1514:, "dashes have a slightly more emphatic feel, making the reader focus on this information". I'm not convinced that adding additional emphasis to these glosses is desirable here. Also, whatever is done to the definition of giant component should certainly be done to the definition of percolation threshold (because those two parts of the sentence are parallel), and I'm not convinced that it's a good idea to have sentences with more than one parenthetical clause (it makes the structure look confused and cumbersome). —
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connected components deserve their own articles: they are fundamental, important, have plenty of algorithmic depth, etc. And while connected components are reasonably intuitive and natural, strongly connected components require more care to define and use; including that material here would necessarily make it shorter and harder to understand while also confusing readers who only care about the undirected case. —
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865:) different subgraphs formed by a path from the top layer to the bottom one, each of these subgraphs fits your description, and they don't form any kind of nice partition of the graph. But instead, if you require that there is both a path from v1 to v2 and a path from v2 to v1, then you do get a nice partition of the vertices into
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yet included in a component, and the more precise part of the reference is formatted as a flow chart at a much lower level of detail than would typically be used now, so I wanted to phrase it in a safe way that would allow for the possibility of some of those low-level details being different in an inessential way. —
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neither does GA criterion 1a). An undergraduate CS student level is a good target for much of this material; at least, for the material in the definition and algorithms sections. The number of components and random graphs sections may need to be a little more advanced, maybe an undergraduate math student level. —
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0" really conveys the intended meaning, because maybe that would allow us to set epsilon=1/n? That's fixing it, isn't it? In fact this sort of choice of epsilon to be a function of n rather than a value independent of n is commonly done (with other functions than 1/n), in studying the transition area
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Not anywhere near as much as finite graphs, definitely, to the point where a lot of references are sloppy and make certain claims as being true for all graphs when really they're true only for finite graphs and require more care for infinite graphs. That's true in many of our
Knowledge articles, too.
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be merged here. I strongly disagree. We could perhaps use an article that would survey various notions of components in graph theory (connected components and biconnected components of undirected graphs, strongly connected components of directed graphs, etc) but both connected components and strongly
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at least tries to show off something of how it works but fails to provide a non-trivial test case (one where a top-down scan has to merge what it thinks are multiple components). And I think the use of the 8-neighborhood instead of the 4-neighborhood in the other ones may be unnecessarily confusing.
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It was intended primarily as a way of giving some history: that the algorithm was already well known in 1973, and therefore presumably invented significantly earlier. It was "essentially this algorithm" because the text of the reference is a little vague about how to find the next vertex that is not
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The
Algorithms section talks about amortized O(|V|) deletion of edges in disjoint-set data structure. Amortized constant time per edge delete can be achieved in disjoint-set while still maintaning the same time complexity of the other operations. Construction of such a data structure is described in
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I don't have any complaints so far. But if you see something that you think could be understandable for someone with your level of technical background, but isn't, please let me know; some of this material is unavoidably technical but I don't want it to be technical when it doesn't have to be (and
1656:
The graph has exactly three components, in exactly the sense of the word "component" used in this article. There is no other number of components that it could have. Qualifiers do not help make the statement more true. Adding qualifiers creates the sense that the qualifiers are added for a reason,
1822:
Makes sense. I have a conceptual question if you don't mind: is the notion of an infinite graph, treated as an object in its own right, ever useful in your experience/research? Most of the graph theory concepts I know of can be sensibly applied to countably infinite graphs, although connectedness
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This is true in isolation and is fine throughout the article, but in this instance it is part of a list. (Indeed the "incidence of" groups implies the commas are parenthetical and not in a list, but this is only confirmed in the second "of" (for a percolation threshold), which means that a reader
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I'd be a bit more explicit that the components are disjoint, or we're just stating something obvious; also, "three components" is stated in the caption. Maybe something like "For instance, the three components of the graph in the first illustration are disjoint, and together constitute the whole
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I didn't mean it in any standard formal sense, just as a way of identifying subsets of vertices. Define a collection of disjoint subsets of vertices, call them "layers", order them into a sequence, and put a directed edge between two vertices if they are in two layers that are consecutive in the
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Do you mean, have I ever used the concept in my own research? Or do you mean, does my experience lead me to believe that it's a worthwhile concept to explore? It would be difficult to do without the infinite grid graphs and their relatives; they've come up repeatedly as an organizing tool in my
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Hi, I'll take this one up. A cursory look through the article reveals it's in good shape. For reference, I know graph theory concepts that would be found in a typical undergrad computer science sequence. Any edits I make to the article will be minor (and not something I'll be a stickler on).
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The term "connected component" does however appear a lot in computer science literature, from what I've seen online. However, this is more of a math article than it is a compsci one, so I would argue the definition and use of the term seen most in Graph Theory texts would be more suitable.
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I think it is a little imprecise. I meant "connected components as defined for topological spaces", with "topological" modifying the noun phrase "connected components", rather than "components that are topologically connected", with "topologically" modifying the adjective "connected".
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I'm confused. Is the "For instance" sentence an example of the definition of component instead of the immediately preceding sentence? If so, I'd remove "For instance" entirely and maybe connect it to the next sentence with a semicolon, to show the natural connection between the ideas.
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several papers, that can be easily found using "union find delete" query in any search engine (Google being probably the best one). I am not familiar with
Knowledge's policies and I don't feel confident to change this article as I am just an undergrad student of computer science.
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1-delta". The wrong order is something like "forall delta: exists N: for all epsilon: forall n: ..." Delta and N aren't even explicit in the text but are implied by the wording "arbitrarily close to one for sufficiently large values". Anyway, I'm not sure "a fixed epsilon:
1440:, or something else? Algorithmically, biconnected and strongly connected are a lot closer to each other than they are to the components of this article. Knuth would argue (and has, recently) that the correct analogy from connected components of undirected graphs is to
2181:
The source had a line or two about this, so I added a line here based on that. That's one reason but not the only reason. Certain kinds of hierarchical image representations, for instance, might allow fast sequential access but not fast random access to the pixels.
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papers despite those papers mostly being about finite things. So yes, infinite graphs are useful. I've only rarely studied infinite graphs directly in my own research; an exception is the paper "Combinatorics and geometry of finite and infinite squaregraphs". —
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I think someone else must have added that phrasing, so I can only speculate on the intended meaning. I agree that it is confusing, and unnecessary. I just removed the "=y(np)" part. I don't think we need to be explicitly told that it only depends on
819:
graph is a subgraph in which for any two vertices v1, v2 in this subgraph there is a path from v1 to v2 or there is a path from v1 to v2, and to which (subgraph) no more vertices or edges (from the larger graph) can be added while preserving its
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I moved the "for instance" sentence earlier in the paragraph, to make clearer that what it is an example of is the definition in the first sentence, and not so much the additional properties in the later sentences of the paragraph.
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So this is intended as a summary (as everything in the lead should be a summary) of the last two lines of the "Definitions and examples" section? It would have to be very brief to summarize those lines rather than repeating them.
1897:"The same number arises in other ways in graph theory as well." Specify number of components so it's not confused with the rank of the graph; can replace "Numbers of components plays" later with "This number plays" if wanted
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Well, I can see that this is somewhat redundant, but we somehow need to disambiguate "objects" meaning things that are visible in the image from "objects" meaning data in the computer code for processing the image.
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of directed graphs. Another concept frequently used for directed graphs and also analogous in some ways are the components of a directed graph obtained by forgetting the directions and using undirected components.
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Indeed it's a question of order of two limit processes, hence why I thought it'd be easiest to just say "choose epsilon first." But I agree it's distracting to mention at the beginning, "choose epsilon :
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graph is a subgraph in which any two vertices are connected to each other by paths, and to which no more vertices or edges (from the larger graph) can be added while preserving its connectivity
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Fair point; maybe "Similar concepts" or "Similar concepts accounting for additional structure". My immediate reaction to the lead sentence was generalizing the idea to other types of graphs.
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How does it suggest that? We're explicitly considering examples of this rule ("For instance"). In any case, the disjoint part should be mentioned, or else the statement feels vacuous.
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Is it really "the" analogous concept? Turn it around: if you're seeking the analogous concept to strongly connected components in undirected graphs, would it be connected components,
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Would it be fair to include something like "the analogous concept for directed graphs is called a strongly connected component" somewhere, perhaps at the end of the first paragraph?
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and then try to take the limit. You can define a limit that way, but the thing that you want to be true with high probability will not actually be true in that limit. —
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Writing it that way would suggest, incorrectly, that it's somehow possible for other examples to have components that are not disjoint, or do not cover the graph. —
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I'd specify "linear time in the number of vertices" to ensure it's not confused as linear in component count. ("sublinear time algorithms ... " later is clear)
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rather than being completely redundant, and therefore suggest that without the qualifier there might be some other number of components, which is false. —
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It's not actually linear in the number of vertices. Linear time always means, linear in the total size of the input, and here that means vertices+edges. —
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I wouldn't call this a "representation" per se, since information about vertices of degree two are lost in the topological setting. Maybe "considering"?
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It is correct grammar to set off parenthetical clauses such as this one with commas. They could alternatively be replaced by dashes, but according to
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vertices per layer, with an edge between every two vertices on consecutive layers (directed from the higher layer to the lower one) — then there are (
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It's really a question of quantifier order. The correct order is something like "for all epsilon: for all delta: exists N: for all n: (n : -->
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What is the utility of this vs. a plain citation? If the main thrust is "well known" then I think "essentially this algorithm" can be removed
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A component, by definition is a connected subgraph of a graph, the term connected component is redundant, and does not appear in most texts.
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This article is definitely not a stub so I have upgraded it to start. I am not sure if it meets the criteria for C-class so left it at that.
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Great, thanks. Overall it was quite understandable, despite being a formal mathematical approach and including the random graphs part.
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0," before introducing n. How about "a positive constant which can be chosen to be arbitrarily close to zero but independently of n"?
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in finer detail. A lot more is known about what happens there, but I didn't think this article was the place to get into details. —
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Perhaps in the sentence on topology, a brief mention of topological separability as the analog of disjointness in the graph case?
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Rename article to
Component (graph theory), and refer to all "Connected components" and just components throughout the article.
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Ok, but I reversed it to put the independence first before the close to zero part; I think it's a little tighter that way. —
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which can be chosen arbitrary close to 0" too imprecise? Also, is the asymptotic width of the transition period in terms of
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The imperative mood feels a bit off here; maybe just "Finding all the components of a graph is/can be done by looping ... "
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Ok, but I changed "as sets" to "as the sets" to make it less ambiguous that it is the same sets already being discussed.
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Besides percolation theory–type questions which you discuss, are there any important applications to infinite graphs?
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Thank you for your fast reply (9 minutes! :). Though I didn't understand it yet, as I don't know the definition of
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might have to backtrack.) If dashes or parentheses are objectionable, a semicolon after "others" works too.
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There's a limiting argument going on in the earlier text about "high probability": we're taking a limit as
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I sprinkled a few more "finite"s through the article to be safe in cases where this was a little unclear. —
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I totally overestimated my knowledge in this area; if you felt my review wasn't thorough let me know.
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This seems a bit redundant, since a construction was just essentially given (so it's just terminology)
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Would "constant time", "roughly constant time" or "amortized constant time" be too technical here?
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and in topological graph theory it can be interpreted as the zeroth Betti number of the graph
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Added something about this as a gloss for the meaning of topological connected components. —
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I'm not sure that's the definition you really want. For instance, consider a graph with
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and not separately on both variables; what use are we making of this information? —
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graph. That is, I'm looking for XYZ, for which the following definition holds:
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For instance, the graph shown in the first illustration has three components.
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I understand that part, but this feels like a convoluted way of saying "fix
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I think I've responded to everything above, so please take another look. —
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I'd say "topologically", but this is minor and perhaps slightly imprecise
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Provide why this is important (I assume it's to do with cache locality?)
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This seems quite clear; removing it would make the sentence more concise
2638:"y=y(np)" I'm guessing you mean that y is only dependent on the value
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I'm looking for the name you can give to a "connected component" of a
830:", though I guess there is already a special name for it. Thanks, --
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It seems infinite graphs aren’t as frequently studied as I thought
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Set off the definition of "giant component" with dashes or parens
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To find all the components of a graph, loop through its vertices
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and representing its edges as line segments between those points
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should remain unchanged. It doesn't work, for instance, to set
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Find pictures for the biographies of computer scientists (see
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I'd just say "for other forms"; advancedness is subjective
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as sets of vertices, the equivalence classes of vertices,
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or as likely to be part of objects depicted in the image
893:. Can you give a definition or point to one? Cheers, --
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How about "part of depicted objects" as a compromise?
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Hopcroft & Tarjan (1973) describe ... "well known"
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The second part can be removed as the meaning is clear
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Awesome; passing. Thank you for the excellent work!
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2167:17:47, 2 March 2022 (UTC)
2143:17:45, 2 March 2022 (UTC)
2084:17:46, 2 March 2022 (UTC)
2070:17:29, 2 March 2022 (UTC)
2056:07:54, 2 March 2022 (UTC)
2029:17:27, 2 March 2022 (UTC)
2015:07:52, 2 March 2022 (UTC)
1990:07:46, 2 March 2022 (UTC)
1966:07:46, 2 March 2022 (UTC)
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1911:07:56, 1 March 2022 (UTC)
1884:17:27, 2 March 2022 (UTC)
1870:06:01, 2 March 2022 (UTC)
1855:17:33, 1 March 2022 (UTC)
1818:07:56, 1 March 2022 (UTC)
1778:07:47, 1 March 2022 (UTC)
1746:07:44, 1 March 2022 (UTC)
1736:with another reference. —
1697:07:44, 1 March 2022 (UTC)
1682:00:53, 1 March 2022 (UTC)
1667:00:47, 1 March 2022 (UTC)
1652:00:05, 1 March 2022 (UTC)
1609:Not actually true, my bad
1595:01:13, 1 March 2022 (UTC)
1581:00:55, 1 March 2022 (UTC)
1553:07:36, 1 March 2022 (UTC)
1539:01:10, 1 March 2022 (UTC)
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1498:01:26, 1 March 2022 (UTC)
1484:00:49, 1 March 2022 (UTC)
1469:00:03, 1 March 2022 (UTC)
694:Category:Computer science
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134:Be welcoming to newcomers
33:Mathematics good articles
2670:{\displaystyle n\cdot p}
2127:Researchers in this area
1614:Definitions and examples
890:glossary of graph theory
696:and sub-categories with
375:project's priority scale
79:Component (graph theory)
27:Component (graph theory)
2824:GA-Class vital articles
2814:Knowledge good articles
2295:{\displaystyle \alpha }
1350:non-free use rationales
1105:reasonably well written
332:WikiProject Mathematics
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2157:Ok, removed. —
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1036:Instructions
958:— Preceding
954:
951:
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667:Unreferenced
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371:Low-priority
370:
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296:Low‑priority
274:WikiProjects
257:
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73:This is the
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2215:The second
2074:Ok, done. —
1136:word choice
1050:transcluded
908:ordering. —
761:Start Class
346:Mathematics
337:mathematics
293:Mathematics
202:free images
85:not a forum
2808:Categories
2518:0}" /: -->
2253:should be
1940:Algorithms
1732:Ok; added
1225:plagiarism
1169:verifiable
1003:Authorship
989:GA toolbox
794:undirected
739:User:DPoon
37:under the
1976:hyphenate
1585:Alright.
1393:Pass/Fail
1062:Reviewer:
1026:Templates
1017:Reviewing
982:GA Review
555:Computing
262:is rated
142:if needed
125:Be polite
75:talk page
2577:Pr : -->
2495:0}": -->
2282:or just
1075:contribs
1031:Criteria
972:contribs
964:Zer0dept
960:unsigned
817:directed
804:directed
603:Maintain
546:Copyedit
264:GA-class
110:get help
83:This is
81:article.
47:reassess
2540:known?
2196:Great.
1624:graph."
1387:Overall
1268:focused
1221:copyvio
1140:fiction
584:Infobox
522:Cleanup
462:on the
373:on the
208:WP refs
196:scholar
2789:Ovinus
2775:Ovinus
2772:-: -->
2749:Ovinus
2731:Ovinus
2701:Ovinus
2599:Ovinus
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2542:Ovinus
2198:Ovinus
2062:Ovinus
2021:Ovinus
1876:Ovinus
1847:Ovinus
1674:Ovinus
1644:Ovinus
1587:Ovinus
1531:Ovinus
1490:Ovinus
1461:Ovinus
1413:Ovinus
1340:images
1315:stable
1313:It is
1291:policy
1243:It is
1162:It is
1142:, and
1132:layout
1103:It is
1088:review
1065:Ovinus
895:Abdull
832:Abdull
815:of an
792:of an
767:Acb314
565:Expand
270:scale.
180:Google
54:Review
2503:: -->
2305:Ok. —
2133:Ok. —
1901:Ok. —
1366:with
1144:lists
1090:(see
1052:from
885:layer
648:Stubs
622:Photo
479:with:
251:This
223:JSTOR
184:books
138:Seek
2793:talk
2779:talk
2759:talk
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2721:talk
2705:talk
2695:Note
2683:talk
2617:talk
2603:talk
2587:talk
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2103:and
2080:talk
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2011:talk
1986:talk
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1426:Lead
1417:talk
1223:and
1166:and
1128:lead
1126:for
1096:here
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1069:talk
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216:FENS
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1790:nvm
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813:XYZ
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