  This paper studies the two-way butterfly network, a class of two-way
four-unicast networks. We first show that bidirectional links do not increase
the degrees of freedom for this network thus giving the first example for
networks, to the best of our knowledge, where bidirectional links do not
increase the degrees of freedom. Further, we see that sufficient caching at the
relays or increasing the number of antennas in the relays can double the
two-way degrees of freedom for butterfly network.
