hypergraph - definition. What is hypergraph
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Hypergraph         
  • This [[circuit diagram]] can be interpreted as a drawing of a hypergraph in which four vertices (depicted as white rectangles and disks) are connected by three hyperedges drawn as trees.
  • An example of a directed hypergraph, with
<math>X = \{1, 2, 3, 4, 5, 6\}</math> and
<math>E = \{a_1, a_2, a_3, a_4, a_5\} = </math>
<math>\{(\{1\}, \{2\}),</math>
<math>(\{2\}, \{3\}),</math>
<math>(\{3\}, \{1\}),</math>
<math>(\{2, 3\}, \{4, 5\}),</math>
<math>(\{3, 5\}, \{6\})\}</math>.
  • url-status=live}}</ref> Edges are vertical lines connecting vertices. V7 is an isolated vertex. Vertices are aligned to the left. The legend on the right shows the names of the edges.
  • An order-4 Venn diagram, which can be interpreted as a subdivision drawing of a hypergraph with 15 vertices (the 15 colored regions) and 4 hyperedges (the 4 ellipses).
GENERALIZATION OF A GRAPH IN WHICH GENERALIZED EDGES MAY CONNECT MORE THAN TWO NODES
Host graph; Gaifman graph; Primal graph (hypergraphs); Dual hypergraph; Hypergraphs; Hypergraph acyclicity; Alpha-acyclic; Hypergraph (mathematics); Directed hypergraph; Hyper-graph
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.
Bipartite hypergraph         
In graph theory, the term bipartite hypergraph describes several related classes of hypergraphs, all of which are natural generalizations of a bipartite graph.
Packing in a hypergraph         
In mathematics, a packing in a hypergraph is a partition of the set of the hypergraph's edges into a number of disjoint subsets such that no pair of edges in each subset share any vertex. There are two famous algorithms to achieve asymptotically optimal packing in k-uniform hypergraphs.