Thank you, I had no idea about "penny graphs". It reminded me of Tousaint's [Spheres of Influence graph](https://www.semanticscholar.org/paper/The-Sphere-of-Influence-Graph%3A-Theory-and-Toussaint-Emirates/233385b0ae6207ac3f99c361dfb5b00e2c58c57d) (two nodes are connected if the (hyper)spheres that are formed by taking the node as the center and their nearest neighbour as a radius, are intersecting). These are used in pattern recognition a lot as they form a "signature" that links a set of landmarks. I have also seen it long time ago refered to as "α-graphs" (alpha graphs), but I could not find a reference with that name anymore.
I hadn’t heard of the spheres of influence graph, but I agree that it’s a similar concept. Thanks for the reference to the literature! An interesting special case of the spheres of influence graph might be if all nearest neighbours in the graph are the same distance apart, as would be the case for various well-known periodic lattices.
Thank you, I had no idea about "penny graphs". It reminded me of Tousaint's [Spheres of Influence graph](https://www.semanticscholar.org/paper/The-Sphere-of-Influence-Graph%3A-Theory-and-Toussaint-Emirates/233385b0ae6207ac3f99c361dfb5b00e2c58c57d) (two nodes are connected if the (hyper)spheres that are formed by taking the node as the center and their nearest neighbour as a radius, are intersecting). These are used in pattern recognition a lot as they form a "signature" that links a set of landmarks. I have also seen it long time ago refered to as "α-graphs" (alpha graphs), but I could not find a reference with that name anymore.
I hadn’t heard of the spheres of influence graph, but I agree that it’s a similar concept. Thanks for the reference to the literature! An interesting special case of the spheres of influence graph might be if all nearest neighbours in the graph are the same distance apart, as would be the case for various well-known periodic lattices.