hüperedge

Hyperedge is a term used in mathematics, particularly in the field of hypergraphs, to describe a generalized concept of an edge. In a standard graph, an edge connects exactly two vertices. A hyperedge, however, can connect any number of vertices, from one to all of the vertices in the hypergraph. This makes hypergraphs a more flexible structure for modeling complex relationships where connections can involve multiple entities simultaneously.

The vertices connected by a hyperedge are often referred to as the "endpoints" or "members" of that hyperedge. A hypergraph is formally defined as a pair (V, E), where V is a set of vertices and E is a set of hyperedges, where each hyperedge is a subset of V. This definition allows for a wide range of structures to be represented, such as social networks where a group of people are interacting, or computer science applications like database schemas or circuit designs.

The study of hypergraphs and hyperedges allows for the analysis of more intricate and multi-way relationships than traditional graph theory. Various algorithms and properties have been developed for hypergraphs, extending concepts like connectivity, paths, and cycles to this generalized setting. The flexibility of hyperedges makes them a powerful tool for modeling real-world phenomena that cannot be adequately captured by simple pairwise connections.