On the Euler characteristic of the commutative graph complex and the top weight cohomology of Mg

We prove an asymptotic formula for the Euler characteristic of Kontsevich's commutative graph complex. This formula implies that the total amount of commutative graph homology grows super-exponentially with the rank and, via a theorem of Chan, Galatius, and Payne, that the dimension of the top weight cohomology of the moduli space of curves, Mg, grows super-exponentially with the genus g.