Related Graphs
The relative neighborhood graph is an example of a lens-based beta skeleton. It is a subgraph of the Delaunay triangulation. In turn, the Euclidean minimum spanning tree is a subgraph of it, from which it follows that it is a connected graph.
The Urquhart graph, the graph formed by removing the longest edge from every triangle in the Delaunay triangulation, was originally proposed as a fast method to compute the relative neighborhood graph. Although the Urquhart graph sometimes differs from the relative neighborhood graph it can be used as an approximation to the relative neighborhood graph.
Read more about this topic: Relative Neighborhood Graph
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“The near explains the far. The drop is a small ocean. A man is related to all nature. This perception of the worth of the vulgar is fruitful in discoveries. Goethe, in this very thing the most modern of the moderns, has shown us, as none ever did, the genius of the ancients.”
—Ralph Waldo Emerson (1803–1882)