The DoF of Two-way Butterfly Networks
  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. 
Mehdi Ashraphijuo and Vaneet Aggarwal and Xiaodong Wang
cs.IT math.IT