hypergraph
Sign in to saveframe|An example of an undirected hypergraph, with X = \{v_1, v_2, v_3, v_4, v_5, v_6, v_7\} and E = \{e_1,e_2,e_3,e_4\} = \{\{v_1, v_2, v_3\}, \{v_2,v_3\}, \{v_3,v_5,v_6\}, \{v_4\}\}. This hypergraph has order 7 and size 4. Here, edges do not just connect two vertices but several, and are represented by colors. alt=PAOH visualization of a hypergraph|thumb|Alternative representation of the hypergraph reported in the figure above, called PAOH. 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
Article
22 sectionsContents
- Applications
- Generalizations of concepts from graphs
- Hypergraph drawing
- Hypergraph coloring
- Properties of hypergraphs
- Related hypergraphs
- Incidence matrix
- Incidence graph
- Adjacency matrix
- Cycles
- Berge cycles
- Tight cycles
- α-acyclicity
- Isomorphism, symmetry, and equality
- Examples
- Symmetry
- Partitions
- Further generalizations
- See also
- Notes
- References
- External links
frame|An example of an undirected hypergraph, with X = \{v_1, v_2, v_3, v_4, v_5, v_6, v_7\} and E = \{e_1,e_2,e_3,e_4\} = \{\{v_1, v_2, v_3\}, \{v_2,v_3\}, \{v_3,v_5,v_6\}, \{v_4\}\}. This hypergraph has order 7 and size 4. Here, edges do not just connect two vertices but several, and are represented by colors. alt=PAOH visualization of a hypergraph|thumb|Alternative representation of the hypergraph reported in the figure above, called PAOH. 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. thumb|An example of a directed hypergraph, with X = \{1, 2, 3, 4, 5, 6\} and E = \{a_1, a_2, a_3, a_4, a_5\} = \{\{(1, 2)\}, \{(2, 3)\}, \{(3, 1)\}, \{(2, 4), (3, 5)\}, \{(3, 6), (5, 6)\}\}
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.