![]() | This ![]() It is of interest to the following WikiProjects: | ||||||||||
|
![]() |
Daily pageviews of this article
A graph should have been displayed here but
graphs are temporarily disabled. Until they are enabled again, visit the interactive graph at
pageviews.wmcloud.org |
This article needs the notation unifying between what I've just added and the rest. Rich Farmbrough 20:54, 26 August 2005 (UTC)
Someone not logged in just changed S(X) (as the set of subsets of X) to P(X). I'll consider it as a vandalism (specially because he or she didn't log in), but there's a reason for the exchange? -- FernandoAires 11:54, 22 August 2006 (UTC)
I would just like to point out that the graph depicted on the page is not really a hypergraph. Since node 7 is not a part of any edge, but is in the nodeset of the graph, taking the dual will lead to an empty edge, not allowed according to the definition. I think also that Berge stated in his book that the superunion of the edges should be equal to the nodeset. /Jonatan —Preceding unsigned comment added by 130.243.173.106 ( talk) 17:52, August 30, 2007 (UTC)
What are hypergraphs used for?
RJFJR (
talk)
21:01, 22 February 2010 (UTC)
For instance, in knowledge representation, by people citing Wikipedia for reference. Therefore, I am annoyed by such vandalism.--
Efidetum (
talk)
19:45, 17 May 2010 (UTC)
The NYTimes had an example of a hypergraph, in describing relations among 2013 Oscar nominees: http://www.nytimes.com/interactive/2013/02/20/movies/among-the-oscar-contenders-a-host-of-connections.html (well, I guess that's a multi-hypergraph, since it has repeated edges). That example is behind a paywall (kinda); it'd be nice to have a [link to] a nice visual javascripty example like this, near the top of the article. — Preceding unsigned comment added by Not-just-yeti ( talk • contribs) 18:22, 21 February 2013 (UTC)
I don't think the text under the circuit diagram example is true:
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.
If you take the circuit components as vertices, you lose information about which terminals the wires/hyperedges are connected to. For example, the hypergraph of that circuit would be the same if the voltage source E was flipped around, but the circuit would most definitely not be the same (unless you also negated the voltage provided by E). Does anyone agree or disagree with me here? Hypergraph ( talk) 01:48, 22 December 2010 (UTC)
There should probably be some mention of how a directed hypergraph is defined (i.e. a prescription for directed edges). — Preceding unsigned comment added by 50.99.141.142 ( talk) 13:37, 12 June 2011 (UTC)
I second this. Also, some mention of a petri net and it's connection to hypergraphs. It also seems like undirected hypergraphs have some connection to the formal definition of a topological space and a well-ordered set, but I don't see mention of these. — Preceding unsigned comment added by 146.186.131.40 ( talk) 20:53, 1 November 2012 (UTC)
This paragraph was just added to the article (and reverted by me):
One difference between the two concepts is that in a mesh it may be important that edges are shared by exactly two facets (something that affects me as I've just designed my first 3d print!). — Tamfang ( talk) 23:20, 24 May 2012 (UTC)
I changed "link" (the alternate name of a hyperedge) to "edge", which is much more common in my experience. Maybe "link" can be added back, but it means something else in graph theory (a "link" is an edge that isn't a loop), and I'm not aware of its being used much (or at all) by hypergraph theorists. Zaslav ( talk) 03:31, 10 July 2012 (UTC)
The comment(s) below were originally left at Talk:Hypergraph/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
Needs material on history, motivation, applications, current state of research, and relations with graphs and graph theory. Tompw ( talk) 15:24, 4 January 2007 (UTC) |
Last edited at 22:58, 19 April 2007 (UTC). Substituted at 02:13, 5 May 2016 (UTC)
The article is just too verbose.
Regarding the Definition, index set is not used to explain anything in the article as far as I've scanned it. If the whole purpose is to introduce the notion of an index set, the heading title might be apt with "terminology", but it seems unmotivated. A clear definition is lacking, anyway, if that should be in the lede, the lede is far too long to be clear. The index set doesn't help to clarify anything, because x_i remains undefined (unbound?), even if was defined. I propose:
although I am not sure if self-adjacent vertices are actually allowed or not as it currently stands. Certainly, the article is messy anyhow, following some comments on the talk page. I'm just curious if we can slowly improve it. 91.66.71.216 ( talk) 20:33, 14 June 2017 (UTC)
The example directed graph is wrong as is all talk about it. An undirected hypergraph is *not* a a set of vertices and a set of edges which is a subset of P(V). The edges are pairs, just as with a graphs. The way undirected hypergraph was defined was simply as a subset of P(V) but that is just a subset of P(V) and not a hypergraph. A hypergraph is a graph on hypervertices(which are elements of P(V)). That is, edges in the graph on the hypervertices are hyperedges in the hypergraph. E should look something like E = {(e1,e2),(e1,e3)} where ek is the sets given in the picture. Edges can be thought of as lines/edges/connections/morphisms between subsets. 173.173.45.154 ( talk) 11:39, 27 February 2023 (UTC)
I was also confused between the mismatch between the intro paragraph which mentions pairs and the example on the right which doesn't have any pairs. So I'd welcome those edits! Either way, what's an authoritative source setting out this definition? Golightlys ( talk) 17:24, 25 July 2024 (UTC)
There is a formal definition of "directed hypergraph" but no formal definition of "hypergraph". Saying that is a generalization of "graph" only helps a little; for example it doesn't say if edges can be the same (as each other), which impacts whether every bicoloured graph can be considered the incidence graph of a hypergraph. McKay ( talk) 06:17, 17 March 2023 (UTC)
![]() | This ![]() It is of interest to the following WikiProjects: | ||||||||||
|
![]() |
Daily pageviews of this article
A graph should have been displayed here but
graphs are temporarily disabled. Until they are enabled again, visit the interactive graph at
pageviews.wmcloud.org |
This article needs the notation unifying between what I've just added and the rest. Rich Farmbrough 20:54, 26 August 2005 (UTC)
Someone not logged in just changed S(X) (as the set of subsets of X) to P(X). I'll consider it as a vandalism (specially because he or she didn't log in), but there's a reason for the exchange? -- FernandoAires 11:54, 22 August 2006 (UTC)
I would just like to point out that the graph depicted on the page is not really a hypergraph. Since node 7 is not a part of any edge, but is in the nodeset of the graph, taking the dual will lead to an empty edge, not allowed according to the definition. I think also that Berge stated in his book that the superunion of the edges should be equal to the nodeset. /Jonatan —Preceding unsigned comment added by 130.243.173.106 ( talk) 17:52, August 30, 2007 (UTC)
What are hypergraphs used for?
RJFJR (
talk)
21:01, 22 February 2010 (UTC)
For instance, in knowledge representation, by people citing Wikipedia for reference. Therefore, I am annoyed by such vandalism.--
Efidetum (
talk)
19:45, 17 May 2010 (UTC)
The NYTimes had an example of a hypergraph, in describing relations among 2013 Oscar nominees: http://www.nytimes.com/interactive/2013/02/20/movies/among-the-oscar-contenders-a-host-of-connections.html (well, I guess that's a multi-hypergraph, since it has repeated edges). That example is behind a paywall (kinda); it'd be nice to have a [link to] a nice visual javascripty example like this, near the top of the article. — Preceding unsigned comment added by Not-just-yeti ( talk • contribs) 18:22, 21 February 2013 (UTC)
I don't think the text under the circuit diagram example is true:
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.
If you take the circuit components as vertices, you lose information about which terminals the wires/hyperedges are connected to. For example, the hypergraph of that circuit would be the same if the voltage source E was flipped around, but the circuit would most definitely not be the same (unless you also negated the voltage provided by E). Does anyone agree or disagree with me here? Hypergraph ( talk) 01:48, 22 December 2010 (UTC)
There should probably be some mention of how a directed hypergraph is defined (i.e. a prescription for directed edges). — Preceding unsigned comment added by 50.99.141.142 ( talk) 13:37, 12 June 2011 (UTC)
I second this. Also, some mention of a petri net and it's connection to hypergraphs. It also seems like undirected hypergraphs have some connection to the formal definition of a topological space and a well-ordered set, but I don't see mention of these. — Preceding unsigned comment added by 146.186.131.40 ( talk) 20:53, 1 November 2012 (UTC)
This paragraph was just added to the article (and reverted by me):
One difference between the two concepts is that in a mesh it may be important that edges are shared by exactly two facets (something that affects me as I've just designed my first 3d print!). — Tamfang ( talk) 23:20, 24 May 2012 (UTC)
I changed "link" (the alternate name of a hyperedge) to "edge", which is much more common in my experience. Maybe "link" can be added back, but it means something else in graph theory (a "link" is an edge that isn't a loop), and I'm not aware of its being used much (or at all) by hypergraph theorists. Zaslav ( talk) 03:31, 10 July 2012 (UTC)
The comment(s) below were originally left at Talk:Hypergraph/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
Needs material on history, motivation, applications, current state of research, and relations with graphs and graph theory. Tompw ( talk) 15:24, 4 January 2007 (UTC) |
Last edited at 22:58, 19 April 2007 (UTC). Substituted at 02:13, 5 May 2016 (UTC)
The article is just too verbose.
Regarding the Definition, index set is not used to explain anything in the article as far as I've scanned it. If the whole purpose is to introduce the notion of an index set, the heading title might be apt with "terminology", but it seems unmotivated. A clear definition is lacking, anyway, if that should be in the lede, the lede is far too long to be clear. The index set doesn't help to clarify anything, because x_i remains undefined (unbound?), even if was defined. I propose:
although I am not sure if self-adjacent vertices are actually allowed or not as it currently stands. Certainly, the article is messy anyhow, following some comments on the talk page. I'm just curious if we can slowly improve it. 91.66.71.216 ( talk) 20:33, 14 June 2017 (UTC)
The example directed graph is wrong as is all talk about it. An undirected hypergraph is *not* a a set of vertices and a set of edges which is a subset of P(V). The edges are pairs, just as with a graphs. The way undirected hypergraph was defined was simply as a subset of P(V) but that is just a subset of P(V) and not a hypergraph. A hypergraph is a graph on hypervertices(which are elements of P(V)). That is, edges in the graph on the hypervertices are hyperedges in the hypergraph. E should look something like E = {(e1,e2),(e1,e3)} where ek is the sets given in the picture. Edges can be thought of as lines/edges/connections/morphisms between subsets. 173.173.45.154 ( talk) 11:39, 27 February 2023 (UTC)
I was also confused between the mismatch between the intro paragraph which mentions pairs and the example on the right which doesn't have any pairs. So I'd welcome those edits! Either way, what's an authoritative source setting out this definition? Golightlys ( talk) 17:24, 25 July 2024 (UTC)
There is a formal definition of "directed hypergraph" but no formal definition of "hypergraph". Saying that is a generalization of "graph" only helps a little; for example it doesn't say if edges can be the same (as each other), which impacts whether every bicoloured graph can be considered the incidence graph of a hypergraph. McKay ( talk) 06:17, 17 March 2023 (UTC)