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Topic: Graph path

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graph theory

Glossary of graph theory

graph of a function

graph mathematics

tree graph theory

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planar graphs

directed graphs

complete graph

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directed acyclic graph

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	PlanetMath: connected graph
		A connected graph is a graph such that there exists a path between all pairs of vertices.
		If the graph is a directed graph, and there exists a path from each vertex to every other vertex, then it is a strongly 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)

	Graphs Glossary (Site not responding. Last check: 2007-10-15)
		A chain in a graph is a sequence of vertices from one vertex to another using the edges.
		A path in a digraph is a sequence of vertices from one vertex to another using the arcs.
		An induced (generated) subgraph is a subset of the vertices of the graph together with all the edges of the graph between the vertices of this subset.
	www-math.cudenver.edu /~wcherowi/courses/m4408/glossary.htm (1926 words)

	Graph theory : Simple path (Site not responding. Last check: 2007-10-15)
		In a weighted graph or digraph, an additional function E → R associates a value with each edge, which can be considered its "cost"; such graphs arise in optimal route problems[?] such as the traveling salesman problem.
		Graphs are often represented "graphically" as follows: draw a dot for every vertex, and for every edge draw an arc connecting its endpoints.
		A loop in a graph or digraph is an edge e in E whose endpoints are the same vertex.
	www.eurofreehost.com /si/Simple_path_2.html (506 words)

	DMP: Definitions from Discrete Mathematics
		When a graph is used to model project scheduling, the critical path is a path from the start to the finish which passes through all of the tasks which are critical to completing the project in the shortest amount of time.[refcomap, p.158]
		A path is a sequence of adjacent vertices.
		The shortest path algorithm is a method for finding the shortest route from one vertex to another in a weighted graph.The shortest path algorithm requires extending a tree from the starting vertex until it reaches the finishing vertex.
	www.colorado.edu /education/DMP/def.html (3248 words)

	Patent 6029162: Graph path derivation using fourth generation structured query language
		Instead of representing graph edges as a 2-dimensional array as in the Warshall procedure, a relational database procedure approach involves representing a directed graph as a set of parent-child edges in a relational database table and then using a powerful declarative programming language such as SQL in a recursive algorithm to navigate through the table.
		The third step is the creation of a transitive closure table, called city.sub.13 path that includes a "path" of concatenated edges between a "source" vertex and a "destination" vertex, along with the total path length between the source and destination vertex.
		Whenever a city is removed from the graph and the corresponding record is deleted from the city table, the following SQL code is executed to maintain the city.sub.-- path transitive closure table.
	www.freepatentsonline.com /6029162.html (3846 words)

	Boost Graph Library: Graph Theory Review
		Fundamentally, a graph consists of a set of vertices, and a set of edges, where an edge is something that connects two vertices in the graph.
		Now a path is a sequence of edges in a graph such that the target vertex of each edge is the source vertex of the next edge in the sequence.
		The primary property of a graph to consider when deciding which data structure to use is sparsity, the number of edges relative to the number of vertices in the graph.
	www.boost.org /libs/graph/doc/graph_theory_review.html (2374 words)

	Docjar: iiuf/util/graph/Path.java (Site not responding. Last check: 2007-10-15)
		48 49 @param singlePath a GraphNode representing the path to a node.
		Two paths are considered equal if they are of 154 the same length, and contain 155 the same elements (`.equals`).
		The hash code of a Path 181 is defined to be the hash code of the last component in the path.
	www.docjar.com /html/api/iiuf/util/graph/Path.java.html (770 words)

	GraphPathFn
		If "the lowest cost path between and " is equal to, then is an instance of "the set of paths between and ".
		If "the highest cost path between and " is equal to, then is an instance of "the set of paths between and ".
		If is a part of and is not an instance of directed graph, then "the set of paths between and " is equal to if and only if "the set of paths between and " is equal to.
	godel.iis.sinica.edu.tw /kifb/en/concepts/_graph_path_fn.html (303 words)

	GraphPathFn
		Se "il cammino col minor costo tra node1 e node2" is uguale a path, allora path é un' istanza di "l' insieme di cammini tra node1 e node2".
		Se "il il cammino col costo maggiore tra node1 e node2" is uguale a path, allora path é un' istanza di "l' insieme di cammini tra node1 e node2".
		Se path é una parte di graph e graph é not un' istanza di GrafoDiretto, allora "l' insieme di cammini tra node1 e node2" is uguale a path se e solo se "l' insieme di cammini tra node2 e node1" is uguale a path.
	virtual.cvut.cz /kifb/it/concepts/_graph_path_fn.html (344 words)

	Department of Computer Science (Site not responding. Last check: 2007-10-15)
		Evaluating path expressions efficiently is an important component of XML data management.
		Graph summaries have been proposed that can be used as a path index.
		The idea is to substitute graph traversal over the data with traversal over a much smaller summary.
	www.cs.uchicago.edu /events/163 (186 words)

	Class rpi.goldsd.graph.Path
		Concatenates the given path with this path by adding all elements of the given path to the end of this path.
		Returns the weight of this path, which is simply the sum of all weighted edges of this path.
		an enumeration of the vertices of this path.
	www.cs.rpi.edu /projects/pb/jgb/jdoc/rpi.goldsd.graph.Path.html (1077 words)

	Patent 4815824: Elliptical LCD bar graph with path outline-defining segments
		LCD bar graphs are analog displays having a plurality discrete segments which represent quantitative increments, i.e, a scale on the graph.
		In a preferred embodiment, the path may be elliptical and the outline segments may be disposed in close proximity to produce the illusion of a continuous outline.
		Bar graph 12 includes an outline 16 which indicates the path of the graph and major pickets 18 which are equally distributed along the bar graph for dividing the graph into a higher order scale.
	www.freepatentsonline.com /4815824.html (3125 words)

	Clearing up the market cycle... best Path Graph (Site not responding. Last check: 2007-10-15)
		In an undirected graph, this is obviously a metric...
		Path Graph -- from MathWorld Path Graph -- from MathWorld The path P_n is a tree with two nodes of vertex degree 1, and the other n-2 nodes of vertex degree 2.
		The path graph of length n is implemented as Path[n] in the Mathematica add-on...
	ascot.pl /th/Fourier5/Path-Graph.htm (1162 words)

	The Ultimate Path (graph theory) - American History Information Guide and Reference
		The length of a path is the number of edges that the path uses, counting multiple edges multiple times.
		In the graph shown, (1, 2, 5, 1, 2, 3) is a path of length 5, and (5, 2, 1) is a simple path of length 2.
		The weight of a path in a weighted graph is the sum of the weights of the traversed edges.
	www.historymania.com /american_history/Simple_path (228 words)

	Diameter - Open Encyclopedia (Site not responding. Last check: 2007-10-15)
		When using the word in the more modern sense, one speaks of the diameter rather than a diameter, because all diameters of a circle have the same length.
		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).
	open-encyclopedia.com /Diameter (313 words)

	David Eppstein - Publications (Site not responding. Last check: 2007-10-15)
		Finds multiple short paths connecting two terminals in a graph (allowing repeated vertices and edges in the paths) in constant time per path after a preprocessing stage dominated by a single-source shortest path computation.
		Some of these results were announced in the conference version of "subgraph isomorphism for planar graphs and related problems" but not included in the journal version.
		Our program searches through a state space related to the de Bruijn graph of the automaton, using a method that combines features of breadth first and iterative deepening search, and includes fast bit-parallel graph reachability and path enumeration algorithms for finding the successors of each state.
	www.ics.uci.edu /~eppstein/pubs/graph-path.html (1036 words)

	Classical Tangent Graph Path Planner (Site not responding. Last check: 2007-10-15)
		The reduced visibility graph is computed by removing all edges which are not tangent to obstacles at their endpoints (by definition, endpoints in freespace are always tangent).
		The initial position is on the left, (0,5), and the path is directed toward the goal on the right, (10,5).
		Red indicates a valid point for path planning, purple marks a point interior to another convex hull, and cyan points are outside the allowable region.
	robotics.jpl.nasa.gov /people/sharon/TG.html (532 words)

	The Hamiltonian Page
		Paths, trees and cycles in tournaments, by J. Bang-Jensen and G. Gutin.
		Paths and cycles in extended and decomposable digraphs, by J. Bang-Jensen and G. Gutin.
		Hamiltonian paths and cycles in hypertournaments, by G. Gutin and A.
	www.densis.fee.unicamp.br /~moscato/Hamilton.html (1318 words)

	CS251B -- Topic #29: Shortest path algorithms
		The term "weight" is used because graphs are not limited to representing locations on a plane or in space; consequently edges could represent time, cost, and so on, generally a quantity which is to be kept minimal when going from any vertex to another.
		There may exist a shorter path which does not lead directly into the current solution set, in which case we will discover it at some later time when the rest of the nodes along that better path have been worked out.
		If we don't want to explore the whole graph but rather measure the distance to a specific destination, all we have to do is stop when the destination vertex enters S and follow the parent pointers back up to the source.
	www.cs.mcgill.ca /%7Ecs251/OldCourses/1997/topic29 (2240 words)

	Dat 119 class library: Class Path
		A path is a sequence of adjecent vertices in a graph (or digraph) without repeated vertices, except maybe the first and last (in which case the path is a cycle).
		The path's length (in the field len) is the total length of the edges joining the path's vertices in the underlying graph.
		For example, with argument [6,7,3] the constructed path is 6--7--3, visiting the 6th, 7th and 3rd vertex in the argument graph in that order.
	www.cs.lth.se /~thore/co/doc/lu/cs/co/graph/Path.html (688 words)

	Results of counting specific spanning subgraphs of the graphs G x P_n
		For explaination of the results presented here, please read the page about counting Hamilton cycles in product graphs first.
		: The graph on 5 vertices with the edges {1,2}, {1,3}, {1,4}, {1,5}, {2,3}, {2,5}, {3,4} and {4,5}.
		See also A lattice path problem by H. Abbott and D. Hanson, in Ars Combin., 6 (1978), 163-178.
	www.iwriteiam.nl /Cresults.html (2716 words)

	6.4 Other Interfaces (Site not responding. Last check: 2007-10-15)
		The path graph interface is a tool to visualize paths, and the sequence of scenes contained in those paths.
		It is called graph, because basically the scenes are the nodes of the graph and the path information itself can be viewed as the edges of the graph.
		While the time line interface focuses on one path, the path graph interface allows a quick overview and comparison of multiple paths.
	www.iicm.edu /thesis/ahollosi_html/node41.html (2034 words)

	GraphPath (Site not responding. Last check: 2007-10-15)
		Formally, a DirectedGraph that is a subGraph of the original Graph and such that no two GraphArcs in the DirectedGraph have the same intial node (see InitialNodeFn) or the same terminal node (see TerminalNodeFn).
		If is an instance of graph and is an instance of graph node and is an instance of graph node and is a part of and is a part of and is not equal to, then there exist, so that
		if is an instance of graph path and is an instance of graph arc and is a part of,
	godel.iis.sinica.edu.tw /kifb/en/concepts/_graph_path.html (343 words)

	Bio::Coordinate::Graph - Finds shortest path between nodes in a graph
		Luckily the difference for small graphs is not signigicant and the implementation is capable to take weights into account if needed at some later time.
		The graph needs to be primed using a hash of hashes where there is a key for each node.
		Root should be '1' and directness of the graph is taken advantage of to speed calculations by assuming that downsream nodes always have larger number as name.
	cpan.uwinnipeg.ca /htdocs/bioperl/Graph.html (910 words)

	Math Guide - Links to find out about Math
		Graph Theory through games that can be played on a table or on the playground.
		Graph Theory is the branch of mathematics that involves the study of graphs.
		Graph theory has been instrumental for analyzing and solving problems in areas as diverse as computer network design, urban planning, and molecular biology.
	www.useekufind.com /learningquest/tmath.htm (2530 words)

	Graph Theory Glossary (Site not responding. Last check: 2007-10-15)
		A circuit is a path which ends at the vertex it begins (so a loop is an circuit of length one).
		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 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)

	Dijkstra (Shortest Graph Path) C++ STL (Site not responding. Last check: 2007-10-15)
		This is a discussion of an STL implementation of Dijkstra's shortest path algorithm utilizing the Standard Template Library (STL) in C++.
		A directed graph is one in which the nodes are connedted by edges that can be traversed in one direction.
		A weighted graph is one in which traversing an edge has an associated cost.
	web.acd.ccac.edu /~kmoore/kcppdoc/Dijkstra.htm (486 words)

	GraphPathFn
		Jestliže "minimal weighted path fn(node1,node2)" se rovná path, potom path je instancí třídy "graph path fn(node1,node2)".
		Jestliže "maximal weighted path fn(node1,node2)" se rovná path, potom path je instancí třídy "graph path fn(node1,node2)".
		Jestliže path je částí graph a graph není instancí třídy orientovaný graf, potom "graph path fn(node1,node2)" se rovná path tehdy a jen tehdy pokud "graph path fn(node2,node1)" se rovná path.
	virtual.cvut.cz /kifb/cz/concepts/_graph_path_fn.html (278 words)

	Sun Path Graph Spreadsheet (Site not responding. Last check: 2007-10-15)
		This Excel spreadsheet creates a graph of the sun's position for a given time of day and month of the year for a point on the earth's surface.
		This type of sunchart or sun path plot is commonly used for designing solar energy installations, but I use it for location and aerial photography.
		Keep in mind that the graph is in standard local clock time.
	www.imagecircuits.com /rb/sunpath.htm (366 words)

	single_pair_shortest_path(+Graph, +DistanceArg, +SourceNode, +SinkNode, -Path) (Site not responding. Last check: 2007-10-15)
		In case of multiple shortest paths with the same length, an arbitrary one is returned.
		DistanceArg refers to the graph's EdgeData information that was specified when the graph was constructed.
		The shortest path is returned as a Length-EdgeList structure where Length is the length of the shortest path and EdgeList is that path (or one of them) in reverse order, i.e.
	www.cs.ecu.edu /~rws/c6810/doc/bips/lib/graph_algorithms/single_pair_shortest_path-5.html (235 words)

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