  We introduce a new correlation measure for tripartite pure states that we
call $G(A:B:C)$. The quantity is symmetric with respect to the subsystems $A$,
$B$, $C$, invariant under local unitaries, and is bounded from above by $\log
d_A d_B$. For random tensor network states, we prove that $G(A:B:C)$ is equal
to the size of the minimal tripartition of the tensor network, i.e., the
logarithmic bond dimension of the smallest cut that partitions the network into
three components with $A$, $B$, and $C$. We argue that for holographic states
with a fixed spatial geometry, $G(A:B:C)$ is similarly computed by the minimal
area tripartition. For general holographic states, $G(A:B:C)$ is determined by
the minimal area tripartition in a backreacted geometry, but a smoothed version
is equal to the minimal tripartition in an unbackreacted geometry at leading
order. We briefly discuss a natural family of quantities $G_n(A:B:C)$ for
integer $n \geq 2$ that generalize $G=G_2$. In holography, the computation of
$G_n(A:B:C)$ for $n>2$ spontaneously breaks part of a $\mathbb{Z}_n \times
\mathbb{Z}_n$ replica symmetry. This prevents any naive application of the
Lewkowycz-Maldacena trick in a hypothetical analytic continuation to $n=1$.
