In the mathematical theory of hypergraphs, a hedgehog is a 3-uniform hypergraph defined from an integer parameter
vertices,
of which can be labeled by the integers from
of which can be labeled by unordered pairs of these integers.
For each pair of integers
in this range, it has a hyperedge whose vertices have the labels
Equivalently it can be formed from a complete graph by adding a new vertex to each edge of the complete graph, extending it to an order-3 hyperedge.
[1][2] The properties of this hypergraph make it of interest in Ramsey theory.