  We express the hairy graph complexes computing the rational homotopy groups
of long embeddings (modulo immersion) of R^m in R^n as "decorated" graph
complexes associated to certain representations of the outer automorphism
groups of free groups. This interpretation gives rise to a natural spectral
sequence, which allows us to shed some light on the structure of the hairy
graph cohomology. We also explain briefly the connection to the deformation
theory of the little discs operads and some conclusions that this brings.
