  To any Feynman graph (with 2n edges) we can associate a hypersurface
X\subset\PP^{2n-1}. We study the middle cohomology H^{2n-2}(X) of such
hypersurfaces. S. Bloch, H. Esnault, and D. Kreimer (Commun. Math. Phys. 267,
2006) have computed this cohomology for the first series of examples, the wheel
with spokes graphs WS_n, n\geq 3. Using the same technique, we introduce the
generalized zigzag graphs and prove that W_5(H^{2n-2}(X))=\QQ(-2) for all of
them (with W_{*} the weight filtration). Next, we study primitively log
divergent graphs with small number of edges and the behavior of graph
hypersurfaces under the gluing of graphs.
