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• CommentRowNumber1.
• CommentAuthorPeter Heinig
• CommentTimeAug 2nd 2017

To comply with

With few exceptions, all edits to the nLab (either the creation of a new page or the revision of an extant one) should be announced at the nForum, in the “Latest Changes” category.

and with

The only real exceptions are very minor edits such as correction of spelling mistakes or obvious typos or indisputable grammatical errors. However, because of this rule there can at times be a large volume of Latest Changes posts; thus a corollary is that Latest Changes posts at the forum should generally be kept very short and to the point. They should also include a link to the nLab page in question (links at the nForum are created with the same syntax as on the nLab itself).

in the rather new writing in the nLab I only now realized that it seems I have to announce that a few days ago I added terminological comments to the pre-existing edge.

This word is often discussed, in particular since it is so geometric-sounding, while graphs nowadays are often considered purely combinatorially.

Reason for the additions was something interelated with working on the nLab coverage of directed graphs, and a consequence was creating Ernst Steinitz.

• CommentRowNumber2.
• CommentAuthorDavidRoberts
• CommentTimeAug 2nd 2017

You do not need to quote chapter and verse to justify posting this here. Even a single post touching all of these edits is enough. I don’t forsee each entry having its own extensive discussion. You will even save yourself time if you keep said post succinct.

• CommentRowNumber3.
• CommentAuthorTodd_Trimble
• CommentTimeAug 2nd 2017

Small edits at edge, mostly to remove some redundancy. I eliminated the assertion about “edge graph” because Wikipedia attests to that term being used.

• CommentRowNumber4.
• CommentAuthorPeter Heinig
• CommentTimeAug 2nd 2017
• (edited Aug 2nd 2017)

Thanks for the comments and edits.

The assertion about “edge graph” was partly the result of my not having found “edge graph” in the indexes of the books I consulted, but mostly due to my perception–and long-year-experience— that “edge graph” is used much more rarely in the research literature. It surprised me that Wikipedia mentions it in the “line graph” article. I extrapolated this into an untenably strong formulation “does not lexically exist”.

Please note I do not think this important, and we should not dwell on this.

Just briefly, while we are at it:

• That the phrase “edge graphs” holds quite steady against “line graph” in search-engine-searches is mostly a fluke, due to artifacts like there being phrases like “m-edge graph” and “weighted coloured-edge graph” which have little to do with the concept “edge graph”.

• In a systematic treatment, one should use neither “line graph of $G$”, nor “edge graph of $G$”, rather

• intersection graph of $G$

a term which uses a more general concept intersection graph, here specialized to $G$, conceived of as a 2-regular hypergraph.

If the nLab ever contains an article “line graph”, then the connection with intersection graph should perhaps be mentioned there; mentioning “intersection graph” in edge is probably too far-fetched.

Finally, to a make a suggestion perhaps usable for developing category of simple graphs further, not only is every line-graph an intersection graph: every graph is an intersection-graph($=$line graph) (of a suitable itself-not-2-regular hypergraph), so it seems there exists an essentially surjective functor

• HGrh $\overset{IntersectionGraph}{\rightarrow}$ SimpGph
• CommentRowNumber5.
• CommentAuthorMike Shulman
• CommentTimeAug 2nd 2017

I edited edge along the lines of the changes to vertex, and also added a mention of the term “arc” which Wikipedia also attests to (although probably it is not common among combinatorialist graph theorists).

• CommentRowNumber6.
• CommentAuthorTim_Porter
• CommentTimeAug 3rd 2017

Can I make a plea that the idea section gives the idea of what the notion is and does NOT wander off into historical discussions about all the other terms used by various people? That discussion could be placed in a different part of the entry, e.g. a section (towards the bottom) on variants in naming conventions and historical perspectives. I use the Lab as a quick route into getting to grips with a concept and a good Ideas section is then marvellous. Some of the time we forget how readers probably use the various pages.

• CommentRowNumber7.
• CommentAuthorMike Shulman
• CommentTimeAug 3rd 2017

Ok, I’ve split it off into another section. It is relatively common for the Idea section to mention alternative terminologies, so that for instance the reader who was redirected from another name for the concept sees right off the bat that they got to the correct page; but I agree that this was a bit long for the Idea.