  Let a torus act on a compact oriented manifold $M$ with isolated fixed
points, with an additional mild assumption that its isotropy submanifolds are
orientable. We associate a signed labeled multigraph encoding the fixed point
data (weights and signs at fixed points and isotropy submanifolds) of the
manifold. We study operations on $M$ and its multigraph, (self) connected sum
and blow up, etc. When the circle group acts on a 6-dimensional $M$, we
classify such a multigraph by proving that we can convert it into the empty
graph by successively applying two types of operations. In particular, this
classifies the fixed point data of any such manifold. We prove this by showing
that for any such manifold, we can successively take equivariant connected sums
at fixed points with itself, $\mathbb{CP}^3$, and 6-dimensional analogue $Z_1$
and $Z_2$ of the Hirzebruch surfaces (and these with opposite orientations) to
a fixed point free action on a compact oriented 6-manifold. We also classify a
multigraph for a torus action on a 4-dimensional $M$.
