymbol{A}(8))=\mathbb{Z}^+$.
  In this paper an inverse Collatz function $\overrightarrow{C}$ with
eliminated initial loop is used as generating function of a Collatz graph
${\boldsymbol{\mathrm{C}}}_{\overrightarrow{C}}$. This graph can be considered
as the union of one forest that stems from sequences of powers of 2 with odd
start values and a second forest that is based on branch values $y=6k+4$ where
two Collatz sequences meet. A proof that the graph
${\boldsymbol{\mathrm{C}}}_{\overrightarrow{C}}(1)$ is an infinite binary tree
$\boldsymbol{A}_{\overrightarrow{C}}$ with vertex set
$V({\boldsymbol{A}}_{\overrightarrow{C}}(1))=\mathbb{Z}^+$ completes the paper.
