Tropical Moduli Space of Rational Graphically Stable Curves

We study moduli spaces of rational graphically stable tropical curves and a refinement given by radial alignment. Given a complete multipartite graph $\mathrm{\Gamma }$, the moduli space of radially aligned $\mathrm{\Gamma }$-stable tropical curves can be given the structure of a balanced fan. This fan structure coincides with the Bergman fan of the cycle matroid of $\mathrm{\Gamma }$.