Numerical semigroups are of great interest in factorization theory due to their highly non-unique factorizations. Given an element n in a numerical semigroup, various graphs can be constructed using the multiple factorizations of n as vertices. In this work, we explore the topological structure of the factorization support graph of n and the minimal trade graphs of n. We first characterize the number of edges in these graphs and then use this characterization to show that the rank of their fundamental groups is a quasipolynomial in n. Additionally, we present data and conjectures on the topological structure of the nonedges in the factorization support graph and the cliques in the minimal trade graphs.
