In joint work with Pratik Misra and Pardis Semnani, we study the spanning tree generating function of a graph. When the graph is chordal, we show that the corresponding statistical model has maximum likelihood degree one; when the graph is a cycle on n vertices, we show that the corresponding statistical model has maximum likelihood degree equal to the nth Eulerian number. These results support our conjecture that the spanning tree generating function is a homaloidal polynomial if and only if the graph is chordal. We also provide an algebraic formulation for the defining equations of these models. I will begin by introducing graphical models and homaloidal polynomials (background knowledge in algebraic statistics is not required).