  First, we extend Otal's result for the trivial knot to trivial spatial
graphs, 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 non-trivial 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 containing
$\Gamma$ and $\mathcal{D}_F$ is the set of all compressing disks for $F$ in
$S^3$. Then we show that for a non-trivial spatial graph $\Gamma$, \[
\displaystyle r(\Gamma)\le \frac{bs(\Gamma)}{2}. \] In particular, if $\Gamma$
is a knot, then $r(\Gamma)\le b(\Gamma)$, where $b(\Gamma)$ denotes the bridge
number. This generalizes Schubert's result on torus knots.
