  The Hankel matrix of type B Narayana polynomials was proved to be totally
positive by Wang and Zhu, and independently by Sokal. Pan and Zeng raised the
problem of giving a planar network proof of this result. In this paper, we
present such a proof by constructing a planar network allowing negative
weights, applying the Lindstr\"om-Gessel-Viennot lemma and establishing an
involution on the set of nonintersecting families of directed paths.
