  A numerical semigroup $S$ is an additively-closed set of non-negative
integers, and a factorization of an element $n$ of $S$ is an expression of $n$
as a sum of generators of $S$. It is known that for a given numerical semigroup
$S$, the number of factorizations of $n$ coincides with a quasipolynomial (that
is, a polynomial whose coefficients are periodic functions of $n$). One of the
standard methods for computing certain semigroup-theoretic invariants involves
assembling a graph or simplicial complex derived from the factorizations of
$n$. In this paper, we prove that for two such graphs (which we call the
factorization support graph and the trade graph), the number of edges coincides
with a quasipolynomial function of $n$, and identify the degree, period, and
leading coefficient of each. In the process, we uncover a surprising geometric
connection: a combinatorially-assembled cubical complex that is homeomorphic to
real projective space.
