  Recent studies have demonstrated that measures of tripartite entanglement can
probe data characterizing topologically ordered phases to which bipartite
entanglement is insensitive. Motivated by these observations, we compute the
reflected entropy and logarithmic negativity, a mixed state entanglement
measure, in tripartitions of bosonic topological orders using the anyon
diagrammatic formalism. We consider tripartitions in which three subregions
meet at trijunctions and tetrajunctions. In the former case, we find a
contribution to the negativity which distinguishes between Abelian and
non-Abelian order while in the latter, we find a distinct universal
contribution to the reflected entropy. Finally, we demonstrate that the
negativity and reflected entropy are sensitive to the $F$-symbols for
configurations in which we insert an anyon trimer, for which the Markov gap,
defined as the difference between the reflected entropy and mutual information,
is also found to be non-vanishing.
