The talk will be based on the recent article by M. Bökstedt and E. Minuz "Graph cohomologies and rational homotopy type of configuration spaces" arXiv:1904.01452v2. We will compare the cohomology complex defined by Baranovsky and Sazdanović, that is the E1 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 will generalize the rational model to any graph and to an algebra over any field. We will show that the dual of the Baranovsky and Sazdanović's complex is quasi equivalent to this generalized version of the Kriz's model.