Average Degree of a Random Geometric Graph A set of $N$ points are distributed randomly on a unit square with uniform distribution. Two points $\mathbf{p}_i$ and $\mathbf{p}_j$ are said to be connected if $\|\mathbf{p}_i - \mathbf{p}_j\| \leq \delta$, where $0 < \delta < \sqrt2$.
What is the expected average degree ($2M/N$) of this graph?

The paper "Small-Worlds: Strong Clustering in Wireless Networks"  (http://arxiv.org/pdf/0706.1063.pdf) is indicating empirically that the average node degree $<k>$ is (or can be approximated by) $\frac{\Pi  r^2  n}{l^2}$ whereby two nodes are connected if they are within range $r$, $n$ is number of nodes, $l$ length of square.
