  We compare the cohomology complex defined by Baranovsky and Sazdanovi\'{c},
that is the $E_{1}$ page of a spectral sequence converging to the homology of
the configuration space depending on a graph, with the rational model for the
configuration space given by Kriz and Totaro. In particular we generalize the
rational model to any graph and to an algebra over any field. We show that, in
the case of configuration spaces of point on a even dimensional manifold, the
dual of the Baranovsky and Sazdanovi\'{c}'s complex is quasi equivalent to this
generalized version of the Kriz's model.
