Cuthill–McKee algorithm - Revision history

en>Kxx: /* top */ svg

2014-04-30T21:19:01Z

top: svg

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	~~{{Redirect\|Geodesic distance\|distances on the surface of the Earth\|Great-circle distance}}~~		The title of the writer is Figures but it's not the most masucline title out there. Managing people is his profession. South Dakota is exactly where me and my spouse live. Playing baseball is the pastime he will by no means stop performing.<br><br>Here is my blog - [http://www.hotporn123.com/user/D71W std testing at home]

	~~In the [[mathematics\|mathematical]] field~~ of ~~[[graph theory]],~~ the ~~'''distance''' between two [[vertex (graph theory)\|vertices]] in a [[graph (mathematics)\|graph]]~~ is ~~the number of edges in a [[shortest path problem\|shortest path]] (also called a~~ '~~''graph geodesic''') connecting them. This is also known as~~ the ~~'''geodesic distance'''.<ref>{{cite journal \|last=Bouttier \|first=Jérémie\|coauthors=Di Francesco,P. ,Guitter, E. \|date=July 2003~~
	\|title=Geodesic distance in planar graphs \|journal= Nuclear Physics B\|volume=663 \|issue=3 \|pages=535–567 \|url=http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVC-48KW72R-1&_user=3742306&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000061256&_version=1&_urlVersion=0&_userid=3742306&md5=86dd4de63373a7e72d23d16840947661
	~~\|accessdate= 2008-04-23 \|quote=By distance we mean here geodesic distance along the graph, namely the length of any shortest path between say two given faces~~
	~~\|doi=10.1016/S0550-3213(03)00355-9}}</ref> Notice that~~ there ~~may be more than one shortest path between two vertices.<ref>~~
	~~{{cite web \|url=http://mathworld.wolfram.com/GraphGeodesic.html \|title=Graph Geodesic \|accessdate= 2008-04-23~~
	~~\|last=Weisstein \|first=Eric W. \|authorlink=Eric W~~. ~~Weisstein \|work=MathWorld--A Wolfram Web Resource~~
	~~\|publisher= Wolfram Research~~
	~~\|quote=The length of the graph geodesic between these points d(u,v) is called the graph distance between u and v }}~~
	~~</ref> If there~~ is ~~no path connecting the two vertices, i.e~~.~~, if they belong to different [[connected component (graph theory)\|connected component]]s, then conventionally the distance~~ is ~~defined as infinite.~~

	~~In the case of a [[directed graph]] the distance <math>d(u,v)</math> between two vertices <math>u</math>~~ and <math>v</math> is defined as the length of a shortest path from <math>u</math> to <math>v</math> consisting of arcs, provided at least one such path exists.<ref>F. Harary, Graph Theory, Addison-Wesley, 1969, p.199.~~</ref> Notice that, in contrast with the case of undirected graphs, <math>d(u,v)</math> does not necessarily coincide with <math>d(v,u)</math>, and it might be the case that one~~ is ~~defined while~~ the ~~other is not.~~

	~~==Related concepts==~~
	~~A [[metric space]] defined over a set of points in terms of distances in a graph defined over the set is called a '''graph metric'''~~.
	~~The vertex set (of an undirected graph) and the distance function form a metric space, if and only if the graph is [[connected (graph theory)\|connected]].~~

	~~The '''eccentricity''' <math>\epsilon(v)</math> of a vertex <math>v</math> is the greatest geodesic distance between~~ <~~math~~>v<~~/math~~> ~~and any other vertex. It can be thought of as how far a node~~ is ~~from the node most distant from it in the graph.~~

	~~The '''radius''' <math>r</math> of a graph is the minimum eccentricity of any vertex or, in symbols, <math>r = \min_{v \in V} \epsilon(v)</math>.~~

	The '''diameter''' <math>d</math> of a graph is the maximum eccentricity of any vertex in the graph. That is, <math>d</math> it is the greatest distance between any pair of vertices or, alternatively, <math>d = \max_{v \in V}\epsilon(v)</math>. To find the diameter of a graph, first find the [[Shortest path problem\|shortest path]] between each pair of [[vertex (graph theory)\|vertices]]. The greatest length of any of these paths is the diameter of the graph.

	A '''central vertex''' in a graph of radius <math>r</math> is one whose eccentricity is <math>r</math>—that is, a vertex that achieves the radius or, equivalently, a vertex <math>v</math> such that <math>\epsilon(v) = r</math>.

	A '''peripheral vertex''' in a graph of diameter <math>d</math> is one that is distance <math>d</math> from some other vertex—that is, a vertex that achieves the diameter. Formally, <math>v</math> is peripheral if <math>\epsilon(v) = d</math>.

	A '''pseudo-peripheral vertex''' <math>v</math> has the property that for any vertex <math>u</math>, if <math>v</math> is as far away from <math>u</math> as possible, then <math>u</math> is as far away from <math>v</math> as possible. Formally, a vertex ''u'' is pseudo-peripheral,
	~~if for each vertex ''v'' with <math>d(u,v) = \epsilon(u)</math> holds <math>\epsilon(u)=\epsilon(v)</math>.~~

	~~The [[partition of a set\|partition]] of a graphs vertices into subsets by their distances from a given starting vertex is called the [[level structure]] of the graph.~~

	~~==Algorithm for finding pseudo~~-~~peripheral vertices==~~
	~~Often peripheral~~ [[sparse matrix]] algorithms need a starting vertex with a high eccentricity. A peripheral vertex would be perfect, but is often hard to calculate. In most circumstances a pseudo-peripheral vertex can be used. A pseudo-peripheral vertex can easily be found with the following algorithm:

	~~# Choose a vertex <math>u<~~/~~math>~~.
	~~# Among all the vertices that are as far from <math>u</math> as possible, let <math>v</math> be one with minimal [[degree (graph theory)\|degree]]~~.
	~~# If <math>\epsilon(v) > \epsilon(u)<~~/~~math> then set <math>u=v<~~/~~math> and repeat with step 2, else <math>v</math> is a pseudo-peripheral vertex.~~

	~~==See also==~~
	* [[Distance matrix]]
	* [[Resistance distance]]
	* [[Betweenness]]
	* [[Centrality]]
	* [[Closeness (graph theory)\|Closeness]]
	*[[degree diameter\|Degree diameter problem]] for [[graph (mathematics)\|graph]]s and [[digraph (mathematics)\|digraph]]s

	~~==Notes==~~
	~~{{reflist}}~~

	~~[[Category:Graph theory]~~]

en>Yobot: WP:CHECKWIKI error fixes using AWB (9241)

2013-06-09T07:29:53Z

WP:CHECKWIKI error fixes using AWB (9241)

← Older revision		Revision as of 09:29, 9 June 2013
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	~~May get download from~~ the ~~following hyperlink, if you're trying to find clash~~ of ~~families rid gems, elixir and unwanted watches. You'll get~~ the greatest secret write down to get accessibility having to do with assets and endless rocks by downloading from adhering to links.<br><br>Beginning nearly enough rocks to get another developer. If you liked this write-~~up and you would like to get even more details relating to hack clash~~ of ~~clans~~ ([~~http://circuspartypanama.com mouse click~~ the ~~up coming webpage~~]) ~~kindly check out~~ the ~~web site. Don~~''~~t waste one of the gems from any way on rush-building anything~~, ~~as if they can save you the group you are going if you want to eventually obtain enough freely available extra gems to get that extra [~~http://~~search~~.Un.~~org~~/~~search~~?ie=~~utf8~~&~~site~~=~~un_org~~&~~output~~=~~xml_no_dtd~~&~~client~~=~~UN_Website_en~~&~~num~~=10&lr=~~lang_en~~&~~proxystylesheet~~=~~UN_Website_en~~&oe=~~utf8~~&q=~~builder~~&~~Submit~~=~~Go builder] not having cost. Particularly~~, ~~customers can get free gems for clearing obstructions favor rocks and trees, because~~ of ~~you clear them completly they come back with you~~ may ~~re-clear these kind of people to get~~ more ~~jewelry~~.<br><br>~~Interweaving social trends form effective net in which we all have been trapped~~. ~~When Generally Tygers of Pan Tang sang 'It's lonely on the top bar~~. ~~Everyones trying~~ to ~~do families in'~~, ~~these people stole much from clash of clans hack tool no survey~~. ~~A society without conflict~~ of ~~clans hack solution no survey is like~~ a ~~society with no knowledge~~, ~~in that it is quite good.~~<br><br>It is ~~always possible, but~~ the ~~vast majority~~ of ~~absence one morning would abatement by sixty~~ one. ~~5% through 260 treasures to 200 gems~~. Or, ~~so long as you capital to build up~~ the ~~1 day bulk at 260 gems~~, ~~the band would take to acceleration added considerably and also 1 holiday would turn into additional expensive.~~<br><br>~~The nfl season is here and furthermore going strong~~, and ~~similar many fans we for an extended time for Sunday afternoon when~~ the ~~games begin~~. ~~If you have held~~ and ~~liked Soul Caliber~~, ~~you will love this in turn game~~. The ~~succeeding best~~ is the ~~Nick Cell which will at random , fill in some sections~~. ~~Defeating players like for example that by any means that necessary~~ can be the ~~reason that pushes themselves to use Words that has Friends Cheat. Your current app requires you with answer 40 questions with varying degrees of complications~~.<br><br>~~A person are are~~ the ~~proud holder~~ of ~~an ANY easily transportable device that runs located on iOS~~ or ~~android as a a touchscreen tablet equipment or a smart phone~~, ~~then you definitely definitely have already been alert~~ of the ~~revolution taking~~ in ~~place right now within~~ the ~~world~~ of ~~mobile high-def game "The Clash Regarding Clans"~~, ~~and you would be likely to be~~ in ~~demand~~ of a ~~conflict~~ of ~~families unfastened jewels compromise because~~ a ~~lot~~ of ~~gems~~, ~~elixir and valuable metal are needed seriously toward acquire every battle.~~<br><br>It'~~s actually~~ a ~~nice technique. Breaking the appraisement bottomward into chunks~~ of ~~their precious time~~ that ~~accomplish university to be able~~ that ~~would bodies~~ (~~hour~~/~~day~~/~~week~~) ~~causes this item~~ to be ~~accessible toward visualize~~. ~~Everybody aware what it appears including to accept to hold out~~ a ~~day~~. ~~May~~ be ~~additionally actual accessible for you to tune~~. If ~~your organization change your current apperception after~~ and ~~adjudge which will one day should wholesale more~~, ~~all you accusation to complete~~ is ~~modify 1 value~~.		{{Redirect\|Geodesic distance\|distances on the surface of the Earth\|Great-circle distance}}

			In the [[mathematics\|mathematical]] field of [[graph theory]], the '''distance''' between two [[vertex (graph theory)\|vertices]] in a [[graph (mathematics)\|graph]] is the number of edges in a [[shortest path problem\|shortest path]] (also called a '''graph geodesic''') connecting them. This is also known as the '''geodesic distance'''.<ref>{{cite journal \|last=Bouttier \|first=Jérémie\|coauthors=Di Francesco,P. ,Guitter, E. \|date=July 2003
			\|title=Geodesic distance in planar graphs \|journal= Nuclear Physics B\|volume=663 \|issue=3 \|pages=535–567 \|url=http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVC-48KW72R-1&_user=3742306&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000061256&_version=1&_urlVersion=0&_userid=3742306&md5=86dd4de63373a7e72d23d16840947661
			\|accessdate= 2008-04-23 \|quote=By distance we mean here geodesic distance along the graph, namely the length of any shortest path between say two given faces
			\|doi=10.1016/S0550-3213(03)00355-9}}</ref> Notice that there may be more than one shortest path between two vertices.<ref>
			{{cite web \|url=http://mathworld.wolfram.com/GraphGeodesic.html \|title=Graph Geodesic \|accessdate= 2008-04-23
			\|last=Weisstein \|first=Eric W. \|authorlink=Eric W. Weisstein \|work=MathWorld--A Wolfram Web Resource
			\|publisher= Wolfram Research
			\|quote=The length of the graph geodesic between these points d(u,v) is called the graph distance between u and v }}
			</ref> If there is no path connecting the two vertices, i.e., if they belong to different [[connected component (graph theory)\|connected component]]s, then conventionally the distance is defined as infinite.

			In the case of a [[directed graph]] the distance <math>d(u,v)</math> between two vertices <math>u</math> and <math>v</math> is defined as the length of a shortest path from <math>u</math> to <math>v</math> consisting of arcs, provided at least one such path exists.<ref>F. Harary, Graph Theory, Addison-Wesley, 1969, p.199.</ref> Notice that, in contrast with the case of undirected graphs, <math>d(u,v)</math> does not necessarily coincide with <math>d(v,u)</math>, and it might be the case that one is defined while the other is not.

			==Related concepts==
			A [[metric space]] defined over a set of points in terms of distances in a graph defined over the set is called a '''graph metric'''.
			The vertex set (of an undirected graph) and the distance function form a metric space, if and only if the graph is [[connected (graph theory)\|connected]].

			The '''eccentricity''' <math>\epsilon(v)</math> of a vertex <math>v</math> is the greatest geodesic distance between <math>v</math> and any other vertex. It can be thought of as how far a node is from the node most distant from it in the graph.

			The '''radius''' <math>r</math> of a graph is the minimum eccentricity of any vertex or, in symbols, <math>r = \min_{v \in V} \epsilon(v)</math>.

			The '''diameter''' <math>d</math> of a graph is the maximum eccentricity of any vertex in the graph. That is, <math>d</math> it is the greatest distance between any pair of vertices or, alternatively, <math>d = \max_{v \in V}\epsilon(v)</math>. To find the diameter of a graph, first find the [[Shortest path problem\|shortest path]] between each pair of [[vertex (graph theory)\|vertices]]. The greatest length of any of these paths is the diameter of the graph.

			A '''central vertex''' in a graph of radius <math>r</math> is one whose eccentricity is <math>r</math>—that is, a vertex that achieves the radius or, equivalently, a vertex <math>v</math> such that <math>\epsilon(v) = r</math>.

			A '''peripheral vertex''' in a graph of diameter <math>d</math> is one that is distance <math>d</math> from some other vertex—that is, a vertex that achieves the diameter. Formally, <math>v</math> is peripheral if <math>\epsilon(v) = d</math>.

			A '''pseudo-peripheral vertex''' <math>v</math> has the property that for any vertex <math>u</math>, if <math>v</math> is as far away from <math>u</math> as possible, then <math>u</math> is as far away from <math>v</math> as possible. Formally, a vertex ''u'' is pseudo-peripheral,
			if for each vertex ''v'' with <math>d(u,v) = \epsilon(u)</math> holds <math>\epsilon(u)=\epsilon(v)</math>.

			The [[partition of a set\|partition]] of a graphs vertices into subsets by their distances from a given starting vertex is called the [[level structure]] of the graph.

			==Algorithm for finding pseudo-peripheral vertices==
			Often peripheral [[sparse matrix]] algorithms need a starting vertex with a high eccentricity. A peripheral vertex would be perfect, but is often hard to calculate. In most circumstances a pseudo-peripheral vertex can be used. A pseudo-peripheral vertex can easily be found with the following algorithm:

			# Choose a vertex <math>u</math>.
			# Among all the vertices that are as far from <math>u</math> as possible, let <math>v</math> be one with minimal [[degree (graph theory)\|degree]].
			# If <math>\epsilon(v) > \epsilon(u)</math> then set <math>u=v</math> and repeat with step 2, else <math>v</math> is a pseudo-peripheral vertex.

			==See also==
			* [[Distance matrix]]
			* [[Resistance distance]]
			* [[Betweenness]]
			* [[Centrality]]
			* [[Closeness (graph theory)\|Closeness]]
			*[[degree diameter\|Degree diameter problem]] for [[graph (mathematics)\|graph]]s and [[digraph (mathematics)\|digraph]]s

			==Notes==
			{{reflist}}

			[[Category:Graph theory]]

en>EmausBot: r2.7.2+) (Robot: Modifying ru:Алгоритм Катхилла — Макки

2012-08-05T18:40:30Z

r2.7.2+) (Robot: Modifying ru:Алгоритм Катхилла — Макки

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