  Let $G$ be a connected graph with vertex set $\{0,1,2,...,n\}$. We allow $G$
to have multiple edges and loops. In this paper, we give a characterization of
external activity by some parameters of $G$-parking functions. In particular,
we give the definition of the bridge vertex of a $G$-parking function and
obtain an expression of the Tutte polynomial $T_G(x,y)$ of $G$ in terms of
$G$-parking functions. We find the Tutte polynomial enumerates the $G$-parking
function by the number of the bridge vertices.
