PPT-Introduction to Graph-Theory

and Applications Irith Hartman 1 Motivation What is the common link between the following problems traffic network design and cancer research Arranging marriages and scheduling flights Finding cure for mental illness computer chip design architectural floor planning fighting terror online. We call the tail of the head of and uv the ends of If there is an edge with tail and head then we let uv denote such an edge and we say that this edge is directed from to Loops Parallel Edges and Simple Digraphs An edge uv in a digraph is a 10 11 Graph Search Methods Many graph problems solved using a search method Path from one vertex to another Is the graph connected Find a spanning tree Etc Commonly used search methods Breadthfirst search Depthfirst search BreadthFirst Search Visit to . Graph . Cluster Analysis. Outline. Introduction to Cluster Analysis. Types of Graph Cluster Analysis. Algorithms for Graph Clustering. k-Spanning Tree. Shared Nearest Neighbor. Betweenness Centrality Based. P. artitioning. a. nd. . Clustering for. Community . Detection. . Presented By: Group One. 1. Outline. Introduction:  . Hong . Hande. Graph Partitioning: . Muthu. Kumar . C . and . Xie . Shudong. Extremal graph theory. L. á. szl. ó. . Lov. á. sz. . Eötvös. . Lor. ánd. . University, Budapest . May 2012. 1. May 2012. 2. Recall some. . math. t. (. F. ,. G. ):. . Probability that random . Hao Wei. 1. , . Jeffrey Xu Yu. 1. , Can L. u. 1. , . Xuemin. Lin. 2. . 1 . The . Chinese University of Hong Kong, Hong Kong. 2 . The . University of New South Wales. , . Sydney, Australia. Graph in Big Data . . social . and neural network data. Darren A. Narayan. Rochester Institute of Technology. Joint work with Roger Vargas, Williams College, Bradford Mahon and Frank Garcea, Rochester Center for Brain Imaging, University of Rochester. ECE 580. 12. Graph Theory, Topological Analysis - Terms. Topological Analysis: General, systematic, suited for CAD. Graph. : Nodes and directed branches, describes the topology of the circuit, ref. direction. Helps visualize CAD. Richard C. Wilson. Dept. of Computer Science. University of York. Graphs and Networks. Graphs . and. networks . are all around us. ‘Simple’ networks. 10s to 100s of vertices. Graphs and networks. Richard C. Wilson. Dept. of Computer Science. University of York. Graphs and Networks. Graphs . and. networks . are all around us. ‘Simple’ networks. 10s to 100s of vertices. Graphs and networks. Using graph theory to solve games and problems. Dr. Carrie Wright. University of Arizona. Teacher’s Circle. November 17, 2011. BRIDGES OF KONIGSBERG. In Konigsberg, East Prussia, a river runs through the city such that in its center is an island, and after passing the island, the river broke into two parts. Seven bridges were built so that the people of the city could get from one part to another. . Distance matrices are graphs .  as useful as any other clustering. Identification of communities in social networks. Webpage clustering for better data management of web data. Outline. Min s-t cut problem. Adjacency List. Adjacency-Matrix. Pointers/memory for each node (actually a form of adjacency list). Adjacency List. List of pointers for each vertex. Undirected Adjacency List. Adjacency List. The sum of the lengths of the adjacency lists is 2|E| in an undirected graph, and |E| in a directed graph.. Fall 2010. Battista, G. D., . Eades. , P., . Tamassia. , R., and . Tollis. , I. G. 1998 . Graph Drawing: Algorithms for the Visualization of Graphs. . 1st. Prentice Hall PTR. . Planarity Testing. Planarity testing.