Title: The cohomology of the full directed graph complex,
Abstract: In his seminal paper "Formality conjecture", M. Kontsevich introduced a graph
complex $GC_{1ve}$ closely connected with the problem of constructing a
formality quasi-isomorphism for Hochschild cochains. In this paper, we express
the cohomology of the full directed graph complex explicitly in terms of the
cohomology of $GC_{1ve}$. Applications of our results include a recent work by
the first author which completely characterizes homotopy classes of formality
quasi-isomorphisms for Hochschild cochains in the stable setting.