  Moduli spaces of hyperbolic surfaces with geodesic boundary components of
fixed lengths may be endowed with a symplectic structure via the Weil-Petersson
form. We show that, as the boundary lengths are sent to infinity, the
Weil-Petersson form converges to a piecewise linear form first defined by
Kontsevich. The proof rests on the observation that a hyperbolic surface with
large boundary lengths resembles a graph after appropriately scaling the
hyperbolic metric. We also include some applications to intersection theory on
moduli spaces of curves.
