  We construct effective GKM $T^3$-actions with connected stabilizers on the
total spaces of the two $S^2$-bundles over $S^6$ with identical GKM graphs.
This shows that the GKM graph of a simply-connected integer GKM manifold with
connected stabilizers does not determine its homotopy type. We complement this
by a discussion of the minimality of this example: the homotopy type of integer
GKM manifolds with connected stabilizers is indeed encoded in the GKM graph for
smaller dimensions, lower complexity, or lower number of fixed points.
Regarding geometric structures on the new example, we find an almost complex
structure which is invariant under the action of a subtorus. In addition to the
minimal example, we provide an analogous example where the torus actions are
Hamiltonian, which disproves symplectic cohomological rigidity for Hamiltonian
integer GKM manifolds.
