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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. Most of the pages of this tutorial require that you pass a quiz before continuing to the next page. 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) How many colors does it take to color a map so that no two countries that share a common border have the same color? Adjacency Matrices (Not yet available.) How do we represent a graph on a computer? Related Resources for these Tutorials: Other Graph Theory Resources on the Internet: Chris Caldwell caldwell@utm.edu

stefanos livos | you're here, so you already know! 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. Requirements: The type of the graph must model the Mutable Graph concept.The type of the iterator must model the Input Iterator concept.The property map value types must be default-constructible. Under certain circumstances, read_graphviz will throw one of the above exceptions.

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: Nodes 4 and 6 are adjacent (as well as many other pairs of nodes) Nodes 1 and 3 are not adjacent (as well as many other pairs of nodes) Edge {2,5} is incident to node 2 and node 5. The neighborhood of a vertex v in a graph G is the set of vertices adjacent to v. The degree of a vertex is the total number of vertices adjacent to the vertex. Each vertex in the undirected graph at right has the following degree: In a directed graph, we define degree exactly the same as above (and note that "adjacent" does not imply any direction or lack of direction). In a directed graph it is important to distinguish between indegree and outdegree. Pay particular attention to nodes 3 and 4 in the above table.

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. Figure 1: Screenshot of RDF-Gravity, showing a part of Wine Ontology 1 Graph Visualisation RDF Gravity defines a visualization package on top of the JUNG Graph API. Configurable renderers for edges and nodes of a graph, including different node shapes and edge decorations etc.A Renderer Factory allowing the configuration of the above node and edge renderers based on the type of an edge or node. For graph layout, it uses the layout algorithms directly supported by the Jung API. 2 Global & Local Filters 3 Full Text Search 4 Visualising Multiple RDF Files

Human resourse development through the exploitation of lifelong learning methods Περίληψη Παρά την μεγάλη έμφαση που δίνεται τις τελευταίες δεκαετίες στη Δια Βίου Μάθηση (ΔΒΜ), υπάρχουν λίγες θεωρητικές και εμπειρικές έρευνες που αναφέρονται στη σύνδεσή της με την ανάπτυξη ανθρώπινων πόρων, στις οποίες μάλιστα η ΔΒΜ εμφανίζεται κυρίως ως αναπόσπαστο τμήμα της ανάπτυξης ανθρώπινων πόρων. Εξ αιτίας της έλλειψης ερευνών σχετικών με το πώς επιδρά η ΔΒΜ μέσω των μεθόδων της στην ανάπτυξη ανθρώπινων πόρων, κυρίως στην προσωπική και επαγγελματική ανάπτυξη των εργαζομένων σε επιχειρήσεις και οργανισμούς, η παρούσα έρευνα ασχολήθηκε με την διερεύνηση και τεκμηρίωση αυτής της επίδρασης. Για αυτό το λόγο, ένα ερωτηματολόγιο με βάση τους σκοπούς της έρευνας και με χρήση της κλίμακας Likert σχεδιάστηκε και δημιουργήθηκε η ποσοτική κλίμακα που ονομάστηκε ΔιΒιΜαΑΑΠ. Η δημιουργία της βασίστηκε σε μεγαλύτερο βαθμό στη θεωρία ότι οι άνθρωποι χαρακτηρίζονται ως πόροι και σε μικρότερο βαθμό στις θεωρίες μάθησης και στη θεωρία με προσανατολισμό στη μάθηση με σκοπό να εκτιμηθεί αυτή ...

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. Screenshots (click to enlarge) Related papers Hassan-Montero, Y.; Herrero-Solana, V. (2007) Visualizing Social Indexing Semantics. Improved Tag-Clouds Tag-Cloud is a simple and widely used visual interface model, but with some restrictions that limit its utility as visual information retrieval interface. Our work presents a novel approach to Tag-Cloud's tags selection, and proposes the use of clustering algorithms for visual layout, with the aim of improve browsing experience. Related papers

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. The three plane drawings of K4 are: The five Platonic graphs are all planar. On the other hand, the complete bipartite graph K3,3 is not planar, since every drawing of K3,3 contains at least one crossing. why? To study planar graphs, we restrict ourselves to simple graphs. If a planar graph has multiple edges or loops. Remove loops and multiple edge. Draw without multiple edge. Insert loops and multiple edges. Euler's Formula If G is a planar graph, then any plane drawing of G divides the plane into regions, called faces. For example, the following graph G has four faces, f4 being the infinite face. It is easy to see from above graph that deg f1=3, deg f2=4, deg f3=9, deg f4=8. n - (m - 1) + (f - 1) = 2 Duality

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. What you will discover here are only facts and reality. Watch_Dogs WeareData gathers available geolocated data in a non-exhaustive way: we only display the information for which we have been given the authorization by the sources.

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