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Topic: Connected graph

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Graph theory

Spanning tree (mathematics)

Adjacency matrix

Adjacency list

Total coloring

Minimal spanning tree

Incidence matrix

Algorithm

Computer science

Diameter

Minimum spanning tree

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	PlanetMath: connected graph (Site not responding. Last check: 2007-10-21)
		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.
	planetmath.org /encyclopedia/ConnectedGraph.html (398 words)

	Graph theory - Wikipedia, the free encyclopedia
		Informally, a graph is a set of objects called vertices (or nodes) connected by links called edges (or arcs) which can be directed (assigned a direction).
		Graphs are represented graphically by drawing a dot for every vertex, and drawing an arc between two vertices if they are connected by an edge.
		Incidence matrix - The graph is represented by a matrix of E (edges) by V (vertices), where [edge, vertex] contains the edge's data (simplest case: 1 - connected, 0 - not connected).
	en.wikipedia.org /wiki/Graph_theory (1209 words)

	Connected component (graph theory) - Wikipedia, the free encyclopedia
		In an undirected graph, a connected component or component is a maximal connected subgraph.
		Connected components are useful because often algorithms or theorems can be applied to each connected component individually, taking advantage of it being a connected graph, and combine these solutions to obtain a solution for the entire graph.
		For example, if we find a minimum spanning tree or a maximum matching for each connected component, their union is a minimum spanning forest or maximum matching for the entire graph.
	en.wikipedia.org /wiki/Connected_component_(graph_theory) (320 words)

	Encyclopedia: Graph theory
		Graphs are usually represented pictorially using dots to represent vertexes, and arcs representing the edges between connected vertexes.
		In graph theory, a perfect graph is a graph in which the chromatic number of every induced subgraph equals the clique number of that subgraph.
		Given a connected, undirected graph, a spanning tree of that graph is a subgraph which is a tree and connects all the vertices together.
	www.nationmaster.com /encyclopedia/Graph-theory (3291 words)

	PlanetMath: ${k}$-connected graph (Site not responding. Last check: 2007-10-21)
		Connectivity of graphs, when it isn't specified which flavor is intended, usually refers to vertex connectivity, unless it is clear from the context that it refers to edge connectivity.
		Note that ``removing a vertex'' in graph theory also involves removing all the edges incident to that vertex.
		For directed graphs there are two notions of connectivity (``weak'' if the underlying graph is connected, ``strong'' if you can get from everywhere to everywhere).
	planetmath.org /encyclopedia/KConnectedGraph.html (286 words)

	Graphs Glossary
		A graph is bipartite if the vertices can be partitioned into two sets, X and Y, so that the only edges of the graph are between the vertices in X and the vertices in Y. Trees are examples of bipartite graphs.
		A chain in a graph is a sequence of vertices from one vertex to another using the edges.
		A connected graph is one in which every pair of vertices are joined by a chain.
	www-math.cudenver.edu /~wcherowi/courses/m4408/glossary.htm (1926 words)

	ipedia.com: Graph theory Article (Site not responding. Last check: 2007-10-21)
		A graph with only vertices and no edges is known as the empty graph, but is sometimes also known as the Null graph.
		An undirected graph can be seen as a simplicial complex consisting of 1-simplices (the edges) and 0-simplices (the vertices).
		Every graph gives rise to a matroid, but in general the graph cannot be recovered from its matroid, so matroids are not truly generalizations of graphs.
	www.ipedia.com /graph_theory.html (901 words)

	Graphs and Networks
		In an undirected graph, the DEGREE of a vertex is the number of vertices it is adjacent with.
		A subgraph of a graph G is a graph G' such that V' is a subset of V and E' is a subset of E. (Of course, only vertices in V' may appear in the pairs in E' if G' is to be a graph).
		C. Recall that we defined a graph in terms of a SET of edges, E. This implies that there cannot be more that one edge connecting any pair of vertices in a graph, or more than one edge connecting any pair of vertices in the same direction in a digraph.
	www.cs.gordon.edu /courses/cs321/lectures/graphs.html (4314 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.
		Some researchers have proposed studying the average distance of a graph, defined to be the length of the shortest path from u to v, averaged over all ordered pairs (u,v); this is referred to as diameter in [Albert, Jeong, and Barabasi 99].
		First, the connectivity of the web graph as an undirected graph is extremely resilient and does not depend on the existence of nodes of high in-degree.
	www.almaden.ibm.com /cs/k53/www9.final (6251 words)

	Graphs
		The second notion, that of the edges being connections between nodes, is by far too important to the Graph Theory to leave it to one's intuitive perception.
		For a graph, the sum of degrees of all its nodes equals twice the number of edges.
		A graph is connected if every two vertices can be connected by a walk.
	www.cut-the-knot.org /do_you_know/graphs.shtml (1002 words)

	Connected Components (Site not responding. Last check: 2007-10-21)
		Testing whether a graph is connected is an essential preprocessing step for every graph algorithm.
		Connectivity is an essential invariant for network design and other structural problems.
		If the graph is connected and has n-1 edges for n vertices, it is a tree.
	www2.toki.or.id /book/AlgDesignManual/BOOK/BOOK4/NODE159.HTM (1115 words)

	search.cpan.org: Graph - graph data structures and algorithms (Site not responding. Last check: 2007-10-21)
		For an undirected graph, return the vertices in the ith biconnected component of the graph as an anonymous arrays of vertices in the component.
		The vertices in the strongly connected graph are formed from the strongly connected elements of the graph (currently by sorting the vertices of the original graph present in the strongly connected component and concatenating the vertex names with
		Two graphs being isomorphic means that they are structurally the same graph, the difference being that the vertices might have been renamed or substituted.
	search.cpan.org /~jhi/Graph/lib/Graph.pod (5736 words)

	Diameter - Wikipedia, the free encyclopedia
		The diameter of a circle is also the longest chord that the circle has.
		The diameter of a connected graph is the distance between the two vertices which are furthest from each other.
		The distance between two vertices a and b is the length of the shortest path connecting them (for the length of a path, see Graph theory).
	en.wikipedia.org /wiki/Diameter (351 words)

	Graph Theory Glossary
		In a digraph (directed graph) the degree is usually divided into the in-degree and the out-degree (whose sum is the degree of the vertex in the underlying undirected graph).
		A digraph (or a directed graph) is a graph in which the edges are directed.
		A path is a sequence of consecutive edges in a graph and the length of the path is the number of edges traversed.
	www.utm.edu /departments/math/graph/glossary.html (816 words)

	Boost Graph Library: Connected Components
		A connected component of an undirected graph is a set of vertices that are all reachable from each other.
		The algorithm computes how many connected components are in the graph, and assigning each component an integer label.
		Read/Write Property Map and its key type must be the graph's vertex descriptor type and the value type of the color map must model ColorValue.
	www.boost.org /libs/graph/doc/connected_components.html (326 words)

	Citations: A linear-time algorithm for finding a sparse k-connected spanning subgraph of a k-connected graph - ...
		Gamma 1) O(kn) If G is (k 1) connected, then G 0 is (k 1) connected, and moreover, G 0 (v; w) min(k 1; G (v; w) for all node pairs v; w, where H (v; w) denotes the maximum number of openly disjoint v w paths in the graph H.
		Given a graph G = V; E) and a flow f, we define E 0 f to be the subset of edges with zero flow and define E 1 f = E Gamma E 0 f.
		In this paper, we concentrate on the minimum size k edge connected spanning subgraph problem: given a positive integer k and a k edge connected graph G, nd a k edge connected spanning subgraph of G with the minimum number of edges.
	citeseer.ist.psu.edu /context/61067/0 (7862 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.
		For instance, what is the structure of the undirected graph induced by the co-citation relation or by bibliographic coupling [White and McCain89].
	www9.org /w9cdrom/160/160.html (6296 words)

	Stata help for graph twoway connected (Site not responding. Last check: 2007-10-21)
		In a connected-line plot, the markers are displayed and the points are connected.
		connected is a plottype as defined in twoway.
		connected is, in fact, scatter, the difference being that by default the points are connected:
	www.stata.com /help.cgi?graph+twoway+connected (120 words)

	connected graph (Site not responding. Last check: 2007-10-21)
		Definition: An undirected graph that has a path between every pair of vertices.
		See also complete graph, biconnected graph, triconnected graph, strongly connected graph, forest, bridge, reachable, maximally connected component, connected components, vertex connectivity, edge connectivity.
		Paul E. Black, "connected graph", from Dictionary of Algorithms and Data Structures, Paul E. Black, ed., NIST.
	www.nist.gov /dads/HTML/connectedGraph.html (88 words)

	connected graph - OneLook Dictionary Search
		Connected graph : A Glossary of Mathematical Terms [home, info]
		Connected Graph : Eric Weisstein's World of Mathematics [home, info]
		Phrases that include connected graph: strongly connected graph, completely connected graph, hamilton connected graph, planar connected graph
	www.onelook.com /cgi-bin/cgiwrap/bware/dofind.cgi?word=connected+graph (151 words)

	COGRE: COnnected GRaph Editor (Site not responding. Last check: 2007-10-21)
		Any kind of graph can be supported through object inheritance via EIEIO See (eieio)Top.
		Graph The graph consists of a buffer, and all child elements in that graph.
		When a node is deleted, all links connected to it in some way are also deleted.
	cedet.sourceforge.net /info/cogre.html (175 words)

	[No title]
		If G is a simple connected graph on more than one vertex, then
		- 1)], where S is the set of maximum degree vertices of the complement of the graph G the neighborhood is taken in the complement.
		If G is a simple connected graph on at least 2 vertices, then
	cms.dt.uh.edu /faculty/delavinae/research/wowII/open.html (1866 words)

	COGRE Homepage
		It is a base library for editing and manipulating connected graphs.
		Additional tools will be available using COGRE for managing diagrams for UML flavors, such as a class hierarchy diagrams.
		Consider creating and maintaining a language definition for Semantic, or helping define the proper blocks and link routing code for COGRE, the base graph editor.
	cedet.sourceforge.net /cogre.shtml (359 words)

	connected graph - FOLDOC Definition (Site not responding. Last check: 2007-10-21)
		A graph such that there is a path between any pair of nodes (via zero or more other nodes).
		Thus if we start from any node and visit all nodes connected to it by a single edge, then all nodes connected to any of them, and so on, then we will eventually have visited every node in the connected graph.
		If you have problems or comments con cerning our WWW service, please send e-mail to the following address: webmaster@NightFlight.com.
	www.nightflight.com /foldoc-bin/foldoc.cgi?connected+graph (87 words)

	connectedgraph
		chemist chemistry chemist's conceited connection connect considerable consider constant construct
		chimiste coincider connecter considérable considérer constamment constant Constantinople constater constellation consterner constituer construction construire coïncider
		changed chemist chemistry cincture coincide coincidence coincident coinciding comestibles concatenate concede conceit conceited "conk out" connect connected connecting connection connections consider considerable considerably considerate consideration considered considering constable constabulary constancy constant constantly constellation consternation constipated constipation constituency constituent constitute constitution constitutional constrain constrained constraint constrict constricted constriction construct construction constructive construe
	dictionary-x.com /connectedgraph.html (480 words)

	allegro-cl mail archive - feilong : strong connected Graph (Site not responding. Last check: 2007-10-21)
		Hallo Friends: I want to define a strong connected graph with lisp: (let ((graph '(a (b nil.
		nil) c))) (setf (second (second graph)) (second graph)) (setf (rest (last (second graph))) (rest (rest graph))) graph) but intepreter displays error messages *** - Lisp stack overflow.
		By the way,how can I correct build a strong-connected graph with lisp and how can I such each atom in this graph?
	www.xach.com /lisp/allegro-cl/2003-1/1103.html (86 words)

	allegro-cl mail archive - BobGia: strong connected Graph (Site not responding. Last check: 2007-10-21)
		> Hallo Friends: > I want to define a strong connected graph with lisp: > (let ((graph '(a (b nil.
		nil) c))) > (setf (second (second graph)) (second graph)) > (setf (rest (last (second graph))) (rest (rest graph))) > graph) > but intepreter displays error messages > *** - Lisp stack overflow.
		The PRINT function (in the top-level read-eval-print loop) gets into infinite recursion trying to print circular list-structure.
	www.xach.com /lisp/allegro-cl/2003-1/1105.html (122 words)

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