An r-uniform friendship hypergraph is an r-uniform hypergraph with the property for any set X of r vertices there is a unique vertex c_{X} so that (X-v)⋃{c_{X}} is a hyperedge for every vertex v in X. c_{X} is called the completion of X.

A 2-uniform friendship hypergraph is exacly a friendship graph.

Friendship hypergraphs were introduced (for r=3) by Sós in

Sós proved that an n vertex 3-uniform friendship hypergraph with a universal friend is equivalent to a Steiner triple system on n-1 vertices.

This result is easily generalized to other values of r.

Some years later, the first five examples of 3-uniform friendship hypergraphs were found in:

^{k} vertices, k=3,4,5, . . ., in:

And we find a 4-uniform friendship hypergraph on 9 vertices.

In this file we list the edges of some friendship hypergraphs.

A 2-uniform friendship hypergraph is exacly a friendship graph.

Friendship hypergraphs were introduced (for r=3) by Sós in

- V. T. Sós, Some remarks on the connection of graph theory, finite geometry and block designs.

Colloquio Internationale sulle Teorie Combinatorie, 223-233, (1976).

Sós proved that an n vertex 3-uniform friendship hypergraph with a universal friend is equivalent to a Steiner triple system on n-1 vertices.

This result is easily generalized to other values of r.

Some years later, the first five examples of 3-uniform friendship hypergraphs were found in:

- S. G. Hartke and J. Vandenbussche, On a question of Sós about 3-uniform friendship hypergraphs.

Journal Combinatorial Designs, vol. 16, 253-261 (2008).

- L. K. Jřrgensen and A. A. Sillasen, On the existence of friendship hypergraphs,

To appear in: Journal of Combinatorial Designs. DOI: 10.1002/jcd.21388

Preprint R-2013-03

And we find a 4-uniform friendship hypergraph on 9 vertices.

In this file we list the edges of some friendship hypergraphs.