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pointing arrows and double headed arrows. I appreciate, the text says this is not the case. But a user who is not familiar with formal definitions may not understand the text and relevance of ordered pairs. In the section "Basic
Terminology", edges are implicitly identified with arrows. I think most people, especially non-mathematicians, would consider a double headed arrow to be a single arrow, not two arrows. ie. an "arrow" being the whole entity, not just the head. The diagram could have 2 separate, single headed arrows between the right most and bottom most nodes. As shown in this diagram
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the inclusion of directed multigraphs, I feel this could easily lead to confusion as to whether there are 3 types of edge, directed each way and directed both ways. I suggest the removal of this diagram from the wiki anywhere it is the primary image reference for this topic. I suggest an alternative where the double headed arrow is replaced with two oppositely directed arrows would be ideal.
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word, unlike the set name "A" (which is easily confused with the word "a" when it is being used at the beginning of a sentence). This has even more value in improving clarity if the article includes the use of the upper-case letter to name the set and the lower-case to name an edge from the set of edges.
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Thank you for your comment
Esponenziale. I appreciate that both (a,b) and (b,a) can be present in the same graph. Sorry, I think my original comment was not very clear. My concern is that a reader new to the concept may think that 3 kinds of edges are allowed: 'forward' pointing arrows, 'backwards'
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One of the arrows is double-headed. I appreciate this my be shorthand for two oppositely directed edges, but I feel that complicates the presentation greatly. Especially since people coming to this article may be meeting the concept for the first time, and there is no accompanying explanation. With
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Either you have a set A of ordered pairs of vertices, or you have just a set A plus two maps 'head' and 'tail'. The two maps GIVE each arrow a direction, namely from the head to the tail. The difference is this option (a plain set plus two maps) allows multiple (or none at all) arrows between two
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I don't know about anyone else, but most of the academic literature I have encountered uses the word "edge" instead of "arc" or "arrow". In the context of the english version, I think this makes even more sense because using the symmetric name for the set "E" is not likely to be confused with a
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I have never seen the term "arrow", but I have seen "arc", especially in older literature. However, every use of "arc" I have so far encountered referred to a directed edge. I think the definition should be cleared up a bit: removing the mentions of "arrows" and "lines" (or at least "directed
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I have made the diagram but unfortunately I can't upload it because I don't have a wikipedia account. Since I have made it programmatically anyone can recreate it so I hope someone else will be kind enough to generate and upload it. To make it save the following code into a text file called
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edges connecting pairs of vertices in opposite directions, but a single bidirected edge is not something that belongs in a directed graph. The caption says it's two edges, but that's not what it looks like and it seems more likely to confuse or misinform readers than help them.
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Why is the third of these needed? Seems to me that it is superfluous; a digraph is a set of nodes, and a (multi)set of ordered pairs (arcs) node→node. I guess the nodes need to all be connected too, but that does't follow from the article, which says:
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I feel this page does not contain enough information about the context of its subject. It is not made clear in what scientific or mathematical fields one is likely to encounter a digraph, nor is any information presented about how they are useful.
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Definitions of
Directed graph on the Web: • A directed graph or digraph is an ordered pair with * is a set, whose elements are called vertices or nodes, * is a set of ordered pairs of vertices, called directed edges, arcs, or arrows. •
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No, it must be a new image under a new name. The existing image is used on far too many articles on far too many different-language versions of
Knowledge to be sure that its replacement by something else would be safe.
963:. Would it be helpful to add Graph Drawing to the See Also section of this article, or would it be better to create a list of software specific to directed graphs and add that new section here directly? --
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It's so huge a topic that it's difficult to know even where to begin. It's like you're on the page for real numbers and you're asking that the article say something about how numbers are used in science.
809:; a discussion will now take place over on Commons about whether to remove the file. This gives you an opportunity to contest the deletion, although please review Commons guidelines before doing so.
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1332:. Into the text box paste the code I put for the file directed_graph.gv above. Then in the dropdown menu select "neato". Finally click the "Generate" button and it will make the graph for you.
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Ok I see what you mean. Feel free to go ahead and edit the image (you can either upload the modified image as a new one or, possibly, upload it as a new revision of the old one). –
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I edited the description under the main diagram to clarify the meaning of the double-headed arrow. I do agree that it should be replaced by a less confusing image, though. –
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I came here specifically to ask why there is nothing in the page about the uses of graphs. Finding a comment from 2008 with no replies is perplexing to say the least.
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You are right: "two maps" is not part of the mathematical definition. Although they may appear useful in some computer representations of digraphs.
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A graph in which the edges are ordered pairs, so that, if the edge (a, b) is in the graph, the edge (b, a) need not be in the graph and is ...
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0∪{∞}. For e∈E, we call u(e) the capacity of that edge. I would go as far as to say that a network really has to be a directed graph."
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When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.
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If you don't want to run this program, there is an online tool that can make a worse version of the diagram. Go to this web page:
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Is there an
English term for an edge connecting a node to itself? In Italian it's called "autoanello" ("self-ring"). Thanks.
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A graph with signed edges is not a directed graph. Signs on edges are independent of whether the graph is directed or not.
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related articles on
Knowledge. If you would like to participate, please visit the project page, where you can join
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The main diagram (which is used elsewhere to illustrate this concept) of the page does not show a directed graph!
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to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the
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No, to my knowledge double-headed arrows are possible within the definition of digraph, because arrows are
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https://web.archive.org/web/20100413104345/http://www.ecp6.jussieu.fr/pageperso/bondy/books/gtwa/gtwa.html
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If you have discovered URLs which were erroneously considered dead by the bot, you can report them with
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http://math.stackexchange.com/questions/222114/what-is-the-definition-of-a-network-in-graph-theory
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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before doing mass systematic removals. This message is updated dynamically through the template
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If you found an error with any archives or the URLs themselves, you can fix them with
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Requested articles/Applied arts and sciences/Computer science, computing, and
Internet
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857:"On the other hand, some texts allow loops, multiple arcs, or both in a digraph."
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then you may need to upload it to
Knowledge (Commons does not allow fair use)
881:"A network is a tuple (G,u) where G=(V,E) is a directed graph and u:E→ℝ: -->
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lines"); defining "arcs" as directed edges and removing "directed arcs".
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Software tools for creating, editing, and drawing directed graphs
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pairs, and therefore arrow (x,y) is different from arrow (y,x).–
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http://www.ecp6.jussieu.fr/pageperso/bondy/books/gtwa/gtwa.html
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Are there any software tools, analogous to those provided for
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Find pictures for the biographies of computer scientists (see
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vertices. This gives the notion of a 'directed multigraph'.
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You need to have the "graphviz" program "neato" installed.
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for additional information. I made the following changes:
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Then in the same folder run this command-line command:
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The last sentence of the introduction is confusing:
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1311:neato -Tsvg -odirected_graph.svg directed_graph.gv
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959:I see a list of software tools in the article on
1391:Here I agree with you. Directed graphs may have
1461:Knowledge level-5 vital articles in Mathematics
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1414:Thanks. Finally someone took action.
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1334:— Preceding
1221:Esponenziale
1200:— Preceding
1181:Esponenziale
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51:WikiProjects
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1253:—Preceding
807:Don't panic
738:—Preceding
614:are called
465:Mathematics
456:mathematics
412:Mathematics
1435:Categories
1079:Report bug
1062:this tool
1055:this tool
965:Lbeaumont
946:Lbeaumont
533:Netscr1be
227:Computing
39:is rated
1336:unsigned
1202:unsigned
1157:unsigned
1111:unsigned
1068:Cheers.—
815:non-free
740:unsigned
655:and its
616:vertices
612:elements
610:, whose
275:Maintain
218:Copyedit
1255:undated
1177:ordered
992:my edit
492:on the
256:Infobox
194:Cleanup
134:on the
41:C-class
1416:Zaslav
1378:Zaslav
1250:Vocchi
920:". --
891:Gunnar
760:Zaslav
638:arrows
624:a set
620:nodes,
237:Expand
47:scale.
1283:c; }
885:says
657:tail.
640:, and
636:, or
591:Three
320:Stubs
294:Photo
151:with:
28:This
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1382:talk
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630:arcs
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126:High
1393:two
1036:RfC
1006:to
912:by
664:JöG
647:to
618:or
605:set
484:Mid
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