  We prove several claims made by Kontsevich about the orbifold Euler
characteristic of the three types of graph homology introduced by him. For this
purpose, first we develop a simplified version of the Feynman diagram method,
which requires integrals in one variable only, to obtain the generating
functions as asymptotic expansions of certain Gaussian integrals. Finally,
following Penner, we relate these integrals to the gamma function in order to
compute the individual coefficients of the generating functions.
