  The discovery of polynomial invariants of knots and links, ignited by V. F.
R. Jones, leads to the formulation of polynomial invariants of spatial graphs.
The Yamada polynomial, one of such invariants, is frequently utilized for
practical distinguishment of spatial graphs. Especially for $\theta$-curves,
the polynomial is an ambient isotopy invariant after a normalization. On the
other hand, to each $\theta$-curve, a 3-component link can be associated as an
ambient isotopy invariant. The benefit of associated links is that invariants
of links can be utilized as invariants of $\theta$-curves.
  In this paper we investigate the relation between the normalized Yamada
polynomial of $\theta$-curves and the Jones polynomial of their associated
links, and show that the two polynomials are equivalent for brunnian
$\theta$-curves as a corollary. For our purpose the Jaeger polynomial of
spatial graphs is observed, a specialization of which is equivalent to the
Yamada polynomial.
