We will explain how to construct a spectral sequence, with E_1 term given by the graph homology of a graded algebra A, which converges to the homology of the graph configuration space graph configuration space of a simplicial space X. In the above, A is the cohomology algebra of X.

We will explain how to use homological perturbation theory to show that the values of higher differentials are given by the (matrix) Massey products of X. On one hand, this gives examples in which the spectral sequence does not degenerate at the E_1 term, and on the other we can conclude that it does degenerate for a formal space X, e.g. a compact Kahler manifold. In a sense, this generalizes and proves an earlier conjecture by Bendersky and Gitler, made in the in 1970s.

We will finish with a conjecture about graph homology of E-infinity algebras.