  T. K\'{a}lm\'{a}n (A version of Tutte's polynomial for hypergraphs, Adv.
Math. 244 (2013) 823-873.) introduced the interior and exterior polynomials
which are generalizations of the Tutte polynomial $T(x,y)$ on plane points
$(1/x,1)$ and $(1,1/y)$ to hypergraphs. The two polynomials are defined under a
fixed ordering of hyperedges, and are proved to be independent of the ordering
using techniques of polytopes. In this paper, similar to the Tutte's original
proof we provide a direct and elementary proof for the well-definedness of the
interior and exterior polynomials of hypergraphs.
