  We describe a generalization of GKM theory for actions of arbitrary compact
connected Lie groups. To an action satisfying the non-abelian GKM conditions we
attach a graph encoding the structure of the non-abelian 1-skeleton, i.e., the
subspace of points with isotopy rank at most one less than the rank of the
acting group. We show that the algebra structure of the equivariant cohomology
can be read off from this graph. In comparison with ordinary abelian GKM
theory, there are some special features due to the more complicated structure
of the non-abelian 1-skeleton.
