  In this paper, we provide degree distributions for $AB$ random geometric
graphs, in which points of type $A$ connect to the closest $k$ points of type
$B$. The motivating example to derive such degree distributions is in 5G
wireless networks with multi-connectivity, where users connect to their closest
$k$ base stations. It is important to know how many users a particular base
station serves, which gives the degree of that base station. To obtain these
degree distributions, we investigate the distribution of area sizes of the
$k-$th order Voronoi cells of $B$-points. Assuming that the $A$-points are
Poisson distributed, we investigate the amount of users connected to a certain
$B$-point, which is equal to the degree of this point. In the simple case where
the $B$-points are placed in an hexagonal grid, we show that all $k$-th order
Voronoi areas are equal and thus all degrees follow a Poisson distribution.
However, this observation does not hold for Poisson distributed $B$-points, for
which we show that the degree distribution follows a compound Poisson-Erlang
distribution in the 1-dimensional case. We then approximate the degree
distribution in the 2-dimensional case with a compound Poisson-Gamma degree
distribution and show that this one-parameter fit performs well for different
values of $k$. Moreover, we show that for increasing $k$, these degree
distributions become more concentrated around the mean. This means that
$k$-connected $AB$ random graphs balance the loads of $B$-type nodes more
evenly as $k$ increases. Finally, we provide a case study on real data of base
stations. We show that with little shadowing in the distances between users and
base stations, the Poisson distribution does not capture the degree
distribution of these data, especially for $k>1$. However, under strong
shadowing, our degree approximations perform quite good even for these
non-Poissonian location data.
