Hypergraphs can arise as Bruhat-Tits buildings of groups, see e.g. here.

Some real world applications: In this article the authors list some applications to biology. Their nice starting example is that if one wants to model a chemical reaction one can write A-->B for a process which transforms A into B and see this as the edge of a graph. Sometimes such a process only works in the presence of some catalyzer (A+C-->B+C), making it a relation between three instead of two ingredients and giving a 2-edge of a hypergraph.

Hypergraphs can arise as Bruhat-Tits buildings of groups, see e.g.

• Alireza Sarveniazi. "Explicit construction of a Ramanujan (n1,n2,…,nd−1)-regular hypergraph." Duke Math. J. 139 (1) 141 - 171, 15 July 2007. doi:10.1215/S0012-7094-07-13913-9.

Some real world applications:

In the article

• Klamt S, Haus U-U, Theis F (2009) Hypergraphs and Cellular Networks. PLoS Comput Biol 5(5): e1000385. doi:10.1371/journal.pcbi.1000385

the authors list some applications to biology. Their nice starting example is that if one wants to model a chemical reaction one can write A-->B for a process which transforms A into B and see this as the edge of a graph. Sometimes such a process only works in the presence of some catalyzer (A+C-->B+C), making it a relation between three instead of two ingredients and giving a 2-edge of a hypergraph.

Hypergraphs can arise as Bruhat-Tits buildings of groups, see e.g. here.

Some real world applications: In this article the authors list some applications to biology. Their nice starting example is that if one wants to model a chemical reaction one can write A-->B for a process which transforms A into B and see this as the edge of a graph. Sometimes such a process only works in the presence of some catalyzer (A+C-->B+C), making it a relation between three instead of two ingredients and giving a 2-edge of a hypergraph.

Hypergraphs can arise as Bruhat-Tits buildings of groups, see e.g. here.

Some real world applications: In this article the authors list some applications to biology. Their nice starting example is that if one wants to model a chemical reaction one can write A-->B for a process which transforms A into B and see this as the edge of a graph. Sometimes such a process only works in the presence of some catalyzer (A+C-->B+C), making it a relation between three instead of two ingredients and giving a 2-edge of a hypergraph.