  We make explicit computations in the formal symplectic geometry of Kontsevich
and determine the Euler characteristics of the three cases, namely commutative,
Lie and associative ones, up to certain weights.From these, we obtain some
non-triviality results in each case. In particular, we determine the integral
Euler characteristics of the outer automorphism groups Out F_n of free groups
for all n <= 10 and prove the existence of plenty of rational cohomology
classes of odd degrees. We also clarify the relationship of the commutative
graph homology with finite type invariants of homology 3-spheres as well as the
leaf cohomology classes for transversely symplectic foliations. Furthermore we
prove the existence of several new non-trivalent graph homology classes of odd
degrees. Based on these computations, we propose a few conjectures and problems
on the graph homology and the characteristic classes of the moduli spaces of
graphs as well as curves.
