Talk:Handshaking lemma

Handshaking lemma has been listed as one of the Mathematics good articles under the good article criteria. If you can improve it further, please do so. If it no longer meets these criteria, you can reassess it. Review: November 13, 2021. (Reviewed version).

A fact from Handshaking lemma appeared on Wikipedia's Main Page in the Did you know column on 25 November 2021 (check views). The text of the entry was as follows: Did you know... that whenever some of the people in a party shake hands, the number of people who shake an odd number of other people's hands is even? A record of the entry may be seen at Wikipedia:Recent additions/2021/November. The nomination discussion and review may be seen at Template:Did you know nominations/Handshaking lemma.

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Mathematics Mid‑priority This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles Mid This article has been rated as Mid-priority on the project's priority scale.

I read: "every finite undirected graph has an even number of vertices with odd degree"

Why is the graph supposed undirected?

It seems to me this this lemma is also valid for directed graphs...

For directed graphs there may exist odd numbers of vertices with odd indegree or odd outdegree (consider the graph with one directed edge). It's true for total degree but that's essentially the same as the degree in the underlying undirected graph. —David Eppstein (talk) 15:52, 28 September 2013 (UTC)[reply]

This review is transcluded from Talk:Handshaking lemma/GA1. The edit link for this section can be used to add comments to the review.

Reviewer: Bryanrutherford0 (talk · contribs) 21:03, 12 November 2021 (UTC)[reply]

GA review (see here for what the criteria are, and here for what they are not)

1. It is reasonably well written.

   a (prose, spelling, and grammar): b (MoS for lead, layout, word choice, fiction, and lists):

   In the very first sentence, on my first reading, I understood it to say that "every finite undirected graph has an even number of vertices" (clearly untrue), and only after a minute's reflection saw that it meant to say that, of the vertices of any finite undirected graph, the number of vertices that have an odd number of edges touching them must be even. The second sentence tends toward the same misunderstanding, in my opinion. Is there a way to accurately state the main idea that eliminates this potential confusion, while staying smooth and easy to read? Otherwise, the prose is clear and professional. The article also appears to comply with the relevant sections of MoS.

   Reworded to avoid this ambiguity. —David Eppstein (talk) 23:30, 12 November 2021 (UTC)[reply]

   Yes, I think that does it. -Bryan Rutherford (talk) 21:04, 13 November 2021 (UTC)[reply]

Also, I think the section that mentions directed graphs would benefit from the point you made in the talk page ("It's true for total degree but that's essentially the same as the degree in the underlying undirected graph.").

Ok, but that would require a reliable source that makes the same point. Do you know of one? —David Eppstein (talk) 23:30, 12 November 2021 (UTC)[reply]

I don't; if you feel that the idea that the sum of a node's indegree and outdegree in a directed graph is equal to the degree of the corresponding node in the underlying undirected graph is non-obvious enough to merit citation, then I guess it can be left out. Probably a good clarification to have if this were to e.g. run for FA. -Bryan Rutherford (talk) 21:04, 13 November 2021 (UTC)[reply]

1. It is factually accurate and verifiable.

   a (reference section): b (citations to reliable sources): c (OR): d (copyvio and plagiarism):

   There is a reference section containing numerous citations to reputable published sources. I don't see any sign of plagiarism from online sources. All of the online sources substantiate the claims they're cited for, and almost all of the cited sources are online. The content looks verifiable.

2. It is broad in its coverage.

   a (major aspects): b (focused):

   The article stays appropriately focused on its topic. I think the statement, proof, and some major applications constitute broad coverage of the topic, though there are probably many other applications that could be explored (I'd love to see something about its relevance to chemistry, but that can wait!).

3. It follows the neutral point of view policy.

   Fair representation without bias:

   The presentation of the topic is suitably neutral, not e.g. exaggerating the importance of the topic or unduly promoting any of the people involved in its development.

4. It is stable.

   No edit wars, etc.:

   No sign of edit wars, and no edits since being nominated for GA.

5. It is illustrated by images and other media, where possible and appropriate.

   a (images are tagged and non-free content have fair use rationales): b (appropriate use with suitable captions):

   The illustrations have suitable licenses and are visually clear, with strong captions explaining their relevance.

6. Overall:

   Pass/Fail:

   A clear, focused article on a well-defined topic! I'll work through the sourcing as soon as I can, and if no issues come up there, then I think I'll just have the prose niggles. -Bryan Rutherford (talk) 22:25, 12 November 2021 (UTC)[reply]

   The only issue I raised has been addressed, and everything else looks great. This article is hereby approved for GA. Well done! -Bryan Rutherford (talk) 21:04, 13 November 2021 (UTC)[reply]

The article is looking great! However, I'm looking to inquire about the consistency of "vertices, nodes, etc" Is there a Wikipedian standard for terms used in Graph Theory such that they don't get used so inconsistently? I am very used to "pick a style and apply it ad infinitum." Obviously the matter is trivial, but I do wish to know.

Cheers Tea-caff (talk) 21:24, 6 February 2023 (UTC)[reply]

I tried to access [3] in the citation for Euler's paper on the Bridges of Konigsberg but the site hosting the PDF no longer has access. May be worth finding another link. 122.106.55.196 (talk) 10:49, 11 October 2024 (UTC)[reply]

Replaced by https://scholarlycommons.pacific.edu/euler-works/53/ . —David Eppstein (talk) 17:47, 11 October 2024 (UTC)[reply]