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Topic: Acyclic graph

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	PlanetMath: acyclic graph
		A directed acyclic graph is often called a DAG for short.
		For example, the following graph and digraph are acyclic.
		This is version 5 of acyclic graph, born on 2002-03-02, modified 2002-03-02.
	planetmath.org /encyclopedia/AcyclicGraph.html (73 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.
		The closure of a graph G with n vertices, denoted by c(G), is the graph obtained from G by repeatedly adding edges between non-adjacent vertices whose degrees sum to at least n, until this can no longer be done.
		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.html (2135 words)

	Graph Definitions
		A Graph has a set of Edges usually denoted E. E = {(v1,v2), (v2,v3)} The number of Edges in a graph is E but is somtimes written in equations as just E. A Graph is called Undirected if the edges have no implied direction.
		A value of zero means the given graph has at least one pair of vertices x, y in V such that there is no path connecting x and y.
		Bipartite - a Graph with a set of vertices that can be divided into exactly two non empty subsets such that no edge connects two vertices within a subset and every vertex in one subset has at least one Edge to a vertex in the other subset.
	www.csee.umbc.edu /~squire/reference/graph_def.shtml (820 words)

	Glossary of graph theory - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-17)
		Likewise, a graph G is said to be homomorphic to a graph H if there is a mapping, called a homomorphism, from V(G) to V(H) such that if two vertices are adjacent in G then their corresponding vertices are adjacent in H.
		The girth and circumference of an acyclic graph are defined to be infinity ∞.
		A vertex of degree 0 is an isolated vertex.
	en.wikipedia.org /wiki/Acyclic_graph (5920 words)

	graph
		Formally, a graph is a set of vertices and a binary relation between vertices, adjacency.
		Moreover, a mathematical graph is not a comparison chart, nor a diagram with an x- and y-axis, nor a squiggly line on a stock report.
		GraphEd -- Graph Editor and Layout Program (C), graph manipulation (C++, C, Mathematica, and Pascal), build, traverse, top sort, etc. weighted, directed graphs (Java), JGraphT (Java) build, traverse, and display directed and undirected graphs, GEF - Graph Editing Framework (Java) a library to edit and display graphs.
	www.nist.gov /dads/HTML/graph.html (573 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 (1162 words)

	ACYCLIC
		acyclic is a filter that takes a directed graph as input and outputs a copy of the graph with sufficient edges reversed to make the graph acyclic.
		acyclic returns 0 if the graph is acyclic; 1 if the graph has a cycle; 2 if the graph is undirected; and 255 if there are any errors.
		If the graph is strict and there is a cycle of length 2, the attributes of the reversed edge are lost.
	www.math.ucla.edu /computing/docindex/graphviz-man-5.html (207 words)

	Directed acyclic graph - Wikipedia, the free encyclopedia
		In computer science and mathematics, a directed acyclic graph, also called a dag or DAG, is a directed graph with no directed cycles; that is, for any vertex v, there is no nonempty directed path starting and ending on v.
		Every directed acyclic graph corresponds to a partial order on its vertices, in which u ≤ v is in the partial order exactly when there exists a directed path from u to v in the graph.
		Among these graphs, the one with the fewest edges is the transitive reduction and the one with the most edges is the transitive closure.
	en.wikipedia.org /wiki/Directed_acyclic_graph (642 words)

	acyclic(1): make directed graph acyclic - Linux man page
		acyclic is a filter that takes a directed graph as input and outputs a copy of the graph with sufficient edges reversed to make the graph acyclic.
		acyclic returns 0 if the graph is acyclic; 1 if the graph has a cycle; 2 if the graph is undirected; and 255 if there are any errors.
		If the graph is strict and there is a cycle of length 2, the attributes of the reversed edge are lost.
	www.die.net /doc/linux/man/man1/acyclic.1.html (224 words)

	Graph Theory - BioInformatics Glossary (Site not responding. Last check: 2007-10-17)
		Graph theory — a branch of mathematics — deals with understanding the properties of graphs, which, at their most fundamental level, express connections among various objects.
		A graph in which each vertex is connected to each of the others (with one edge between each pair of vertices).
		A cycle in a directed or undirected graph such that every vertex of the graph is in the cycle, but each vertex appears exactly once (except the first and last vertices).
	big.mcw.edu /topic.php/8.html (440 words)

	Testing whether a graph is acyclic
		A graph that has at least one such loop is called cyclic, and one which doesn't is called acyclic.
		If a graph is acyclic, then it must have at least one node with no targets (called a leaf).
		This condition (having a leaf) is necessary for the graph to be acyclic, but it isn't sufficient.
	www.cs.hmc.edu /~keller/courses/cs60/s98/examples/acyclic (843 words)

	Biopathways Graph Data Manager (BGDM)
		I have broad interests in graphs, their role in databases and knowledge representation, graph algorithms (esp. parallel graph algorithms) for biology (phylogenetic tree construction, NMR peak assignment, shotgun sequence assembly, etc.), and graph grammars (for modeling graph query languages, evolution of biopathways, schema evolution and integration).
		A general purpose graph data manager would have a library of specialized routines for various classes of graphs and choose the query processing plan and graph algorithms accordingly, just as conventional relational DBMS query optimizers select query execution plans and join algorithms depending on relational sizes, predicate and join selectivities, availability of indices.
		Graph matchings attempt to match entire graphs and are the graph analogs of global sequence alignments.
	hpcrd.lbl.gov /staff/olken/graphdm/graphdm.htm (7829 words)

	Scene Graph Basics
		The hierarchy of the scene graph encourages a natural spatial grouping on the geometric objects found at the leaves of the graph.
		A leaf node's state is defined by the nodes in a direct path between the scene graph's root and the leaf.
		Java 3D defines five scene graph viewing objects that are not part of the scene graph per se but serve to define the viewing parameters and to provide hooks into the physical world.
	java.sun.com /products/java-media/3D/forDevelopers/j3dguide/SceneGraphOverview.doc.html (2606 words)

	CSE 392 - Programming Challenges Graph Traversal (Week 9) (Site not responding. Last check: 2007-10-17)
		Graphs are one of the unifying themes of computer science.
		A typical graph format consists of an initial line featuring the number of vertices and edges in the graph, followed by a listing of the edges at one vertex pair per line.
		The connected components of an undirected graph are the separate ``pieces'' of the graph such that there is no connection between the pieces.
	www.cs.sunysb.edu /~skiena/392/lectures/week9 (1570 words)

	Deterministic selection
		In fact trees can be defined as the undirected graphs that are connected (there is a path between any two vertices) and acyclic (there aren't any sequences of edges that go around in a loop).
		Typical graph algorithm problems for this example would be to determine how two people are related, or to draw this graph as a nice picture of the family tree.
		We can make a graph, in which the vertices represent holes, and each two vertices are connected by an edge labeled with the amount of time it would take to move the drill from one hole to the other.
	www.ics.uci.edu /~eppstein/161/960201.html (2744 words)

	SQL Tree and Graph Algorithms
		This script assumes that the graph may not be a tree, so it checks that each node it reaches has not already been inserted, and uses DISTINCT to handle the case where a node is reached via multiple paths during the same iteration.
		The transitive closure of a graph G is a set of node pairs (a,b) where there exists a path from a to b in G. Warshall's algorithm starts by finding paths of length 1 (edges), then length 2, 4, 8, and so on.
		In addition, cycles in the graph are shown by identical pairs (a,a), which indicate that a non-trivial path from a to a exists in the graph.
	willets.org /sqlgraphs.html (1216 words)

	Graph Theory
		An acyclic graph (also known as a forest) is a graph with no cycles.
		G is acyclic, and whenever any two arbitrary nonadjacent vertices in G are joined by and edge, the resulting enlarged graph G' has a unique cycle.
		A graph is connected if and only if it has a spanning tree.
	www.personal.kent.edu /~rmuhamma/GraphTheory/MyGraphTheory/trees.htm (812 words)

	Method for representing a directed acyclic graph of worlds using an assumption-based truth maintenance system - Patent ...
		1 is an illustration of a directed acyclic graph of worlds in a knowledge base constructed in accordance with the invention.
		2 is an illustration of a graph of assertions, assumptions and justifications.
		3 is an illustration of a directed acyclic graph of worlds in a knowledge base constructed in accordance with the invention for showing merge ambiguity.
	www.freepatentsonline.com /4918621.html (7654 words)

	Directed Acyclic Word Graphs
		A Directed Acyclic Word Graph, or DAWG, is a data structure that permits extremely fast word searches.
		In other words, you can move from A to B, but you can't move from B to A. It's Acyclic because there are no cycles.
		In the CITY-PITY graph, the algorithm would see that the S's at the end are the same.
	www.wutka.com /dawg.html (1389 words)

	Index (Site not responding. Last check: 2007-10-17)
		Returns the join of the given graphs, which is the graph built by taking their (disjoint) union and then adding edges from all of the vertices of the first graph to the vertices of the second graph.
		Sets the edge at the given index to an edge with the given head and tail, unless such an edge is already on the edge list or one or both of its two endpoints are not on the vertex list, in which case nothing happens.
		Sets the edge at the given index to an edge with the given head and tail names, unless such an edge is already on the edge list or one or both of its two endpoints are not on the vertex list, in which case nothing happens.
	www.wku.edu /~leyla.zhuhadar/GraphBase/GraphDocs/index-all.html (7325 words)

	95.202 Notes 8 - Graphs
		The sum of the degrees of all vertices in a graph is exactly twice the number of edges.
		A path in a graph is a sequence of alternating vertices and edges that starts at a vertex and ends at a vertex such that an edge is incident to its predecessor and successor vertex.
		A traversal is a systematic procedure for exploring a graph by examining all of its vertices and edges.
	www.scs.carleton.ca /~lanthier/teaching/202/Graph/Graph.html (3358 words)

	Graph Theory Glossary - a (Site not responding. Last check: 2007-10-17)
		The set E of edges of a graph (V, E), being a set of unordered pairs of elements of V, constitutes a relation on V.
		Given a graph G, the anarboricity is the maximum number of line-disjoint nonacyclic subgraphs whose union is G.
		Given a graph G, the arboricity is the minimum number of line-disjoint acyclic subgraphs whose union is G.
	www.cc.ioc.ee /jus/gtglossary/gtglos_a.htm (2973 words)

	The Graph ADT (Site not responding. Last check: 2007-10-17)
		A graph is a structure composed of a set of vertices and edges that connect the vertices.
		Given the graph in Example 1, the vertices can be represented as V = {A, B, C, D} and the edges as E = {AB, AC, BC, BD, CD, BA, CA, CB, DC, DB}.
		Example 3 is also a graph with parallel edges and self-loops.
	www.cis.cau.edu /123/notes/GraphADT.htm (1136 words)

	R: Graphs induced by marginalization or conditioning
		Functions to find induced graphs after conditioning on a set of variables and marginalizing over another set.
		Given a directed acyclic graph representing a set of conditional independencies it is possible to obtain other graphs of conditional independence implied after marginalizingover and conditionig on sets of nodes.
		Such graphs are the covariance graph, the concentration graph, the multivariate regression graph and the chain graph with different interpretations (see Cox and Wermuth, 1996, 2004).
	rss.acs.unt.edu /Rdoc/library/ggm/html/InducedGraphs.html (639 words)

	Paths (yFiles.NET 2.4.0.1 API) (Site not responding. Last check: 2007-10-17)
		It is not guaranteed though that the returned path is actually the longest path within the given graph, since that is a well known hard to solve problem.
		The longest path is defined as one of all directed paths within the graph for which the edge lengths of all contained edges sum up to a maximum.
		A chain in a graph is a paths of maximal length, where each internal node on the path has degree 2.
	www.yworks.de /products/yfilesdotnet/doc/api/y/algo/Paths.html (704 words)

	CMPSCI 601 Solutions to Homework #4, Summer 2003
		Unfortunately for them the language ACYCLIC is the set of graphs that are acyclic, not the set of acyclic graphs and pairs of points having paths.
		Prove that the set {G: G is a directed acyclic graph with a Hamilton path} is in P.
		We need a function f that inputs a graph G and outputs a graph H, such that H is 5-colorable iff G is 3-colorable.
	www.cs.umass.edu /~barring/cs601sum03/hw/4sol.html (2218 words)

	Directed Acyclic Graph Matcher
		The directed acyclic graph (DAG) matcher is an extension to the indexing and matching framework for hierarchical structures proposed by Shokoufandeh et al.
		The indexing performance is improved by a vote accumulation algorithm that efficiently solves a multiple one-to-one assignment of votes.
		In turn, the matching algorithm is extended by ensuring the satisfaction of all the hierarchical constraints encoded in the graphs.
	www.cs.toronto.edu /~dmac/dagmatcher.html (217 words)

	Scene Graph Basics
		Once a scene graph object is created and connected to other scene graph objects to form a subgraph, the entire subgraph can be attached to a virtual universe---via a high-resolution Locale object-making the object live (see Section 4.6.2, "Locale Object").
		An important characteristic of all scene graph objects is that they can be accessed or modified only during the creation of a scene graph, except where explicitly allowed.
		The coordinates of all scene graph objects are relative to the HiResCoord of the Locale in which they are contained.
	java.sun.com /products/java-media/3D/forDevelopers/J3D_1_2_API/j3dguide/SceneGraphOverview.doc.html (2392 words)

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