First, we extend the Otal's result for the trivial knot to the trivial
spatial graph, namely, we show that for any bridge tangle decomposing sphere
$S^2$ for a trivial spatial graph $\Gamma$, there exists a 2-sphere $F$ such
that $F$ contains $\Gamma$ and $F$ intersects $S^2$ in a single loop.

Next, we introduce two invariants for spatial graphs. As a generalization of
the bridge number for knots, we define the {\em bridge string number}
$bs(\Gamma)$ of a spatial graph $\Gamma$ as the minimal number of $|\Gamma\cap
S^2|$ for all bridge tangle decomposing sphere $S^2$. As a spatial version of
the representativity for a graph embedded in a surface, we define the {\em
representativity} of a spatial graph $\Gamma$ as \[
r(\Gamma)=\max_{F\in\mathcal{F}} \min_{D\in\mathcal{D}_F} |\partial D\cap
\Gamma|, \] where $\mathcal{F}$ is the set of all closed surfaces of positive
genus containing $\Gamma$ and $\mathcal{D}_F$ is the set of all compressing
disks for $F$ in $S^3$. Then we show that the representativity $r(\Gamma)$ does
not exceed the half of the bridge string number $bs(\Gamma)$. In particular, if
$\Gamma$ is a knot, then $r(\Gamma)\le b(\Gamma)$, where $b(\Gamma)$ denotes
the bridge number.