# Directed hypergraph

There are many ways to define directed hypergraphs. More precisely, there are many ways to define directed hyperedges (or hyperarcs). A quite general definition taken from ^{[1]} is the following.

Given a finite node set *V*, a **directed hyperedge** (or **hyperarc**) above *V* is an ordered pair *(T,H)* of disjoint subsets of *V*. The set *T* is the **tail set** of the hyperarc, while *H* is called the **head set** of the hyperarc. A **directed hypergraph** is a pair *(V,A)*, where *V* is a finite node set and *A* is a set of hyperarcs above *V*.

When studying connectivity properties of directed hypergraphs, we can assume that neither the tail set, nor the head set is empty in a hyperarc. Sometimes the notion "directed hypergraph" is used for the restricted case where each hyperarc has only one head (called **B-graphs** in ^{[1]}).

## References

- ↑
^{1.0}^{1.1}G. Gallo, G. Longo, S. Nguyen, S. Pallottino,*Directed hypergraphs and applications*, DOI link, Citeseer link.