  The goal of this paper is to express the extended Goldman symplectic
structure on the $SL(n)$ character variety of a punctured Riemann surface in
terms of Fock-Goncharov coordinates. The associated symplectic form has integer
coefficients expressed via the inverse of the Cartan matrix. The main technical
tool is a canonical two-form associated to a flat graph connection. We discuss
the relationship between the extension of the Goldman Poisson structure and the
Poisson structure defined by Fock and Goncharov. We elucidate the role of the
Rogers' dilogarithm as generating function of the symplectomorphism defined by
a graph transformation.
