Editing Hypergraph (section)

==Hypergraph drawing==
[[File:CircuitoDosMallas.png|thumb|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.]]
Although hypergraphs are more difficult to draw on paper than graphs, several researchers have studied methods for the visualization of hypergraphs.

In one possible visual representation for hypergraphs, similar to the standard [[graph drawing]] style in which curves in the plane are used to depict graph edges, a hypergraph's vertices are depicted as points, disks, or boxes, and its hyperedges are depicted as trees that have the vertices as their leaves.<ref>{{citation
 | last = Sander
 | first = G.
 | contribution = Layout of directed hypergraphs with orthogonal hyperedges
 | pages = 381–6
 | publisher = Springer
 | isbn = 978-3-540-24595-7
 | series = [[Lecture Notes in Computer Science]]
 | title = Proc. 11th International Symposium on Graph Drawing (GD 2003)
 | contribution-url = http://gdea.informatik.uni-koeln.de/585/1/hypergraph.ps
 | volume = 2912
 | year = 2003
 | title-link = International Symposium on Graph Drawing
 | access-date = 2010-05-17
 | archive-date = 2011-07-18
 | archive-url = https://web.archive.org/web/20110718171911/http://gdea.informatik.uni-koeln.de/585/1/hypergraph.ps
 | url-status = live
 }}.</ref><ref>{{citation
 | last1 = Eschbach
 | first1 = Thomas
 | last2 = Günther
 | first2 = Wolfgang
 | last3 = Becker
 | first3 = Bernd
 | issue = 2
 | journal = [[Journal of Graph Algorithms and Applications]]
 | pages = 141–157
 | title = Orthogonal hypergraph drawing for improved visibility
 | url = http://jgaa.info/accepted/2006/EschbachGuentherBecker2006.10.2.pdf
 | volume = 10
 | year = 2006
 | doi = 10.7155/jgaa.00122
 | doi-access = free
 | access-date = 2010-05-17
 | archive-date = 2011-07-18
 | archive-url = https://web.archive.org/web/20110718121435/http://jgaa.info/accepted/2006/EschbachGuentherBecker2006.10.2.pdf
 | url-status = live
 }}.</ref> If the vertices are represented as points, the hyperedges may also be shown as smooth curves that connect sets of points, or as [[simple closed curve]]s that enclose sets of points.<ref>{{citation
 | last = Mäkinen | first = Erkki
 | doi = 10.1080/00207169008803875
 | issue = 3
 | journal = International Journal of Computer Mathematics
 | pages = 177–185
 | title = How to draw a hypergraph
 | volume = 34
 | year = 1990}}.</ref><ref>{{citation
 | last1 = Bertault | first1 = François
 | last2 = Eades | first2 = Peter | title = Graph Drawing
 | author2-link = Peter Eades
 | contribution = Drawing hypergraphs in the subset standard
 | doi = 10.1007/3-540-44541-2_15
 | pages = 45–76
 | publisher = Springer-Verlag
 | series = Lecture Notes in Computer Science
 | volume = 1984
 | year = 2001| title-link = International Symposium on Graph Drawing
 | isbn = 978-3-540-41554-1
 | doi-access = free
 }}.</ref><ref>{{citation
 | last1 = Naheed Anjum | first1 = Arafat
 | last2 = Bressan | first2 = Stéphane
 | title = Database and Expert Systems Applications
 | contribution = Hypergraph Drawing by Force-Directed Placement
 | doi = 10.1007/978-3-319-64471-4_31
 | pages = 387–394
 | publisher = Springer International Publishing
 | series = Lecture Notes in Computer Science
 | volume = 10439
 | year = 2017| isbn = 978-3-319-64470-7
 }}.</ref>

[[File:Venn's four ellipse construction.svg|thumb|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).]]
In another style of hypergraph visualization, the subdivision model of hypergraph drawing,<ref>{{citation
 | last1 = Kaufmann | first1 = Michael
 | last2 = van Kreveld | first2 = Marc
 | last3 = Speckmann | first3 = Bettina | title = Graph Drawing
 | author3-link = Bettina Speckmann
 | contribution = Subdivision drawings of hypergraphs
 | doi = 10.1007/978-3-642-00219-9_39
 | pages = 396–407
 | publisher = Springer-Verlag
 | series = Lecture Notes in Computer Science
 | volume = 5417
 | year = 2009| title-link = International Symposium on Graph Drawing
 | isbn = 978-3-642-00218-2
 | doi-access = free
 }}.</ref> the plane is subdivided into regions, each of which represents a single vertex of the hypergraph. The hyperedges of the hypergraph are represented by contiguous subsets of these regions, which may be indicated by coloring, by drawing outlines around them, or both. An order-''n'' [[Venn diagram]], for instance, may be viewed as a subdivision drawing of a hypergraph with ''n'' hyperedges (the curves defining the diagram) and 2<sup>''n''</sup>&nbsp;−&nbsp;1 vertices (represented by the regions into which these curves subdivide the plane). In contrast with the polynomial-time recognition of [[planar graph]]s, it is [[NP-complete]] to determine whether a hypergraph has a planar subdivision drawing,<ref>{{citation
 | last1 = Johnson | first1 = David S. | author1-link = David S. Johnson
 | last2 = Pollak | first2 = H. O.
 | doi = 10.1002/jgt.3190110306
 | issue = 3
 | journal = [[Journal of Graph Theory]]
 | pages = 309–325
 | title = Hypergraph planarity and the complexity of drawing Venn diagrams
 | volume = 11
 | year = 2006}}.</ref> but the existence of a drawing of this type may be tested efficiently when the adjacency pattern of the regions is constrained to be a path, cycle, or tree.<ref>{{citation
 | last1 = Buchin | first1 = Kevin
 | last2 = van Kreveld | first2 = Marc
 | last3 = Meijer | first3 = Henk
 | last4 = Speckmann | first4 = Bettina
 | last5 = Verbeek | first5 = Kevin
 | title = Graph Drawing
 | contribution = On planar supports for hypergraphs
 | doi = 10.1007/978-3-642-11805-0_33
 | pages = 345–356
 | publisher = Springer-Verlag
 | series = Lecture Notes in Computer Science
 | volume = 5849
 | year = 2010| title-link = International Symposium on Graph Drawing
 | isbn = 978-3-642-11804-3
 | doi-access = free
 }}.</ref>

An alternative representation of the hypergraph called PAOH<ref name="paoh" /> is shown in the figure on top of this article. Edges are vertical lines connecting vertices. Vertices are aligned on the left. The legend on the right shows the names of the edges. It has been designed for dynamic hypergraphs but can be used for simple hypergraphs as well.