  We give a Conway-Gordon type formula for invariants of knots and links in a
spatial complete four-partite graph $K_{3,3,1,1}$ in terms of the square of the
linking number and the second coefficient of the Conway polynomial. As an
application, we show that every rectilinear spatial $K_{3,3,1,1}$ contains a
nontrivial Hamiltonian knot.
