  The interior polynomial is an invariant of bipartite graphs, and a part of
the HOMFLY polynomial of a special alternating link coincides with the interior
polynomial of the Seifert graph of the link. We extend the interior polynomial
to signed bipartite graphs, and we show that, in the planar case, it is equal
to a part of the HOMFLY polynomial of a naturally associated link. We also
establish some other, more basic properties of this new notion. This leads to
new identities involving the original interior polynomial.
