What is "hypertree"

n. (context maths English) A form of hypergraph based on trees

Hypertree may refer to one of the following:

• Hypertree, a special kind of hypergraph, e.g., a hypergraph without cycles
• Hypertree network, a type of computer/communication network topology
• Hyperbolic tree, a visualization method for hierarchical structures

A hypergraph H is called a hypertree if it admits a host graph T such that T is a tree. In other words H is a hypertree if there exists a tree T such that every hyperedge of H is the set of vertices of a connected subtree of T. Hypertrees have also been called arboreal hypergraphs or tree hypergraphs.

Every tree T is itself a hypertree: T itself can be used as the host graph, and every edge of T is a subtree of this host graph. Therefore, hypertrees may be seen as a generalization of the notion of a tree for hypergraphs.