  Xue and Kumar have established that the number of neighbors required for
connectivity of wireless networks with N uniformly distributed nodes must grow
as log(N), and they also established that the actual number required lies
between 0.074log(N) and 5.1774log(N). In this short paper, by recognizing that
connectivity results for networks where the nodes are distributed according to
a Poisson point process can often be applied to the problem for a network with
N nodes, we are able to improve the lower bound. In particular, we show that a
network with nodes distributed in a unit square according to a 2D Poisson point
process of parameter N will be asymptotically disconnected with probability one
if the number of neighbors is less than 0.129log(N). Moreover, similar number
of neighbors is not enough for an asymptotically connected network with N nodes
uniformly in a unit square, hence improving the lower bound.
