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1210:, even setting aside the questions of relevance (why a complete digraph + loops between trigrams rather than a complete bipartite graph between lower and upper sets of trigrams, or a complete system of combinations of elements rather than a graph, or a Boolean algebra, or...) and of whether there is sufficient significance to either topic. —
461:
how many subgraphs are there (where I would like to differentiate between subgraphs that are NOT isomophic to one another - clearly it is simple to enumerate all the subgraphs, calculate their adjacency matrices and get a computer program to get rid of all of the similar matrices so that you are left
173:
In the current version, the sentence "(..) a complete graph can be the worst case for large connected systems like social and computer networks" is POV. It needs explanation. Otherwise the statement is not generally true and needs to be removed. Why should a complete social network be any bad? Worse
682:, it states "The complete graph K4 is planar" and links to this article. Then, here, we have a drawing of K4 which makes it look non-planar (i.e. two of the edges cross in the drawing). This is bound to be confusing to people. I think it would make sense to either use the drawing of K4 from
1243:"complete" for digraphs, the graph with 4 edges (2 of them being of xy-type and 2 being yx-type) between each pair of vertices (x,y), would also be a complete digraph to those people who allow directed graphs to have such multiple arcs. So in this sense, the definition should be that there's
1242:
article says that "some authors consider a broader definition that allows directed graphs to have such multiple arcs", in which case there could be four edges between (x,y), for example two of them corresponding to xy and two of them corresponding to yx. According to the above definition of
1238:". Couldn't you have just added the citation and not complained about how "basic and obvious" it was and not mention me? The reference that you added says that a digraph is "complete" if for every pair vertices (x,y), the edges xy and yx both exist. But the
1262:
Unless otherwise specified, usually only one edge would be allowed in each direction in a digraph. I don't remember ever seeing a definition of complete graphs (without additional qualification in the name) that allowed the edge multiplicities to vary.
402:
It's completely inappropriate and I'm going to remove it. Even at the highest resolution it is hard to see the edges but only the interference pattern they make. It will only confuse people who come to this page for information on complete graphs.
1159:
of trigrams with the lower considered first, the upper second. Since there is a hexagram for every pair of bagua, in both orders, there is a directed edge in each direction for each pair of trigrams. Eight
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I guess the person who wrote it was thinking of benefit-cost-ratio. But that needs some elaboration and possibly sources to make it credible. Otherwise not worthy of an existence in an encyclopedia.
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As I understand, the term "complete graph" means the same as "full mesh" in computer science (especially networking). Does anyone object to mentioning this fact in this article? --
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yes, it is, but it adds little to the article. More like "ooh, look what my computer can do". I suppose it might illustrate that the number of connections increases rapidly
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supply requested notation for basic and obvious notation for which User:Dr. Universe could easily have run a search instead of making busywork for other editors
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686:, or at least have a note on the drawing here pointing out that there is an alternate way to draw the graph which makes its planarity more apparent. --
657:
Every German source I have seen says that the K is in honour of
Kuratowski. "Complete graph" is "vollständiger Graph" in German, not "kompletter Graph".
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So you're trying to use content you yourself wrote on another open Wiki (Wikibooks) as a reference for content here? It is very obviously not a
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are included in the directed graph since there is a hexagram for each doubled trigram. The 56 edges and 8 loops are labeled 1 to 64 in a
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Silly point - but this wiki could also define the concept for directional graphs. This request is motivated by the next two entries.
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Same as above request, but everything is to do with directed graphs (so their should be more subgraphs up to isomorphism...).
219:. The triangle has nothing but its sides and corners, but the octagon looks very complicated. Can anyone see how complicated an
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1107:, which is still connected. In this context, removing a vertex means also removing all edges incident to that vertex. —
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They are maximally connected as the only vertex cut which disconnects the graph is the complete set of vertices.
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Any graph, no matter how many vertices, can be embedded without crossings in 3d, for instance by placing the
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has 10 × (10 - 1) / 2 = 45. So yeah, they can look quite complicated! :-) I guess since we've already got
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I appreciate you adding the citation, but I don't understand why you had to attack me in the edit summary: "
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And of course, you can also find the number through summation, though that may actually be more verbose:
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on
Knowledge (XXG). If you would like to participate, please visit the project page, where you can join
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Yes, this is a simple exercise, and I will probably hunt it down on the internet. But, say, for
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Er, although this statement is poorly-written, I think this just means that it's the worst-case
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1172:(Earth ☷, Water ☵, Air ☰, and Fire ☲.), the oppositely directed edges are consecutive.<ref
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Not sure if there is any reason to mention it in the article or to add it to the infobox, but
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edge going in each direction right? I wasn't sure about this so I wanted to see a reference.
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with ONLY isomorphically distinct subgraphs - but, surely, this has been done already?).
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I agree, thanks. I was going to remove it myself, and I am glad you did it first. --
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I have yet to see one but I think it would be very interesting. -
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Alternative formula for the number of edges in a complete graph
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Is there a general way of determining all of the subgraphs of
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787:{\displaystyle \textstyle {\frac {n(n-1)}{2}}={n \choose 2}}
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mentioned in lede. Very old topic. Supports article well.
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This article has pictures of all regular polygons from a
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family has vertex/edge sets as complete graphs, so the
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1191:) 04:20, 17 February 2022 (UTC) Provide WB link
1047:No, it doesn't. If you remove two vertices from
435:Extending this wiki to include complete digraphs
1029:(Because they are the endpoints of some edge.)
1024:removing any two vertices disconnects the graph
303:just to illustrate how messy they can get... --
1298:Knowledge (XXG) vital articles in Mathematics
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126:Knowledge (XXG):WikiProject Mathematics
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1293:Knowledge (XXG) level-5 vital articles
1018:But if n ≥ 3, for the complete graph K
1313:B-Class vital articles in Mathematics
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1143:or trigrams form the verticies of a
1135:I Ching as complete digraph on bagua
1034:2601:200:C000:1A0:87C:FF45:2757:A6C9
1032:Or am I misunderstanding something?
971:{\displaystyle \sum _{i=1}^{n}(i-1)}
839:), and the latter is more succinct.
674:K4 example makes it look non-planar.
275:has 9 × (9 - 1) / 2 = 36 edges, and
106:This article is within the scope of
364:K100 added! It's really beautiful.
49:It is of interest to the following
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1323:Mid-priority mathematics articles
703:; that could be the way to go...
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899:{\displaystyle {n+1 \choose 2}}
146:This article has been rated as
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854:It's similar to a formula for
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557:th vertex at the coordinates (
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1220:06:32, 17 February 2022 (UTC)
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827:{\displaystyle {n \choose 2}}
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699:French Knowledge (XXG) has a
648:05:04, 3 September 2008 (UTC)
622:11:13, 9 September 2009 (UTC)
425:03:37, 30 December 2006 (UTC)
408:01:56, 30 December 2006 (UTC)
354:11:12, 9 September 2009 (UTC)
120:and see a list of open tasks.
1318:B-Class mathematics articles
988:10:04, 5 February 2018 (UTC)
917:09:40, 5 February 2018 (UTC)
849:12:52, 3 February 2018 (UTC)
369:18:41, 30 October 2006 (UTC)
1127:The following example of a
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534:Interesting. So shouldn't
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152:project's priority scale
1100:{\displaystyle K_{n-2}}
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174:in comparison to what?
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1245:at least one
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73:Mid‑priority
51:WikiProjects
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519:pentachoron
517:is 3D, and
515:tetrahedron
377:—Preceding
123:Mathematics
114:mathematics
70:Mathematics
1282:Categories
1179:Reverted!
1139:The eight
1002:Properties
253:vertices,
1176:/ref: -->
1149:hexagrams
1147:given by
661:Pluslucis
634:Full mesh
609:Professor
341:Professor
235:You mean
39:is rated
705:AnonMoos
688:RoySmith
615:Fiendish
523:Tom Ruen
391:contribs
379:unsigned
347:Fiendish
221:enneagon
213:triangle
198:Dcoetzee
1193:Rgdboer
1185:Rgdboer
1153:I Ching
1151:in the
794:(where
640:chrylis
536:simplex
521:is 4D.
511:simplex
422:Dominus
225:decagon
217:octagon
150:on the
41:B-class
691:(talk)
260:, has
215:to an
47:scale.
1162:loops
1141:bagua
835:is a
405:McKay
28:This
1269:talk
1253:talk
1216:talk
1197:talk
1189:talk
1113:talk
1038:talk
984:talk
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709:talk
665:talk
644:talk
619:Esq.
588:Eeky
569:). —
540:Eeky
509:The
501:Eeky
387:talk
366:Alpt
360:K100
351:Esq.
305:Ejrh
242:and
194:size
183:talk
858::
678:In
301:100
289:to
264:× (
223:or
142:Mid
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344:M.
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1195:(
1187:(
1111:(
1093:2
1087:n
1083:K
1060:n
1056:K
1036:(
1020:n
1008:"
982:(
966:)
963:1
957:i
954:(
949:n
944:1
941:=
938:i
911:(
891:)
886:2
882:1
879:+
876:n
870:(
843:(
819:)
814:2
811:n
806:(
778:)
773:2
770:n
765:(
759:=
754:2
750:)
747:1
741:n
738:(
735:n
707:(
663:(
642:(
567:i
563:i
561:,
559:i
555:i
479:j
476:K
459:4
456:K
448:j
445:K
385:(
321:K
298:K
294:8
291:K
287:1
284:K
277:K
273:9
270:K
266:n
262:n
258:n
255:K
251:n
244:K
240:9
237:K
181:(
154:.
53::
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