  We study the modular graph functions introduced by Green, Russo, Vanhove in
the context of type II superstring scattering amplitudes of 4 gravitons on a
torus. In particular we describe a method to algorithmically compute the
coefficients in their expansion at the cusp in terms of conical sums. We
perform explicit computations for 3-graviton functions, which naturally suggest
to conjecture that only single-valued multiple zeta values appear.
