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Topic: Directed graphs

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Glossary of graph theory

graph of a function

graph mathematics

tree graph theory

Graph coloring

planar graphs

directed graphs

complete graph

graphing calculator

directed acyclic graph

Perfect graph

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	Graphviz
		Graph visualization is a way of representing structural information as diagrams of abstract graphs and networks.
		In practice, graphs are usually generated from an external data sources, but they can also be created and edited manually, either as raw text files or within a graphical editor.
		The Input is a description of the graph in the dot language and the output is a rendering of the graph in a choice of vector or bitmap graphics formats.
	www.graphviz.org (1200 words)

	Kids.net.au - Encyclopedia Graph theory - (Site not responding. Last check: 2007-10-08)
		Graph theory is the branch of mathematics that examines the properties of graphs.
		In computers, a finite directed or undirected graph (with n vertices, say) is often represented by its adjacency matrix: an n-by-n matrix whose entry in row i and column j gives the number of edges from the i-th to the j-th vertex.
		A subgraph of the graph G is a graph whose vertex set is a subset of the vertex set of G, whose edge set is a subset of the edge set of G, and such that the map w is the restriction of the map from G.
	www.kids.net.au /encyclopedia-wiki/gr/Graph_theory (1664 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).
		Another way to extend basic graphs is by making the edges to the graph directional (A links to B, but B does not necessarily link to A, as in webpages), technically called a directed graph or digraph.
		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.
	en.wikipedia.org /wiki/Graph_theory (1205 words)

	Graph (mathematics) - Wikipedia, the free encyclopedia
		A directed graph may or may not be allowed to have loops, that is, edges where the start and end vertices are the same.
		A quiver is sometimes said to be simply a directed graph, but in practice it is a directed graph with vector spaces attached to the vertices and linear transformations attached to the arcs.
		In a weighted graph or digraph, each edge is associated with some value, variously called its cost, weight, length or other term depending on the application; such graphs arise in many contexts, for example in optimal route problems such as the traveling salesman problem.
	en.wikipedia.org /wiki/Directed_graph (1370 words)

	Graph theory - Open Encyclopedia (Site not responding. Last check: 2007-10-08)
		Informally, a graph is a set of objects called vertices (or nodes) connected by links called edges (or arcs).
		Depending on the applications, edges may or may not have a direction; edges joining a vertex to itself may or may not be allowed, and vertices and/or edges may be assigned weights, that is, numbers.
		This can also apply to directed graphs by ensuring the first vertex be defined as the source or destination while the second should be defined as the opposite.
	open-encyclopedia.com /Graph_theory (881 words)

	Graphs
		A graph G= consists of a set of vertices (also known as nodes) V and a set of edges (also known as arcs) E. An edge connects two vertices u and v; v is said to be adjacent to u.
		Graphs are useful for representing networks and maps of roads, railways, airline routes, pipe systems, telephone lines, electrical connections, prerequisites amongst courses, dependencies amongst tasks in a manufacturing system and a host of other data.
		Note that a rooted tree is a special kind of directed graph and that an unrooted tree is a special kind of undirected graph.
	www.csse.monash.edu.au /~lloyd/tildeAlgDS/Graph (1170 words)

	Directed Graphs
		A directed graph, or "digraph", is a graph whose edges have direction and are called arcs.
		Arrows on the arcs are used to encode the directional information: an arc from vertex A to vertex B indicates that one may move from A to B but not from B to A. Suppose that you wished to go to the main branch of the Cincinnati Public Library.
		In a directed graph, vertices have both "indegrees" and "outdegrees": the indegree of a vertex is the number of arcs leading to that vertex, and the outdegree of a vertex is the number of arcs leading away from that vertex.
	www.rwc.uc.edu /koehler/comath/33.html (723 words)

	Graph manager for a reduction processor evaluating programs stored as binary directed graphs employing variable-free ... (Site not responding. Last check: 2007-10-08)
		This combinator notation may be conveniently represented as a binary directed graph in which each node represents the application of a function to an argument.
		The substitutions performed to reduce a graph require the manipulation of a number of different pieces of data, such as pointers and combinator codes, which are shifted from one location to another in a register file.
		The principal element is graph manager 10, which contains a data section which caches some of the nodes of a graph that is to be reduced and allows for those nodes to be manipulated to perform the series of substitutions required for the graph reduction.
	www.freepatentsonline.com /4644464.html (3609 words)

	Introduction to Graphs
		Note that in a directed graph, the edges are arrows (are directed from one node to another) while in the undirected graph the edges are plain lines (they have no direction).
		This means that in a directed graph it is possible to reach a "dead end" (to get to a node from which you cannot leave).
		A directed graph can also be a complete graph; in that case, there must be an edge from every node to every other node.
	www.itu.dk /research/algorithms/Kurser/Intro/WWWkursus/notes/GRAPH.html (1791 words)

	Introduction to Graphs
		Note that in a directed graph, the edges are arrows (are directed from one node to another) while in the undirected graph the edges are plain lines (they have no direction).
		This means that in a directed graph it is possible to reach a "dead end" (to get to a node from which you cannot leave).
		A directed graph can also be a complete graph; in that case, there must be an edge from every node to every other node.
	pages.cs.wisc.edu /~hasti/cs367-common/notes/GRAPH.html (1791 words)

	Directed acyclic graph (Site not responding. Last check: 2007-10-08)
		In mathematics more specifically its branch graph theory a directed acyclic graph is a directed graph which is That is it is a graph in each edge has a direction (the directed graph part) and no node is its ancestor (the acyclic part).
		The phrase acyclic directed graph is sometimes used as a synonym.
		This book reflects the main achievements of the last three decades in the directed graphs theory as well as many applications including combinatorial optimization, operations research and the fascinating area of mathematics and computer science called dis...
	www.freeglossary.com /Dag (265 words)

	SGML: Groves as trees, graphs
		It happens that one obvious >>application of directed graphs is the representation of parse trees, but >>that's not the only thing groves are used for.
		If not, groves are part of that subset of >directed graphs known as trees, and you are spreading more smoke into the >air, instead of shedding light on the issues.
		Groves are directed graphs (not acyclic), but they can also be considered as trees.
	xml.coverpages.org /grovesXML0.html (589 words)

	Good Math, Bad Math
		Basically, the division of the graph into components is also a partition of the vertices of the graph into disjoint sets: union find is a problem which focuses on a particular kind of disjoint set problem, where you can modify the sets over time.
		A digraph is a graph where each edge distinguished between its source and its target - so an edge is from one node, and to another node.
		Unlike a simple graph, where if A is adjacent to B, then you can follow the edge either from A to B, or from B to A, in a directed graph, A to B and B to A are different edges.
	scienceblogs.com /goodmath (1425 words)

	Generalising XPath for Directed Graphs
		One of these tools, the Emu system [Cassidy 01], views annotations as directed graphs where each node represents a token in the corpus and may be labelled with various attributes including a type (phoneme, word, paragraph), start and end times and one or more labels.
		An AG is a directed graph representation of an annotation which foregrounds the sequential structure of annotations; nodes in the graph are anchor points and edges represent linguistic elements.
		In a more general graph structure, it is clearly more difficult to foresee what axes will be needed and in general it is more useful to define what an axis is than a particular set of axes being prescribed.
	www.ics.mq.edu.au /~cassidy/papers/extreme03.html (4057 words)

	H3: Laying Out Large Directed Graphs in 3D Hyperbolic Space
		Directed graphs are an appealing target for visualization because of their pervasive presence in information systems.
		Many directed graphs which appear to be unstructured meshes when considered as abstract graphs do in fact have a hierarchical structure when we exploit domain-specific knowledge.
		Traditional graph layout techniques which work on general graphs are extremely effective for dozens of nodes, can sometimes handle hundreds, and generally break down completely for thousands of nodes.
	graphics.stanford.edu /papers/h3/html.nosplit (6925 words)

	Walrus - Graph Visualization Tool - CAIDA : TOOLS : visualization : walrus
		It is technically possible to display graphs containing a million nodes or more, but visual clutter, occlusion, and other factors can diminish the effectiveness of Walrus as the number of nodes, or the degree of their connectivity, increases.
		A graph with a few hundred thousand nodes and only a slightly greater number of links is likely to be comfortable to work with.
		Laying out graphs in 3D is challenging, as occlusion along the line of sight diminishes some of the benefits of the additional dimension.
	www.caida.org /tools/visualization/walrus (1742 words)

	BibTeX bibliography trees.bib (Site not responding. Last check: 2007-10-08)
		This paper describes a tool which is used to rapidly extend base classes to create graph editors as a user-interface to these information domains.
		As such, this paper describes a number of example graph editors that have been developed with these mechanisms which satisfy the requirements.
		For graphs of modest size it produces good results, competitive with those produced by other methods, notably, the ``spring method'' and its variants.", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf F.2.2}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Computations on discrete structures.
	www.math.utah.edu /pub/tex/bib/trees.html (771 words)

	Graph (mathematics) Details, Meaning Graph (mathematics) Article and Explanation Guide
		In mathematics and computer science, a graph is a generalization of the simple concept of a set of dots, called vertices or nodes, connected by links, edges or arcs.
		Graphs are often represented pictorially as follows: draw a dot for every vertex, and for every edge draw an arc connecting its endpoints.
		There are different approaches to graph layout, and these are considered under a branch of graph theory termed as graph drawing.
	www.e-paranoids.com /g/gr/graph__mathematics_.html (793 words)

	H3: Laying Out Large Directed Graphs in 3D Hyperbolic Space
		We present the H3 layout technique for drawing large directed graphs as node-link diagrams in 3D hyperbolic space.
		We impose a hierarchy on the graph by using domain-specific knowledge to find an appropriate spanning tree.
		Our implementation accommodates navigation through graphs too large to be rendered interactively by allowing the user to explicitly prune or expand subtrees.
	graphics.stanford.edu /papers/h3 (297 words)

	Directed graphs
		A directed graph is a mathematical structure that consists of a set of values (which are called the vertices of the directed graph) and a set of arcs connecting certain vertices.
		Walker suggests two methods of traversing the part of a graph that is reachable from a given vertex, so as to visit each vertex in that part of the graph once, presumably to perform some operation on it.
		Union and intersection are meaningful operations on directed graphs, and there is also a plausible notion of a complement: The complement of a given graph as the same vertex set, but its arc set contains exactly those ways of connecting vertices that are not members of the original graph's arc set.
	www.math.grin.edu /~stone/courses/fundamentals/graphs.html (1554 words)

	List of selected publications of Tom Snijders
		Markov graphs and exponential random graph models are an important family of probability distributions for graphs and digraphs because they allow the kind of dependency that is often considered in social network analysis, e.g., transitivity of choice.
		A statistical approach to a posteriori blockmodeling for graphs is proposed.The model assumes that the vertices of the graph are partitioned into two unknown blocks and that the probability of an edge between two vertices depends only on the blocks to which they belong.
		For several types of graphs, the maximum value of the degree variance is given, and the mean and variance of the degree variance under a simple stochastic null model are computed.
	stat.gamma.rug.nl /snijders/publ.htm (11082 words)

	CITIDEL: Viewing 'Graph Parsing Techniques for Visualizing Directed Graphs' (Site not responding. Last check: 2007-10-08)
		Directed graphs, or digraphs, are an excellent means of conveying the structure and operation of many types of systems.
		The objective of the system is to provide, automatically, an aesthetically pleasing visual layout for arbitrary directed graphs.
		The innovative strategy of clan-based graph decomposition is the first digraph drawing technique to analyze locality in the graph in two dimensions.
	www.citidel.org /?op=getobj&identifier=oai:ncstrlh:auburn_eng:AUBURN_ENG//CSE95-01 (251 words)

	ALCOMFT-TR-01-98 (Site not responding. Last check: 2007-10-08)
		Abstract: The quest for a linear-time single-source shortest-path (SSSP) algorithm on directed graphs with positive edge weights is an ongoing hot research topic.
		We give simple label-setting and label-correcting algorithms for arbitrary directed graphs with random real edge weights uniformly distributed in [0,1] and show that they need linear time O(n+m) with high probability.
		Furthermore, we propose a general method to construct graphs with random edge weights which incur large non-linear expected running times on many traditional shortest-path algorithms.
	www.brics.dk /ALCOM-FT/TR/ALCOMFT-TR-01-98.html (147 words)

	Directed Graphs
		Initially P reflects the direct edges from the source.
		On the first iteration of the main loop, the vertex with the shortest direct connection from the source is chosen.
		Its time-complexity is therefore O(V All Pairs Shortest Paths in a Directed Graph
	www.csse.monash.edu.au /~lloyd/tildeAlgDS/Graph/Directed (1314 words)

	Rankings of Directed Graphs
		A ranking of a graph is a coloring of the vertex set with positive integers in such a way that on every path connecting two vertices of the same color there is a vertex of larger color.
		We consider the directed variant of this problem, where the above condition is imposed only on those paths in which all edges are oriented consecutively.
		Unlike the undirected case, however, deciding whether the ranking number of a directed (and even of an acyclic directed) graph is bounded by a constant is NP-complete.
	epubs.siam.org /sam-bin/dbq/article/33024 (185 words)

	OpenBSD Package Details - graphviz-1.7.6.tgz (Site not responding. Last check: 2007-10-08)
		Graph drawing addresses the problem of visualizing structural information by constructing geometric representations of abstract graphs and networks.
		The goal of graphviz has been twofold: to find efficient algorithms for making very readable drawings of graphs up to several hundreds of nodes, approaching the quality of manual layouts (made with CAD tools).
		The package includes dot - makes hierarchical layouts of directed graphs neato - makes "spring" model layouts of undirected graphs dotty - a customizable interface written in LEFTY tcldot - a customizable graphical interface written in tcl7.6 libgraph - the base library for graph tools More information on http://www.research.att.com/sw/tools/graphviz/ Refer to http://www.research.att.com/sw/tools/graphviz//refs.html for documentation.
	www.openbsd.org /3.4_packages/sparc64/graphviz-1.7.6.tgz-long.html (176 words)

	ALCOMFT-TR-02-49 (Site not responding. Last check: 2007-10-08)
		Abstract: Computing the strong components of a directed graph is an essential operation for a basic structural analysis of it.
		Considering the definite need to analyze very large graphs (web graph, telephone call graphs, \dots), we have developed a set of heuristics which together allow to perform semi-external DFS for directed graphs in practice.
		The heuristics have been applied to graphs with very different graph properties, including ``web graphs'' as described in the most recent literature (which are not exceptionally hard) and some call graphs from ATT.
	www.brics.dk /ALCOM-FT/TR/ALCOMFT-TR-02-49.html (171 words)

	Publications by William Trotter (Site not responding. Last check: 2007-10-08)
		Triangle-free graphs with restricted bandwidth, in Progress in Graph Theory, A. Bondy and R. Murty, eds., Academic Press (1984), 175-190 (with F. Chung).
		Graphs and orders in ramsey theory and in dimension theory, in Graphs and Order, I. Rival, ed., Reidel (1985), 351-394 (with M. Paoli and J. Walker).
		A generalization of threshold graphs with tolerance, Congressus Numerantium 55 (1986) 187-197 (with C. Monma and B. Reed).
	www.math.gatech.edu /~trotter/pubs.html (1880 words)

	Topic #30: Directed Acyclic Graphs
		Directed acyclic graphs are directed graphs with no cycles.
		A topological sort of a graph can be viewed as an ordering of its vertices along a horizontal line so that all directed edges go in one direction.
		Looking at a previously-examined node implies that there is a cycle in the graph, which is impossible in the case of a dag.
	www.cs.mcgill.ca /~cs251/OldCourses/1997/topic30 (1764 words)

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