  In this note we investigate under which conditions the dual of the flow
polytope (henceforth referred to as the `dual flow polytope') of a quiver is
k-neighborly, for generic weights near the canonical weight. We provide a lower
bound on k, depending only on the edge connectivity of the underlying graph,
for such weights. In the case where the canonical weight is in fact generic, we
explicitly determine a vertex presentation of the dual flow polytope. Finally,
we specialize our results to the case of complete, bipartite quivers where we
show that the canonical weight is indeed generic, and are able to provide an
improved bound on k. Hence, we are able to produce many new examples of
high-dimensional, k-neighborly polytopes.
