  The multiplexing gain (MUXG) of $K$-user interference channel (IC) with
partially connected interfering links is analyzed. The motivation for the
partially connected IC comes from the fact that not all interferences are
equally strong in practice. The MUXG is characterized as a function of the
number ($K$) of users and the number ($N \geq 1$) of interfering links. Our
analysis is mainly based on the interference alignment (IA) technique to
mitigate interference. Our main results are as follows: One may expect that
higher MUXG can be attained when some of interfering links do not exist.
However, when $N$ is odd and $K=N+2$, the MUXG is not increased beyond the
optimal MUXG of fully connected IC, which is $\frac{KM}{2}$. The number of
interfering links has no influence on the achievable MUXG using IA, but affects
the efficiency in terms of the number of required channel realizations: When
N=1 or 2, the optimal MUXG of the fully connected IC is achievable with a
finite number of channel realizations. In case of $N \geq 3$, however, the MUXG
of $\frac{KM}{2}$ can be achieved asymptotically as the number of channel
realizations tends to infinity.
