Supersymmetry and cohomology of graph complexes

I describe a combinatorial construction of the cohomology classes in compactified moduli spaces of curves \widehat{Z}_I\in H^{*}( \bar{M}_{g,n}) starting from the following data: Z/2Z-graded finite-dimensional associative algebra equipped with odd scalar product and an odd compatible derivation I, whose square is nonzero in general, I²≠ 0. As a byproduct I obtain a new combinatorial formula for products of ψ -classes, ψ _i=c₁( T_{p_i}^{*}) , in the cohomology H^{*}( \bar{M}_{g,n}).