PPT-Graphs 1 Graph Terminology and Representations

Presentation for use with the textbook Algorithm Design and Applications by M T Goodrich and R Tamassia Wiley 2015 Graphs 2 Graphs A graph is a pair V E where V is a set of nodes called . Sometimes, two graphs have exactly the same form, in the sense that there is a one-to-one correspondence between their vertex sets that preserves edges. In such a case, we say that the two graphs are . Dr. Andrew Wallace PhD . BEng. (hons) . EurIng. andrew.wallace@cs.umu.se. Overview. Sets. Implementation. Complexity. Graphs. Constructing . Graphs. Graph examples. Sets. Collection of items. No specified ordered. Isabelle Stanton, UC Berkeley. Gabriel . Kliot. , Microsoft Research XCG. Modern graph datasets are huge. The web graph had over a trillion links in 2011. Now?. . facebook. has “more than 901 million users with average degree 130”. What is a graph?. Directed vs. undirected graphs. Trees vs graphs. Terminology: Degree of a Vertex . Graph terminology. Graph Traversal. Graph representation. Topics to be discussed…. What is a graph?. Graphs. Goals . Introduction and Motivation. Representations. Why do we care about graphs?. Many Applications. Social Networks – Facebook. Video Games - Motion Graphs. Machine Learning/AI . Delivery Networks/Scheduling – UPS?. Instructor. Neelima Gupta. ngupta@cs.du.ac.in. Table . of Contents. Directed Graphs. Simple Digraph. May contain one loop at each vertex.. Distance: we say that a vertex y is at a distance d from a vertex x, if d is the length of a shortest path from x to y.. Sometimes, two graphs have exactly the same form, in the sense that there is a one-to-one correspondence between their vertex sets that preserves edges. In such a case, we say that the two graphs are . 24-28 October 2016. 11. Graphs and Trees 1. . Graphs: Definitions. . Trails, Paths, and Circuits Matrix Representations Isomorphisms. 1. . . Graphs: Definitions . Trails, Paths, and Circuits Matrix Representations Isomorphisms. Section . 10.3. Representing Graphs: . Adjacency Lists. Definition. : An . adjacency list . can be used to represent a graph with no multiple edges by specifying the vertices that are adjacent to each vertex of the graph.. The type of graph you draw depends on the types of observations you make. Bar Graph. Line Graph. Pie Graph. Bar and Column Graphs. Bar and column graphs. Some observations fall into . discrete. groupings. http://courses.cs.washington.edu/courses/cse373. /. Douglas . W. . Harder, U Waterloo. 12/26/03. Graph Terminology - Lecture 13. 2. What are graphs?. Yes, this is a graph….. But we are interested in a different kind of “graph”. William L. Hamilton, Rex Ying, Jure . Leskovec. Keshav Balasubramanian. Outline. Main goal: generating node embeddings. Survey of past methods. GCNs. GraphSAGE. Algorithm. Optimization and learning. Aggregators. 11. Graphs and Trees 1. . Graphs: Definitions. . Trails, Paths, and Circuits Matrix Representations Planar Graphs. 1. . . Graphs: Definitions . Trails, Paths, and Circuits Matrix Representations Planar Graphs. (from 4.2 Graphical representations). KS3 Mastery PD Materials: Exemplified Key Ideas. Materials for use in the classroom or to support professional development discussions. Summer 2021. About this resource.