Graph homology and graph configuration spaces

If R is a commutative ring, M a compact R-oriented manifold and G a finite graph without loops or multiple edges, we consider the graph configuration space MG and a Bendersky–Gitler type spectral sequence converging to the homology H∗(M, R). We show that its E1 term is given by the graph cohomology complex CA(G) of the graded commutative algebra A = H∗(M, R) and its higher differentials are obtained from the Massey products of A, as conjectured by Bendersky and Gitler for the case of a complete graph G. Similar results apply to the spectral sequence constructed from an arbitrary finite graph G and a graded commutative DG algebra A.