This procedure finds the nearest neighbor to every point. The nearest neighbor for a point is simply the point that is closest to it. A nearest-neighbor connections matrix does not have to be symmetric, because the nearest neighbor of one point is not necessarily the neighbor of the other point. Furthermore, a nearest-neighbor network does not have to completely span the points; usually it will not. One also has the option of specifying the number of neighbors to connect; the standard default is one, which is the traditional nearest-neighbor network, but one can choose to connect the closest two neighbors, or closest three, etc.
Example of a nearest-neighbor network. Points are only connected to their (single) nearest neighbor; multiple connections to a single point occur when one point is the nearest neighbor of multiple other points. Note that the network is not spanning (you cannot travel a path from one point to any other point).