The Scattering Correspondence of a Graph

The CHY scattering equations on the moduli space M_{0,n} play an important role at the interface of particle physics and algebraic statistics. We present the scattering correspondence when the Mandelstam parameters are restricted to a fixed graph G on n vertices. This leads us to associate a partial compactification M_G of M_{0,n}, which yields a combinatorial formula for the maximum-likelihood degree of the graph. Of particular interest is a family of hypertrees known as the bipyramids, a special kind of non-planar MHV on-shell diagram.