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Topic: Strongly connected component

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	strongly connected component
		Definition: A strongly connected subgraph, S, of a directed graph, D, such that no vertex of D can be added to S and it still be strongly connected.
		Note: If a graph is strongly connected, it has only one strongly connected component.
		The strongly connected components partition the vertices in the graph.
	www.nist.gov /dads/HTML/stronglyConnectedCompo.html (222 words)

	PlanetMath: connected graph
		A connected graph is a graph such that there exists a path between all pairs of vertices.
		A connected component is a maximal (under inclusion) subset of vertices of any graph and any edges between them that forms a connected graph.
		This is version 4 of connected graph, born on 2002-03-02, modified 2005-08-09.
	www.planetmath.org /encyclopedia/ConnectedComponents.html (404 words)

	Boost Graph Library: Strongly Connected Components
		The number of components is the return value of the function.
		A strongly connected component of a directed graph G=(V,E) is a maximal set of vertices U which is in V such that for every pair of vertices u and v in U, we have both a path from u to v and path from v to u.
		The algorithm then records which component each vertex in the graph belongs to by recording the component number in the component property map.
	www.boost.org /libs/graph/doc/strong_components.html (450 words)

	Glossary of graph theory - Wikipedia, the free encyclopedia
		Informally, a strongly connected component of a graph is a subgraph where all nodes in the subgraph are reachable by all other nodes in the subgraph.
		Connectivity extends the concept of adjacency and is essentially a form (and measure) of concatenated adjacency.
		A component is a maximally connected subgraph; a block, either a maximally 2-connected subgraph or a bridge with its endvertices; and a biconnected component, a maximal set of edges in which any two members lie on a common simple cycle.
	en.wikipedia.org /wiki/Glossary_of_graph_theory (5717 words)

	Strongly connected component - Wikipedia, the free encyclopedia
		A directed graph is called strongly connected if for every pair of vertices u and v there is a path from u to v and a path from v to u.
		The strongly connected components (SCC) of a directed graph are its maximal strongly connected subgraphs.
		It makes use of the fact that the transpose graph (the same graph with the direction of every edge reversed) has exactly the same connected components as the original graph.
	en.wikipedia.org /wiki/Strongly_Connected_Components (149 words)

	graphs (Site not responding. Last check: )
		A connected component, H, of an undirected graph is a maximal connected subgraph.
		The set of connected components of a graph can be obtained by making repeated calls to either DFS or BFS on vertices which are not in a connected component yet.
		A biconnected component of a connected graph G is a maximal biconnected subgraph H of G. By maximal, we mean that no other subgraph that is both biconnected and properly contains H. The biconnected components of a connected, undirected graph G can be found by using any depth-first spanning tree of G.
	www.ecst.csuchico.edu /~amk/foo/javanotes/graphintro.html (890 words)

	Connected
		Cloud Connected Cloud Connected is a single by the Swedish melodic 2002.
		Connected In mathematics, the term connected is used for: a certain class of topological spaces (see connected space) a...
		Connected sum In connected -dimensional manifolds is a manifold formed by deleting a ball inside each manifold and gluei...
	www.brainyencyclopedia.com /topics/connected.html (182 words)

	Strongly Connected Components, CS 410 Opt
		This chapter outlines an algorithm by Robert Tarjan, ref [1], that identifies all strongly connected components in a directed graph G with entry point e.
		Strongly connected components (SCC) are those subgrahs of G in which every node can be reach from every node in the SCC.
		A loop is a strongly connected component with additional restrictions.
	www.cs.pdx.edu /~herb/cs410f99/scc.htm (666 words)

	Connected Components
		The distributed strong components algorithm uses the sequential strong components algorithm to identify components local to a processor.
		These three sets are the vertices in the predecessor set not contained in the identified strongly connected component, the vertices in the successor set not in the strongly connected component, and the remaing vertices in the initial vertex set not in the predecessor or successor sets.
		To boost performance in sparse graphs when identifying small components, when less than a given portion of the initial number of vertices remain in active vertex sets, a filtered graph adapter is used to limit the graph seen by the breadth first search algorithm to the active vertices.
	www.osl.iu.edu /research/pbgl/documentation/graph/strong_components.html (873 words)

	Strong connectivity
		We say that a vertex a is strongly connected to b if there exist two paths, one from a to b and another from b to a.
		Strongly connected components also have a use in other graph algorithms: if you replace every strongly connected component by a single vertex, you get a smaller directed acyclic graph, known as the component graph or condensation (Baase ex.
		Since the components of the graph are just subtrees of the DFS tree, to find components, we just have to break tree at certain edges, and the components will be formed by what's left of the tree.
	www.ics.uci.edu /~eppstein/161/960220.html (2041 words)

	graphconncomp :: Functions (Bioinformatics Toolbox)
		A weakly connected component is a maximal group of nodes that are mutually reachable by violating the edge directions.
		A strongly connected component is a maximal group of nodes that are mutually reachable without violating the edge directions.
		Find the number of strongly connected components in the directed graph and determine to which component each of the 10 nodes belongs.
	www.mathworks.com /access/helpdesk/help/toolbox/bioinfo/ref/graphconncomp.html (446 words)

	www9 paper
		Given a directed graph, a strongly connected component (strong component for brevity) of this graph is a set of nodes such that for any pair of nodes u and v in the set there is a path from u to v.
		We refer to the components of the undirected graph obtained from a directed graph by ignoring the directions of its arcs as the weak components of the directed graph.
		By running the strongly connected component algorithm, we find that there is a single large SCC consisting of about 56M pages, all other components are significantly smaller in size.
	www.almaden.ibm.com /cs/k53/www9.final (6251 words)

	EE382C Embedded Software Systems - Single Appearance Schedules (Site not responding. Last check: )
		Connected consistent acyclic SDF graphs always have single appearance schedules.
		Clustering a strongly connected component into a single actor A never results in deadlock since there can be no cycle containing A.
		Since clustering all strongly connected components yields an acyclic graph, an arbitrarily connected consistent SDF graph has a valid single appearance schedule if and only if each strongly connected component has a valid single appearance schedule.
	www.ece.utexas.edu /~bevans/courses/ee382c/lectures/18_sdf_looped/single.html (440 words)

	Answers for April 4 Reading Qestions (Site not responding. Last check: )
		Therefore the strongly connected components are {a, b, e}, {c}.
		Therefore the strongly connected components are {a}, {b} {c, d, e}, and {f}.
		Therefore the strongly connected components are {a, b, c, d, f, g, h, i}, {e}.
	www-scf.usc.edu /~csci271/rq_apr4_answers.html (691 words)

	HTTP/1.1: Security Considerations
		We very strongly recommend that a convenient interface be provided for the user to control dissemination of such information, and that designers and implementors be particularly careful in this area.
		strongly correlated to the membership of a particular ethnic group.
		User agents which offer the option to configure the contents of an Accept-Language header to be sent in every request are strongly encouraged to let the configuration process include a message which makes the user aware of the loss of privacy involved.
	www.w3.org /Protocols/rfc2616/rfc2616-sec15.html (1913 words)

	The Small World Web
		Informal observation suggests that pages which do not belong to any large SCC tend to focus on either a narrow topic, don't have many outlinks, or don't have many pages referencing them (which implies that they are probably not worth reading).
		In fact, the largest strongly connected component was a group of pro life pages which had mentioned "pro choice" in their content.
		The largest strongly connected components for all three queries had a high clustering coefficient and a small average shortest path, showing that groups of people with common interests are linked to one another via a small world network on the Web.
	www.hpl.hp.com /shl/papers/smallworld/smallworldpaper.html (2973 words)

	Method for thinning a protocol - Patent 5574919
		A directed graph is strongly connected if for each pair of distinct states in the FSM graph there exists a directed path from one to the other.
		As noted previously, a strongly connected component or a strongly connected graph is defined as a subgraph in which there is a path from every state to every other state.
		Whenever a component FSM F.sub.i is removed from L construct the strongly connected component that contains the initial state.
	www.freepatentsonline.com /5574919.html (5977 words)

	Strongly Connected Components
		This decomposition is important as it is used to divide a single directed graph into pieces for further processing.
		Output the vertices of each tree in the depth-first forest of step 3 as a separate strongly connected component.
		V is in a strongly connected component that consists of al v
	www.cs.fsu.edu /~cop4531/slideshow/chapter23/23-5.html (175 words)

	analysis of the strong set in the PGP web of trust
		At first, the amsd decreases more than average because the the largest connected component becomes 'rounder'.
		The scc of the graph remains big, almost all the way down.
		Dissecting the Leaf of Trust by Jörgen Cederlöf is an analysis of trust relations in the strongly connected component of the pgp web of trust.
	pgp.cs.uu.nl /plot (966 words)

	Strongly Connected Components
		Two vertices of directed graph are in the same component if and only if they are reachable from each other.
		From any vertex v, one can visit to any other vertex in the same component as v and then return back v; if one visits a vertex in a different component the return to v is impossible.
		corresponds to a strongly connected component (SCC) of component graph
	www.personal.kent.edu /~rmuhamma/Algorithms/MyAlgorithms/GraphAlgor/strongComponent.htm (389 words)

	Synchronizing Graphs
		A strongly connected component C with a set of vertices W of a SA is called initial if for every vertex w in C and every vertex
		The first representation (a) is synchronizing: aa is a synchronizing word for the vertex 1, aab is synchronizing for 2, c is synchronizing for 3 and cb is synchronizing for the vertex 4.
		The second representation (b) on the same figure is not synchronizing since the vertices in the initial component don't have synchronizing words.
	www.math.usf.edu /~jonoska/symbolic/node17.html (471 words)

	Graph structure in the web
		Thus, the web is not the ball of highly-connected spaghetti we believed it to be; rather, the connectivity is strongly limited by a high-level global structure.
		By running the strongly connected component algorithm, we find that there is a single large SCC consisting of about 56 million pages, all other components are significantly smaller in size.
		Since the second largest strong component is of size 150 thousand, we infer that SCC is the unique strong component that contains all nodes exploding following in- as well as out-links.
	www9.org /w9cdrom/160/160.html (6296 words)

	Graph Theory Applied to Topology Analysis - CAIDA : ANALYSIS : topology
		In that case, the stubs of the graph, i.e., trees connected to the rest of the graph by a single link, are stripped.
		A strongly connected component of a graph is a set of nodes such that each node pair (A,B) has a path from A to B and a path from B to A. Connected Component
		A connected component is called giant component if it contains more than 50% of the nodes in the graph.
	www.caida.org /analysis/topology/graphtheory.xml (489 words)

	Sensei's Library: Cyclic positions taxonomy
		From general theory we take the idea of strongly connected component: for us a set of positions each of which can be reached from any other, and to which no further positions can be added while still having that property.
		An approach ko is different: its states give rise to at least two distinct strongly connected components.
		The underlying acyclic component graph, consisting of the components and the possible transitions between them, is a fundamental object of study, however complex the position.
	senseis.xmp.net /?path=SecondCourseOnKo&page=CyclicPositionsTaxonomy (383 words)

	return
		A bi-connected component is a maximally connected subgraph in which for every triple of vertices a, v, and w there exists a chain between v and w which does not include the vertex a.
		If we set a minimum size for the bi-connected components to ten journals, 62 bi-components are distinguished that are very homogenous and meaningful; but the groups vary in size.
		However, there is one bi-connected component which is more strongly connected than the other 61, notably the large one of 1,417 journals.
	www.leydesdorff.net /jcr01/art/index.htm (4765 words)

	strong from FOLDOC
		In a strongly typed language, conversion between types requires the use of explicit conversion functions as opposed to implicit type coercion.
		Typing strength is a continuum; ML is more strongly typed than Java, which is more strongly typed than C.
		Among strongly typed languages, Ada, Java, Haskell and ML are statically typed, whereas Python and Ruby are dynamically typed.
	wombat.doc.ic.ac.uk /foldoc/foldoc.cgi?strong (385 words)

	HW10 - CS280
		There is one weakly connected component of size 800 and several other weakly connected components of smaller size.
		There is one strongly connected component of size 500 and several other strongly connected components of smaller size.
		Is this vertex in the large strongly connected component?
	www.cs.cornell.edu /courses/cs280/2002sp/homework/hw10.htm (596 words)

	The Size of the Largest Strongly Connected Component of a Random Digraph With a Given Degree Sequence - Cooper, Frieze ... (Site not responding. Last check: )
		A full characterization is provided, in probability, of the fan-in and fan-out of all vertices including the number of vertices with small (o(n)) and large (cn) fan-in or fan-out.
		We also give the size of the giant strongly connected component, if any, and the structure of the bowtie digraph induced by the vertices with large fan-in or fan-out.
		The size of the largest strongly connected component of a random digraph with a given degree sequence.
	citeseer.ist.psu.edu /576697.html (612 words)

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