  We explore the interplay between interference, cooperation and connectivity
in heterogeneous wireless interference networks. Specifically, we consider a
4-user locally-connected interference network with pairwise clustered decoding
and show that its degrees of freedom (DoF) are bounded above by 12/5.
Interestingly, when compared to the corresponding fully connected setting which
is known to have 8/3 DoF, the locally connected network is only missing
interference-carrying links, but still has lower DoF, i.e., eliminating these
interference-carrying links reduces the DoF. The 12/5 DoF outer bound is
obtained through a novel approach that translates insights from interference
alignment over linear vector spaces into corresponding sub-modularity
relationships between entropy functions.
