  For a rational map $\phi$ from a metric graph $\varGamma$ to a tropical
projective space $\boldsymbol{TP^n}$ defined by a ratio of rational functions
$f_1, \ldots, f_{n + 1}$, an automorphism $\sigma$ of $\varGamma$ induces a
permutation of the coordinates of $\boldsymbol{TP^n}$ if $\{ f_1, \ldots, f_{n
+ 1} \}$ is $\langle \sigma \rangle$-invariant. Through this description, we
can realize the automorphism group of $\Gamma$ as ambient automorphism group
such as tropical projective general linear group, tropical general linear group
and $\boldsymbol{Z}$-linear transformation group of Euclidean space.
