If you think of a plain old physical map, say the map of a territory, you can imagine a function that transforms it into a graph:
- Every entity of interest in the map is a node. The node's location is the entity's location.
- Edges can be links to the nearest nodes.
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Edges can be assigned through other principles; they are just relations that are interesting.
If you want to relate more than two things with the same relation, that makes it a hypergraph.
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I've never considered hypergraphs. Can you break it down a little more?
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I'm no expert :) But:
They are a generalization of graphs: graphs have nodes connected by lines, in such a way that a line goes from precisely one node to precisely another. Hypergraphs are more like a set of subsets: they are good for modeling tertiary or higher relations.
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Applications of hypergraphs are actually relatively rare, I think? At least I don't remember covering them in algorithms and data structures classes, whereas simple graphs are all over the place (they are very useful).
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Yet recently I ran into them because is into them; they are part of his theory of Geometric Unity, although I don't want to give you the impression I understand it or anything :)
He's got a great podcast that touches on this with .
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These are the weak recent references I have about them in my cache :)
(If you are famous and I @ you: please excuse the intrusion, I just try to include platform references when referring to well known entities, and that's @-ing people on Twitter).
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I am personally unsure about how/why to use hypergraphs; for the problems I've been modelling simple graphs seem sufficient. Note you can model a relationship between n nodes in graphs by adding a "hub" node that represents the relationship, call it R, and linking every n with R.
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But... perhaps we should ask , if he's interested (see screenshot resulting from my searching for hypergraph applications).
mathoverflow.net/questions/1375
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lol i was about to jump in and say “hypergraphs are absurdly general objects” but i see past-me already did it, good job past-me
seriously tho they are