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Topic: Out degree (graph theory)

	Degree (graph theory) - Wikipedia, the free encyclopedia
		In graph theory, the degree (or valency) of a vertex is the number of edges incident to the vertex.
		The degree of a vertex v is denoted deg(v).
		For an undirected graph, the degree of a vertex is the number of edges incident to the vertex.
	en.wikipedia.org /wiki/Degree_(graph_theory) (402 words)

	Category:Graph theory - Wikipedia, the free encyclopedia
		Graph theory is the branch of mathematics that examines the properties of graphs.
		Informally, a graph is a set of objects called vertices (or nodes) connected by links called edges (or arcs), which can also have associated directions.
		Typically, a graph is depicted as a set of dots (i.e., vertices) connected by lines (i.e., edges), with an arrowhead on a line representing a directed arc.
	en.wikipedia.org /wiki/Category:Graph_theory (173 words)

	Graph theory glossary
		A coclique in a graph is a clique in its complementary graph (q.v.).
		The sum of the degrees of all vertices in a graph G equals twice the number of edges of G (why?); in particular, this sum must be an even number.
		girth (n.): The girth of a graph is the length of the shortest cycle(s) in the graph.
	www.math.harvard.edu /~elkies/FS23j.03/glossary_graph.html (1288 words)

	Graph Theory
		Graph Theory was born to study problems of this type.
		The degree, d(v), of a vertex v is the number of edges with which it is incident.
		In an undirected graph, this is obviously a metric.
	www.math.fau.edu /locke/GRAPHTHE.HTM (1165 words)

	Intro to Graph Theory
		A subgraph of a graph is a subset of its points together with all the lines connecting members of the subset.
		The degree of a point is defined as the number of lines incident upon that node.
		A local bridge of degree k is an edge whose removal causes the distance between the endpoints of the edge to be at least k.
	www.analytictech.com /mb021/graphtheory.htm (1984 words)

	Network Design: the Diameter-Degree Problem at MROB
		The "Diameter-Degree Problem" is a graph theory problem that comes up in the design of computer networks, particularly peer-to-peer software networks or "virtual networks" (such as Gnutella) and parallel processing architectures using node-to-node links for inter-CPU data exchange (Beowulf clusters are a prominent example).
		As mentioned before, "3-regular" means that all nodes have degree 3, and "girth" is the length of the shortest cycle (closed path) in the graph.
		Graph theorists have a more cryptic way of expressing this, which they refer to as the properties of the graph's "symmetry group".
	home.earthlink.net /~mrob/pub/math/ttl-problem.html (3425 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.
		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.
		For the algorithm to keep track of where it is in the graph, and which vertex to visit next, BFS needs to color the vertices (see the section on Property Maps for more details about attaching properties to graphs).
	www.boost.org /libs/graph/doc/graph_theory_review.html (2374 words)

	Games on Graphs (Site not responding. Last check: 2007-11-02)
		When mathematicians talk about graphs, they are most likely to be thinking of the collections of dots and lines that you see in the illustrations of this section.
		The degree of a vertex is the number of edges that touch it.
		Similarly, the diameter of a graph is the distance between the two vertices of the graph that are farthest apart.
	www.cs.uidaho.edu /~casey931/mega-math/workbk/graph/grbkgd.html (1491 words)

	Graph Theory Tutorial
		The vertices in directed graph families are so proud with the number of arrow going out of these vertices and the number of arrow going into the vertices.
		To distinguish those degrees, they give name in-degree to count number of arrow going in to a vertex, and they give name out-degree to count number of arrow going out of a vertex.
		Vertices a, b and c in the graph below have 1 in-degree and 1 out-degree.
	people.revoledu.com /kardi/tutorial/GraphTheory/Degree.html (160 words)

	Graphs
		A degree of a vertex is the number of edges incident to it (loops being counted twice).
		For a graph, the sum of degrees of all its nodes equals twice the number of edges.
		A degree of a node is the number of edges incident to this node.
	www.cut-the-knot.org /do_you_know/graphs.shtml (1301 words)

	Hayes00: Graph Theory in Practice (Site not responding. Last check: 2007-11-02)
		A graph is made up of a set of vertices V and a set of edges E. Each edge is a set of two vertices.
		The degree of a vertex is the number of edges that begin or end at the vertex.
		This is a directed graph because each call originates at one number and is received at a different number.
	cs.colgate.edu /~parks/core/147/reading/Hayes00.html (403 words)

	Graph structure in the web
		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].
		The in-degree distribution in our data shows a striking fit with a Zipf (more so than the power law) distribution; Figure 8 shows the in-degrees of pages from the May 1999 crawl plotted against both ranks and magnitudes (corresponding to the Zipf and power law cases).
	www9.org /w9cdrom/160/160.html (6296 words)

	Graph Theory Lesson 2
		The degree of a vertex is the number of edges incident to it, i.e.
		A simple graph is a graph that does not have more than one edge between any two vertices and no edge starts and ends at the same vertex.
		Restore graphs 10 through 20 and make a table showing the sum of the degrees, and the number of edges and another table showing the number of vertices with odd degree and the number of vertices with even degree.
	www.utc.edu /~cpmawata/petersen/lesson2.htm (383 words)

	05C: Graph theory
		A graph is a set V of vertices and a set E of edges -- pairs of elements of V. This simple definition makes Graph Theory the appropriate language for discussing (binary) relations on sets, which is clearly a broad topic.
		A graph may be viewed as a one-dimensional CW-complex and hence studied with tools from Algebraic Topology, in particular, questions of planarity (and genus).
		Determining the genus of a graph is NP-complete.
	www.math.niu.edu /~rusin/known-math/index/05CXX.html (1204 words)

	Ideas, Concepts, and Definitions (Site not responding. Last check: 2007-11-02)
		Graph paper is not particularly useful for drawing the graphs of Graph Theory.
		In Graph Theory, a graph is a collection of dots that may or may not be connected to each other by lines.
		If you look at a graph and your eyes want to zip all around it like a car on a race course, or if you notice shapes and patterns inside other shapes and patterns, then you are looking at the graph the way a graph theorist does.
	www.c3.lanl.gov /mega-math/gloss/graph/gr.html (215 words)

	Tom's Combinatorial Geometry Class
		A graph is called a planar graph if it is drawn in such a way that the edges never cross, except at where they meet at vertices.
		There is a direct connection between polyhedra and planar graphs, namely that we can take any polyhedron and "project" it down onto a flat piece of paper, turning it into a graph.
		Similarly, the degree of a face f in a planar graph is the number of edges going around the face.
	www.merrimack.edu /~thull/combgeom/graphnotes.html (1055 words)

	"Introduction to Graph Theory - new problems"
		Determine whether the graph obtained by deleting a diagonal edge is isomorphic to the graph obtained by deleting one of the edges on the cycle.
		Count the spanning trees in a graph that is the union of a k-cycle and an l-cycle with one common edge.
		(!) The Kneser graph K(n,k) is the disjointness graph of the k-element subsets of [n].
	www.math.uiuc.edu /~west/igt/newprob.html (9557 words)

	The Math Forum - Math Library - Graph Theory (Site not responding. Last check: 2007-11-02)
		A graph is a set V of vertices and a set E of edges - pairs of elements of V. This simple definition makes Graph Theory the appropriate language for discussing (binary) relations on sets.
		A series of short interactive tutorials introducing the basic concepts of graph theory, designed with the needs of future high school teachers in mind and currently being used in math courses at the University of Tennessee at Martin.
		An Introduction to Graph Theory tutorial uses three motivating problems to introduce the definition of graph along with terms like vertex, arc, degree, and planar.
	mathforum.org /library/topics/graph_theory (2440 words)

	Math Forum - Ask Dr. Math
		Date: 09/29/2001 at 06:41:58 From: Kate Rogers Subject: Graph Theory Can you please explain to me briefly why a graph with five vertices each having a degree of 3 is not possible ?
		Date: 09/30/2001 at 01:16:09 From: Doctor Jodi Subject: Re: Graph Theory Hi Kate, It might help to draw some pictures of small graphs.
		Degree 3 means that each vertex has three edges coming from it.
	mathforum.org /library/drmath/view/54305.html (122 words)

	Graph Theory Lesson 5 (Site not responding. Last check: 2007-11-02)
		A graph in which every vertex has the same degree is called a regular graph.
		A trivalent graph is one that is regular of degree 3.
		It is the graph that this program is named after.
	www.utc.edu /Faculty/Christopher-Mawata/petersen/lesson5.htm (172 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)

	Question on Graph theory
		Given a graph G(p,q) is a tree where p is the number of vertices and q is the number of edges.
		Sum up the degrees of the vertices in two ways, once as a sum over the vertices and once as a sum over the edges.
		Assume you don't have two vertices with degree one, use this assumption to get a lower bound for the sum of the degrees and you'll find a contradiction.
	www.physicsforums.com /showthread.php?p=477919 (626 words)

	Graph theory in Tcl (Site not responding. Last check: 2007-11-02)
		Graphs as in Graph theory (see also tcllib::graph; http://www.math.fau.edu/locke/graphthe.htm for a compact page of definitions and pointers) are defined as a tuple of: a set of nodes or "vertices" (which might be visualized as points on a canvas); a set of edges (e.g.
		Now for some routines dealing with directed graphs, where, in contrast to general graphs, edges are "one-way streets" and would have to be explicitly mirrored (X,Y Y,X) for two-way usability.
		AM As Tcllib has a graph module for manipulating general graphs, I used that to implement a basic algorithm for finding the shortest paths in a graph.
	wiki.tcl.tk /2473 (1376 words)

	Graphs: Theory - Algorithms - Complexity (Site not responding. Last check: 2007-11-02)
		Groups and Graphs: a software package for graphs, digraphs, combinatorial designs, and their automorphism groups, by B.
		Scheinerman, E.R., Ullman, D.H.: Fractional graph theory: a rational approach to the theory of graphs, John Wiley and Sons, New York, 1997.
		Graph connections -- relationships between graph theory and other areas of mathematics, Eds.
	people.freenet.de /Emden-Weinert/graphs.html (1244 words)

	Graph Theory Tutorials (Site not responding. Last check: 2007-11-02)
		This is the home page for a series of short interactive tutorials introducing the basic concepts of graph theory.
		Starting with three motivating problems, this tutorial introduces the definition of graph along with the related terms: vertex (or node), edge (or arc), loop, degree, adjacent, path, circuit, planar, connected and component.
		This question can be changed to "how many colors does it take to color a planar graph?" In this tutorial we explain how to change the map to a graph and then how to answer the question for a graph.
	www.utm.edu /departments/math/graph (282 words)

	Erdos Faudree Pubs (Site not responding. Last check: 2007-11-02)
		Staton, William, Degree sequence and independence in K(4)-free graphs.
		Graph theory and its applications: East and West (Jinan, 1986), 155--162, Ann.
		Graph Theory, and Computing (Florida Atlantic Univ., Boca Raton, Fla., 1978), pp.
	cas.memphis.edu /rfaudree/ErdosFau.htm (868 words)

	Entropy approach through graph theory for studying the degree of order in one-dimensional distributions of objects
		Entropy approach through graph theory for studying the degree of order in one-dimensional distributions of objects
		Graph theory, through the minimal spanning tree (MST), and information theory, through the concept of entropy, are used to define a new parameter
		which quantitatively characterizes the degree of order (or disorder) in 1D sets of points.
	stacks.iop.org /0305-4470/29/2969 (270 words)

	Muhammad von Aurum's Encyclopedia of Graph Theory - Degree
		The degree of of vertex is the number of edges with which it is incident.
		A vertex v is even or odd if its degree is even or odd respectively.
		See also In-degree, Local Degree, Maximum Degree, Minimum Degree, Out-degree
	www.cs.rit.edu /~maa2454/Graphs?D:Degree&print (49 words)

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