I am teaching a course involving hypergraphs. I would like to have a physical analogy/motivating problem for hypergraphs similarly to how the Seven Bridges of Königsberg motivate graphs. Can you help me out?
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2$\begingroup$ Hypergraphs are extremely general objects (sets of subsets, basically), and somehow slightly less "visual" than graphs are, so it's hard to give something that feels very concrete. $\endgroup$– Sam HopkinsCommented Mar 22, 2021 at 16:38
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3$\begingroup$ But for something very classic: the "Happy Ending Problem" (en.wikipedia.org/wiki/Happy_ending_problem) can be resolved using hypergraph Ramsey numbers (for specifically 3-uniform hypergraphs). $\endgroup$– Sam HopkinsCommented Mar 22, 2021 at 16:40
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Imagine a virus spreads between individuals when they are in the same room. Then, consider the hypergraph where each hyperedge is the set of individuals who happened to be together in a same room. It may represent the network on which the virus spreads (although adding time information seems needed).
More generally, since hypergraphs are equivalent to bipartite graphs, they model many real-world situations.
Another example is the co-authoring hypergraph, in which each paper leads to an hyperedge between its authors. It is used to study the structure of scientific fields.
In recommender systems, one also considers hypergraphs over products, where hyperedges are sets of products bought by a same client.
The wikipedia hypergraph page has some pointers to various applications.
Also, there is a great discussion here, that mentions many math-oriented examples: What are the applications of hypergraphs
I hope this helps, good luck with your course!
answered Mar 22, 2021 at 14:41