Definitions for hypergraph
hy·per·graph

WiktionaryRate this definition:3.0 / 2 votes

1. hypergraphnoun

   A generalization of a graph, in which edges can connect any number of vertices.

WikipediaRate this definition:0.0 / 0 votes

1. Hypergraph

   In mathematics, a hypergraph is a generalization of a graph in which an edge can join any number of vertices. In contrast, in an ordinary graph, an edge connects exactly two vertices. Formally, an undirected hypergraph H {\displaystyle H} is a pair H = ( X , E ) {\displaystyle H=(X,E)} where X {\displaystyle X} is a set of elements called nodes or vertices, and E {\displaystyle E} is a set of non-empty subsets of X {\displaystyle X} called hyperedges or edges. Therefore, E {\displaystyle E} is a subset of P ( X ) ∖ { ∅ } {\displaystyle {\mathcal {P}}(X)\setminus \{\emptyset \}} , where P ( X ) {\displaystyle {\mathcal {P}}(X)} is the power set of X {\displaystyle X} . The size of the vertex set is called the order of the hypergraph, and the size of edges set is the size of the hypergraph. A directed hypergraph differs in that its hyperedges are not sets, but ordered pairs of subsets of X {\displaystyle X} , with each pair's first and second entries constituting the tail and head of the hyperedge respectively. While graph edges connect only 2 nodes, hyperedges connect an arbitrary number of nodes. However, it is often desirable to study hypergraphs where all hyperedges have the same cardinality; a k-uniform hypergraph is a hypergraph such that all its hyperedges have size k. (In other words, one such hypergraph is a collection of sets, each such set a hyperedge connecting k nodes.) So a 2-uniform hypergraph is a graph, a 3-uniform hypergraph is a collection of unordered triples, and so on. An undirected hypergraph is also called a set system or a family of sets drawn from the universal set. Hypergraphs can be viewed as incidence structures. In particular, there is a bipartite "incidence graph" or "Levi graph" corresponding to every hypergraph, and conversely, most, but not all, bipartite graphs can be regarded as incidence graphs of hypergraphs. Hypergraphs have many other names. In computational geometry, an undirected hypergraph may sometimes be called a range space and then the hyperedges are called ranges. In cooperative game theory, hypergraphs are called simple games (voting games); this notion is applied to solve problems in social choice theory. In some literature edges are referred to as hyperlinks or connectors.The collection of hypergraphs is a category with hypergraph homomorphisms as morphisms.

WikidataRate this definition:0.0 / 0 votes

1. Hypergraph

   In mathematics, a hypergraph is a generalization of a graph in which an edge can connect any number of vertices. Formally, a hypergraph is a pair where is a set of elements called nodes or vertices, and is a set of non-empty subsets of called hyperedges or edges. Therefore, is a subset of, where is the power set of . While graph edges are pairs of nodes, hyperedges are arbitrary sets of nodes, and can therefore contain an arbitrary number of nodes. However, it is often desirable to study hypergraphs where all hyperedges have the same cardinality; a k-uniform hypergraph is a hypergraph such that all its hyperedges have size k. So a 2-uniform hypergraph is a graph, a 3-uniform hypergraph is a collection of unordered triples, and so on. A hypergraph is also called a set system or a family of sets drawn from the universal set X. The difference between a set system and a hypergraph is in the questions being asked. Hypergraph theory tends to concern questions similar to those of graph theory, such as connectivity and colorability, while the theory of set systems tends to ask non-graph-theoretical questions, such as those of Sperner theory.

How to pronounce hypergraph?

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   British

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   Australian

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How to say hypergraph in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of hypergraph in Chaldean Numerology is: 4

2. Pythagorean Numerology

   The numerical value of hypergraph in Pythagorean Numerology is: 5

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References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Hypergraph
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Hypergraph
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=hypergraph