  We propose a new proof, as well as a generalization of Mirzakhani's recursion
for volumes of moduli spaces. We interpret those recursion relations in terms
of expectation values in Kontsevich's integral, i.e. we relate them to a Ribbon
graph decomposition of Riemann surfaces. We find a generalization of
Mirzakhani's recursions to measures containing all higher Mumford's kappa
classes, and not only kappa1 as in the Weil-Petersson case.
