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I don't think this page should be merged into graph theory. It was deliberately created to list definitions. Charles Matthews 16:41, 21 Mar 2005 (UTC)
This page is 30K of minor definitions. The idea is to have many redirects to it, rather than one page for each small definition. That is what a glossary page is supposed to do. Clearly 30K is too much to put into graph theory, which should give a broad introduction only.
So, I really don't see what the problem is with this. There are quite a few other examples, e.g. general topology and glossary of general topology.
Charles Matthews 20:38, 21 Mar 2005 (UTC)
OK, it seems that the correct idea is to merge graph (mathematics) into graph theory. But this page is fine as it is. Charles Matthews 20:41, 21 Mar 2005 (UTC)
As you know, we are all free to edit here as we see fit. That being said, it is more helpful to be more explicit. Charles Matthews 10:02, 22 Mar 2005 (UTC)
I think (as a newbie to graph theory) that we should remember who our audience is. It is me. I was directed to the glossary by several of the pages, because I thought I would get a better grasp of the term that was being defined on another page. What I found was a very incomplete definition that was disjointed from the supporting terms and concepts. For a glossary (which is typically a collection of disjointed definitions) to be useful, it should contain concepts which are easy to understand on their own, without having to understand the rest of the glossary. Otherwise, I, the learner, end up skipping back and forth between concepts trying to piece together a picture of what is being said. When I do that, I am essentially creating my own encyclopedia article in my mind in order to construct the full picture of the concept. But what if I don't have some of the pieces? As a learner of new information, it would be much better to have someone break down the knowledge ontologically into the correct sequence or taxonomy of ideas so that one idea builds upon the other. A glossary is a cheap imitation of doing that and should be reserved for more disjointed kinds of understanding, like quickly finding the definitions of acronyms used in telecommunications or something like that.
What I would like to see is each idea more fully developed to include separate illustrations to provide examples of each type of graph element. The concepts are much easier to understand when you have that kind of visual map presented to you. We are talking about graphs, here, so more graphs are better. Each graph should have more explicit instructions on how we are explaining it, by using colors and numbers, perhaps, to highlight various sections. That's just my two cents worth. TimIngalls 22:58, 15 November 2006 (UTC)
It seems to me that no definition on this page should incorporate a term that is defined later on the page. It should be that any term that requires another term as part of its definition should come after the other term is defined, so that someone with no knowledge of graph theory reading the page from top to bottom would never have to stop and say "Oh, I don't even know what that means," and have to go search for it before continuing. Thus, the section on trees should come after the section on connectivity because trees and subtrees are defined to be connected.
The other option is to put everything in alphabetical order so that if someone does have to look up another term in the definition they won't have to search, but this is a huge change.-- Quintopia 09:17, 25 October 2006 (UTC)
Under Direction an arc is defined to de directed from the head to the tail. This is just the opposite of the definition in Graph (mathematics). There, the edge is directed from x to y, where x is the tail and y is the head. Who's wrong?
Hi! I put to discussion what is the direction of the link between A and B, if it is written that "A is linked to B". Is it A->B or B->A? I'm not a native speaker of English, and this issue is hard for me to decide. I feel that A->B is appropriate for "A is linked to B", however also for "A links to B", and "A is linked to B" seems to be the passive form of "B links to A".. Is there a consensus on this, or could you refer me a book or scientific paper where this is explicitly defined? It would be also nice if this could make it into the article. Ron85 01:43, 5 February 2007 (UTC)
what's this definition of knots? it should be written if there is a link with knots of knots theory. and it should be explained more what are they and what they mean and what they imply! achab
This is not a term from graph theory. It doesn't match at all the concept of knot in knot theory. This brings much confusion, because links between graph and know theories do exist. The term has popped in books about "(Social) Network analysis", but with distinct definitions (some of them being sloppy). And finally, this term is useless because given definition simply describes a (weakly) connected component. 62.23.57.18 ( talk) 19:47, 14 January 2013 (UTC)egery
I find the definition of "minor" given here to be incomprehensible. What on earth does "every edge in E2 corresponds to a path (disjoint from all other such paths) in G1 such that every vertex in V1 is in one or more paths, or is part of the injection from V1 to V2" mean? I suggest defining "edge contraction" first then defining "minor" like at Minor (graph theory). 202.45.98.61 12:43, 13 June 2006 (UTC)
The discussion above regarding whether there needs to be a glossary or not could
For example, (a,b) is the edge from the vertex a to the vertex b, and ((a,b),c) would be an edge from the edge (a,b) to the vertex c. 217.83.100.240 13:55, 28 September 2006 (UTC)How is a graph called, where edges might also be vertices?
I think it is extremely helpful to have a glossary page. Thank you to whoever started this. I found a small problem, however, with the formula for the length of a walk (open, l=n-1; closed, l=n; n is number of vertices visited). It doesn't work for the example given directly below it. I believe this formula would work for a trail, but it doesn't work for a walk that has repeated edges. Of course you could decompose each walk into trails and then apply the formula, and that should work. I should mention that I am merely a lowly undergraduate, and I could be wrong about all this. If so, boy won't my face be red. Anywho, great page. -Jesse Supina, U of L (still don't know how that signature thing works)
I was taught by Doug West 20 years ago that the edge was "incident" the node and vice versa, so that one spoke of adjacent nodes (sharing an edge) but co-incident edges (sharing a node). The article combines these concepts, calling edges adjacent if they share a node. The two concepts are not dual. If G is a graph the line graph of G, styled L(G), has as nodes the edges of G and they are adjacent nodes of L(G) if they are co-incident edges of G. G is called a line graph if it is the line graph of some graph H. Not all graphs are line graphs. There is a forbidden subgraph characterization: G is a line graph just in case it does not contain as subgraph any of a list of nine little graphs.
Perhaps the nomenclatural distinction has evaporated in the interim, but I hope not, since the logical one certainly hasn't. In any case I propose "line graph" as candidate glossary entry. Lewis Goudy 66.82.51.210 01:32, 5 January 2007 (UTC)
I propose we split some of this material into an article List of graphs, which would list links to many or all of the specific kinds of graphs in Category:Graphs and Category:Graph families, plus bundle together a bunch of dicdefs for things like "path graphs", "caterpillar graphs", "lobster graphs", "gear graphs", "web graphs", and so on. (Those would all become redirects to the new page.) However, I can't do the page split all by myself; I'll start it tonight, if all goes well, and any help in adding definitions to List of graphs will be greatly appreciated. -- Quuxplusone 01:47, 18 January 2007 (UTC)
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-- CopyToWiktionaryBot 15:23, 1 February 2007 (UTC)
The shopping list of textbook references and their links are not directly related to the content of the Glossary of graph theory and begs the questions: "Why THAT list?" and "Why THOSE links?". Unless one or more of the references specifically contributed the definitions in the glossary, and this can be cited, they should be removed.
I plan to remove the references section from this article after 25 March 2008. If you have any objections or suggestions, please voice them prior to this date. Aarond144 ( talk) 07:26, 17 March 2008 (UTC)
I read and re-read the definition of the word "induced" and it didn't help me understand what it meant. I then found the following very helpful definition in another book. Please consider using it.
"An induced subgraph is a subset of the edges of a graph together with any edges whose endpoints are both in this subset. - in "CRC Concise Encyclopedia of Mathematics" By Eric W. Weisstein (Published 2003 CRC Press, ISBN:1584883472 )
A figure included on page 1478 of that book was also very helpful. Cf. Google Books: http://books.google.com/books?id=aFDWuZZslUUC&pg=PA1478&dq=induced+graph+%7C+subgraph&lr=&sig=MsbTYy4gxQzdRc96cePtsB0X4IM —Preceding unsigned comment added by Kmote ( talk • contribs) 19:21, 14 April 2008 (UTC)
As noted by Lasunncty, numerous references are made in the article to "the example graph". This goes back to the time there was only one for the whole article (the one on the basics, "labeled simple graph..."). The problem is that since there are now many of them, most references are unclear or even plain wrong. I suggest giving this graph the title "reference graph" and replacing occurrences of "the example graph" by "the reference graph". Any other ideas? I'm opposed to numbering graphs, because the numbering and the references would have to be changed every time anybody adds or removes a graph. Ratfox ( talk) 15:41, 14 August 2008 (UTC)
I've found in some literature (about planar graphs) the term "separating cycle". I can't find any concise definition of it. Anyone happens to know what does it mean? Stdazi ( talk) 23:47, 8 September 2008 (UTC)
The current definition of an undirected graph is: "A graph that represents a symmetric, transitive relationship between nodes. Its edges are rendered as plain lines or arcs." How is this relation transitive? — 3mta3 ( talk) 10:32, 9 September 2009 (UTC)
This makes me confused. —Preceding unsigned comment added by 75.152.169.231 ( talk) 07:00, 12 September 2009 (UTC)
![]() | This page is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
![]() | This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 | Archive 2 |
I don't think this page should be merged into graph theory. It was deliberately created to list definitions. Charles Matthews 16:41, 21 Mar 2005 (UTC)
This page is 30K of minor definitions. The idea is to have many redirects to it, rather than one page for each small definition. That is what a glossary page is supposed to do. Clearly 30K is too much to put into graph theory, which should give a broad introduction only.
So, I really don't see what the problem is with this. There are quite a few other examples, e.g. general topology and glossary of general topology.
Charles Matthews 20:38, 21 Mar 2005 (UTC)
OK, it seems that the correct idea is to merge graph (mathematics) into graph theory. But this page is fine as it is. Charles Matthews 20:41, 21 Mar 2005 (UTC)
As you know, we are all free to edit here as we see fit. That being said, it is more helpful to be more explicit. Charles Matthews 10:02, 22 Mar 2005 (UTC)
I think (as a newbie to graph theory) that we should remember who our audience is. It is me. I was directed to the glossary by several of the pages, because I thought I would get a better grasp of the term that was being defined on another page. What I found was a very incomplete definition that was disjointed from the supporting terms and concepts. For a glossary (which is typically a collection of disjointed definitions) to be useful, it should contain concepts which are easy to understand on their own, without having to understand the rest of the glossary. Otherwise, I, the learner, end up skipping back and forth between concepts trying to piece together a picture of what is being said. When I do that, I am essentially creating my own encyclopedia article in my mind in order to construct the full picture of the concept. But what if I don't have some of the pieces? As a learner of new information, it would be much better to have someone break down the knowledge ontologically into the correct sequence or taxonomy of ideas so that one idea builds upon the other. A glossary is a cheap imitation of doing that and should be reserved for more disjointed kinds of understanding, like quickly finding the definitions of acronyms used in telecommunications or something like that.
What I would like to see is each idea more fully developed to include separate illustrations to provide examples of each type of graph element. The concepts are much easier to understand when you have that kind of visual map presented to you. We are talking about graphs, here, so more graphs are better. Each graph should have more explicit instructions on how we are explaining it, by using colors and numbers, perhaps, to highlight various sections. That's just my two cents worth. TimIngalls 22:58, 15 November 2006 (UTC)
It seems to me that no definition on this page should incorporate a term that is defined later on the page. It should be that any term that requires another term as part of its definition should come after the other term is defined, so that someone with no knowledge of graph theory reading the page from top to bottom would never have to stop and say "Oh, I don't even know what that means," and have to go search for it before continuing. Thus, the section on trees should come after the section on connectivity because trees and subtrees are defined to be connected.
The other option is to put everything in alphabetical order so that if someone does have to look up another term in the definition they won't have to search, but this is a huge change.-- Quintopia 09:17, 25 October 2006 (UTC)
Under Direction an arc is defined to de directed from the head to the tail. This is just the opposite of the definition in Graph (mathematics). There, the edge is directed from x to y, where x is the tail and y is the head. Who's wrong?
Hi! I put to discussion what is the direction of the link between A and B, if it is written that "A is linked to B". Is it A->B or B->A? I'm not a native speaker of English, and this issue is hard for me to decide. I feel that A->B is appropriate for "A is linked to B", however also for "A links to B", and "A is linked to B" seems to be the passive form of "B links to A".. Is there a consensus on this, or could you refer me a book or scientific paper where this is explicitly defined? It would be also nice if this could make it into the article. Ron85 01:43, 5 February 2007 (UTC)
what's this definition of knots? it should be written if there is a link with knots of knots theory. and it should be explained more what are they and what they mean and what they imply! achab
This is not a term from graph theory. It doesn't match at all the concept of knot in knot theory. This brings much confusion, because links between graph and know theories do exist. The term has popped in books about "(Social) Network analysis", but with distinct definitions (some of them being sloppy). And finally, this term is useless because given definition simply describes a (weakly) connected component. 62.23.57.18 ( talk) 19:47, 14 January 2013 (UTC)egery
I find the definition of "minor" given here to be incomprehensible. What on earth does "every edge in E2 corresponds to a path (disjoint from all other such paths) in G1 such that every vertex in V1 is in one or more paths, or is part of the injection from V1 to V2" mean? I suggest defining "edge contraction" first then defining "minor" like at Minor (graph theory). 202.45.98.61 12:43, 13 June 2006 (UTC)
The discussion above regarding whether there needs to be a glossary or not could
For example, (a,b) is the edge from the vertex a to the vertex b, and ((a,b),c) would be an edge from the edge (a,b) to the vertex c. 217.83.100.240 13:55, 28 September 2006 (UTC)How is a graph called, where edges might also be vertices?
I think it is extremely helpful to have a glossary page. Thank you to whoever started this. I found a small problem, however, with the formula for the length of a walk (open, l=n-1; closed, l=n; n is number of vertices visited). It doesn't work for the example given directly below it. I believe this formula would work for a trail, but it doesn't work for a walk that has repeated edges. Of course you could decompose each walk into trails and then apply the formula, and that should work. I should mention that I am merely a lowly undergraduate, and I could be wrong about all this. If so, boy won't my face be red. Anywho, great page. -Jesse Supina, U of L (still don't know how that signature thing works)
I was taught by Doug West 20 years ago that the edge was "incident" the node and vice versa, so that one spoke of adjacent nodes (sharing an edge) but co-incident edges (sharing a node). The article combines these concepts, calling edges adjacent if they share a node. The two concepts are not dual. If G is a graph the line graph of G, styled L(G), has as nodes the edges of G and they are adjacent nodes of L(G) if they are co-incident edges of G. G is called a line graph if it is the line graph of some graph H. Not all graphs are line graphs. There is a forbidden subgraph characterization: G is a line graph just in case it does not contain as subgraph any of a list of nine little graphs.
Perhaps the nomenclatural distinction has evaporated in the interim, but I hope not, since the logical one certainly hasn't. In any case I propose "line graph" as candidate glossary entry. Lewis Goudy 66.82.51.210 01:32, 5 January 2007 (UTC)
I propose we split some of this material into an article List of graphs, which would list links to many or all of the specific kinds of graphs in Category:Graphs and Category:Graph families, plus bundle together a bunch of dicdefs for things like "path graphs", "caterpillar graphs", "lobster graphs", "gear graphs", "web graphs", and so on. (Those would all become redirects to the new page.) However, I can't do the page split all by myself; I'll start it tonight, if all goes well, and any help in adding definitions to List of graphs will be greatly appreciated. -- Quuxplusone 01:47, 18 January 2007 (UTC)
![]() | This page has been
transwikied to
Wiktionary. The article has content that is useful at Wiktionary. Therefore the article can be found at either here or here ( logs 1 logs 2.) Note: This means that the article has been copied to the Wiktionary Transwiki namespace for evaluation and formatting. It does not mean that the article is in the Wiktionary main namespace, or that it has been removed from Wikipedia's. Furthermore, the Wiktionarians might delete the article from Wiktionary if they do not find it to be appropriate for the Wiktionary. Removing this tag will usually trigger CopyToWiktionaryBot to re-transwiki the entry. This article should have been removed from Category:Copy to Wiktionary and should not be re-added there. |
-- CopyToWiktionaryBot 15:23, 1 February 2007 (UTC)
The shopping list of textbook references and their links are not directly related to the content of the Glossary of graph theory and begs the questions: "Why THAT list?" and "Why THOSE links?". Unless one or more of the references specifically contributed the definitions in the glossary, and this can be cited, they should be removed.
I plan to remove the references section from this article after 25 March 2008. If you have any objections or suggestions, please voice them prior to this date. Aarond144 ( talk) 07:26, 17 March 2008 (UTC)
I read and re-read the definition of the word "induced" and it didn't help me understand what it meant. I then found the following very helpful definition in another book. Please consider using it.
"An induced subgraph is a subset of the edges of a graph together with any edges whose endpoints are both in this subset. - in "CRC Concise Encyclopedia of Mathematics" By Eric W. Weisstein (Published 2003 CRC Press, ISBN:1584883472 )
A figure included on page 1478 of that book was also very helpful. Cf. Google Books: http://books.google.com/books?id=aFDWuZZslUUC&pg=PA1478&dq=induced+graph+%7C+subgraph&lr=&sig=MsbTYy4gxQzdRc96cePtsB0X4IM —Preceding unsigned comment added by Kmote ( talk • contribs) 19:21, 14 April 2008 (UTC)
As noted by Lasunncty, numerous references are made in the article to "the example graph". This goes back to the time there was only one for the whole article (the one on the basics, "labeled simple graph..."). The problem is that since there are now many of them, most references are unclear or even plain wrong. I suggest giving this graph the title "reference graph" and replacing occurrences of "the example graph" by "the reference graph". Any other ideas? I'm opposed to numbering graphs, because the numbering and the references would have to be changed every time anybody adds or removes a graph. Ratfox ( talk) 15:41, 14 August 2008 (UTC)
I've found in some literature (about planar graphs) the term "separating cycle". I can't find any concise definition of it. Anyone happens to know what does it mean? Stdazi ( talk) 23:47, 8 September 2008 (UTC)
The current definition of an undirected graph is: "A graph that represents a symmetric, transitive relationship between nodes. Its edges are rendered as plain lines or arcs." How is this relation transitive? — 3mta3 ( talk) 10:32, 9 September 2009 (UTC)
This makes me confused. —Preceding unsigned comment added by 75.152.169.231 ( talk) 07:00, 12 September 2009 (UTC)
![]() | This page is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |