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Graph Theory Tutorials

Graph Theory Tutorials
Chris K. Caldwell (C) 1995 This is the home page for a series of short interactive tutorials introducing the basic concepts of graph theory. There is not a great deal of theory here, we will just teach you enough to wet your appetite for more! Most of the pages of this tutorial require that you pass a quiz before continuing to the next page. So the system can keep track of your progress you will need to register for each of these courses by pressing the [REGISTER] button on the bottom of the first page of each tutorial. Introduction to Graph Theory (6 pages) 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. Euler Circuits and Paths Beginning with the Königsberg bridge problem we introduce the Euler paths. Coloring Problems (6 pages) Adjacency Matrices (Not yet available.) How do we represent a graph on a computer?

http://primes.utm.edu/graph/

read_graphviz The read_graphviz function interprets a graph described using the GraphViz DOT language and builds a BGL graph that captures that description. Using these functions, you can initialize a graph using data stored as text. The DOT language can specify both directed and undirected graphs, and read_graphviz differentiates between the two. One must pass read_graphviz an undirected graph when reading an undirected graph; the same is true for directed graphs. Furthermore, read_graphviz will throw an exception if it encounters parallel edges and cannot add them to the graph. To handle properties expressed in the DOT language, read_graphviz takes a dynamic_properties object and operates on its collection of property maps.

Graph Theory Two vertices are called adjacent if they share a common edge, in which case the common edge is said to join the two vertices. An edge and a vertex on that edge are called incident. See the 6-node graph below right for examples of adjacent and incident: RDF-Gravity Sunil Goyal, Rupert Westenthaler {sgoyal, rwestenthaler}@salzburgresearch.at Salzburg Research, Austria RDF Gravity is a tool for visualising RDF/OWL Graphs/ ontologies. Its main features are: Graph VisualizationGlobal and Local Filters (enabling specific views on a graph) Full text SearchGenerating views from RDQL QueriesVisualising multiple RDF files RDF Gravity is implemented by using the JUNG Graph API and Jena semantic web toolkit.

Visualizious: Visualizing Social Indexing Visualizious Visualizious is a research project about social indexing (a.k.a. social tagging), information retrieval and visualization. The project is carried out by Yusef Hassan Montero and Víctor Herrero Solana (University of Granada, Spain). Visualizing Social Indexing Semantics This prototype allows visualizing both the overview and detail of semantic relationships intrinsic in the folksonomy. Pathfinder Network Scaling, clustering and interactive techniques has been used for this purpose. Graph Planarity A graph G is planar if it can be drawn in the plane in such a way that no two edges meet each other except at a vertex to which they are incident. Any such drawing is called a plane drawing of G. For example, the graph K4 is planar, since it can be drawn in the plane without edges crossing.

Watch_Dogs WeAreData In the video game Watch_Dogs, the city of Chicago is run by a Central Operating System (CTOS). This system uses data to manage the entire city and to solve complex problems,such as traffic,crime, power distribution and more... This is not fiction anymore. Smart cities are real, it’s happening now. Huge amounts of data are collected and managed every day in our modern cities, and this data is available to anyone. Watch_Dogs WeareData is the first website to gather publicly available data about Paris, London and Berlin, in one location.

a Directed Graph Library implementation by GRASS Development Team Introduction The Directed Graph Library or DGLib (Micarelli 2002) provides functionality for vector network analysis. Euler's Formula Many theorems in mathematics are important enough that they have been proved repeatedly in surprisingly many different ways. Examples of this include the existence of infinitely many prime numbers, the evaluation of zeta(2), the fundamental theorem of algebra (polynomials have roots), quadratic reciprocity (a formula for testing whether an arithmetic progression contains a square) and the Pythagorean theorem (which according to Wells has at least 367 proofs). This also sometimes happens for unimportant theorems, such as the fact that in any rectangle dissected into smaller rectangles, if each smaller rectangle has integer width or height, so does the large one. This page lists proofs of the Euler formula: for any convex polyhedron, the number of vertices and faces together is exactly two more than the number of edges.

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