  Let $K_n$ be a complete graph with $n$ vertices. An embedding of $K_n$ in
$S^3$ is called a spatial $K_n$-graph. Knots in a spatial $K_n$-graph
corresponding to simple cycles of $K_n$ are said to be constituent knots. We
consider the case $n=4$. The boundary of an oriented band surface with zero
Seifert form, constructed for a spatial $K_4$, is a four-component associated
link. There are obtained relations between normalized Yamada and Jaeger
polynomials of spatial graphs and Jones polynomials of constituent knots and
the associated link.
