Is the number of neighbors in ad hoc wireless networks a good indicator of connectivity?

Finding the minimum necessary number of neighbors required to provide full connectivity in wireless networks is an important problem which has been addressed by several researchers. In this paper, we show that the number of neighbors is a meaningful parameter to describe the connectivity only if the ad hoc wireless network has a perfectly uniform node distribution, i.e., the nodes lie approximately on the vertices of a regular grid. It is also shown that, in the case of nonuniform ad hoc wireless networks the number of neighbors becomes less meaningful. In this case, we propose instead, as indicator of the connectivity level, a reasonable measure of the likelihood of broadcast percolation for a given average number of neighbors.