  We introduce a new class of quantum and classical correlation measures by
generalizing the reflected entropy to multipartite states. We define the new
measures for quantum systems in one spatial dimension. For quantum systems
having gravity duals, we show that the holographic duals of these new measures
are various types of minimal surfaces consist of different entanglement wedge
cross sections. One special generalized reflected entropy is $\Delta_R$, with
the holographic dual proportional to the so called multipartite entanglement
wedge cross section $\Delta_W$ defined before. We then perform a large $c$
computation of $\Delta_R$ and find precise agreement with the holographic
computation of 2$\Delta_{W}$. This agreement shows another candidate $\Delta_R$
as the dual of $\Delta_W$ and also supports our holographic conjecture of the
new class of generalized reflected entropies.
