  Let $G=G_{n,k}$ denote the graph formed by placing points in a square of area
$n$ according to a Poisson process of density 1 and joining each pair of points
which are both $k$ nearest neighbours of each other. Then $G_{n,k}$ can be used
as a model for wireless networks, and has some advantages in terms of
applications over the two previous $k$-nearest neighbour models studied by
Balister, Bollob\'{a}s, Sarkar and Walters, who proved good bounds on the
connectivity models thresholds for both. However their proofs do not extend
straightforwardly to this new model, since it is now possible for edges in
different components of $G$ to cross. We get around these problems by proving
that near the connectivity threshold, edges will not cross with high
probability, and then prove that $G$ will be connected with high probability if
$k>0.9684\log n$, which improves a bound for one of the models studied by
Balister, Bollob\'{a}s, Sarkar and Walters too.
