I am reading Kontsevich' famous paper on deformation quantization of Poisson manifolds. In section 1.4.2 on page 4 he gives the general formula for the star product associated to a Poisson structure on $\mathbb{R}^n$ up to and including order 2. Now I have noticed that in the second order term, terms of the form (for example) $\partial_k(\alpha^{ij})\partial_i(\alpha^{kl})\partial_j(f)\partial_l(g)$, and I do not understand why. This term would correspond to the following graph:

I.e., there is an edge going from 1 to 2 and an edge going from 2 to 1; all such terms would be of the form $\partial_j(\alpha^{i\cdot})\partial_i(\alpha^{j\cdot})\times\text{derivatives of $f$ and $g$}$, and none of them occur in his formula in section 1.4.2. As far as I can see, such graphs would be admissible under the rules on page 5 in the paper. I have yet to find a way to evaluate the weight associated to this kind of graphs, but at least the integrand of the weight for the graph above is nonzero. So my question is:

Why do terms of this form not contribute to the second order term of the star product?