The relative neighborhood network is a connection scheme in which two points are connected if the intersection between the two circles (or spheres in three dimensions) centered on the two points with radii equal to the distance between the points does not contain any additional points. Mathematically, another way to think of this is that points i and j are connected if the distance between them, dij, is less than the maximum of dik and djk for all other points k.
Connect i and j if dij < Maximum(dik , djk) for all k
Diagram explaining the concept of the relative neighborhood network.
This network may produce closed loops but will not produce connections which cross each other. The minimum spanning tree is a subset of the relative neighborhood network.
Example of a relative neighborhood network.