Graphs and Networks. CS Information Visualization March 2, 2004 John Stasko

Transcription

1 Graphs and Networks CS Information Visualization March 2, 2004 John Stasko Connections Spence s chapter 8 is called Connectivity Connections throughout our lives and the world Circle of friends Delta s flight plans Model connected set as a Graph Spring 2004 CS

2 What is a Graph? Vertices (nodes) connected by Edges (links) Adjacency matrix Adjacency list 1: 2 2: 1, 3 3: Drawing 3 Spring 2004 CS Graph Terminology Graphs can have cycles Graph edges can be directed or undirected The degree of a vertex is the number of edges connected to it In-degree and out-degree for directed graphs Graph edges can have values (weights) on them (nominal, ordinal or quantitative) Spring 2004 CS

3 Trees are Different Subcase of general graph No cycles Typically directed edges Special designated root vertex Already examined them Spring 2004 CS Graph Uses In information visualization, any number of data sets can be modeled as a graph US telephone system World Wide Web Distribution network for on-line retailer Call graph of a large software system Semantic map in an AI algorithm Spring 2004 CS

4 Graph Visualization Problems Graph layout and positioning Make a concrete rendering of abstract graph Scale Not too much of a problem for small graphs, but large ones are much tougher Navigation How to support user changing focus and moving around the graph Spring 2004 CS Layout Algorithms Entire research community s focus Good references: Tutorial (talk slides) G. dibattista, P. Eades, R. Tamassia, and I. Tollis, Graph Drawing: Algorithms for the Visualization of Graphs, Prentice Hall, Article by Herman et al Spring 2004 CS

5 Vertex Issues Shape Color Size Location Label Spring 2004 CS General GD Information Good web links rw4.cs.uni-sb.de/users/sander/html/gstools.html Spring 2004 CS

6 Edge Issues Color Size Label Form Polyline, straight line, orthogonal, grid, curved, planar, upward/downward,... Spring 2004 CS Aesthetic Considerations Crossings -- minimize towards planar Total Edge Length -- minimize towards proper scale Area -- minimize towards efficiency Maximum Edge Length -- minimize longest edge Uniform Edge Lengths -- minimize variances Total Bends -- minimize orthogonal towards straight-line Spring 2004 CS

7 Layout Heuristics Layout algorithms can be planar grid-based orthogonal curved lines hierarchies circular... Spring 2004 CS Scale Challenge May run out of space for vertices and edges (turns into ball of string ) Can really slow down algorithm Often use clustering to help Extract highly connected sets of vertices Collapse some vertices together Spring 2004 CS

8 Layout Examples Homework assignment Let s judge! Spring 2004 CS Layout Examples Cool java applet Examples of dynamic graph layout algorithms Spring 2004 CS

9 Graph Uses Facilitate understanding of complex socioeconomic patterns Social Science visualization gallery (Lothar Krempel): Next slides: Krempel & Plumper s study of World Trade between OECD countries, 1981 and 1992 Spring 2004 CS

10 1992 Graph Uses Facilitate understanding of network flows, relations Even information with a geographical content can best appear as a network rail maps Spring 2004 CS

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12 3 Subway Diagrams Geographic landmarks largely suppressed on maps, except water (rivers in Paris, London) and asphalt (highways in Atlanta) Rather fitting, no? These are more graphs than maps! Spring 2004 CS

13 Social Network Visualization Social Network Analysis (Linton Freeman) Spring 2004 CS People connections Charles Isbell, Cobot Spring 2004 CS

14 Case Study SeeNet Visualizing network data (phone traffic) R. Becker, S. Eick and A. Wilks AT&T Spring 2004 CS Domain AT&T long distance phone network 110 Nodes (switches) Geographical location Connected by 12,000 links Directed, almost completely connected Data every 5 minutes EARTHQUAKE!!! Oct. 17, 1989 Spring 2004 CS

15 Questions Where are the overloads? Which links are carrying most traffic? Was there network damage? Is there underutilized capacity? Are calls getting in to affected area or are there bottlenecks? Is overload increasing or decreasing? Spring 2004 CS Edge Drawing Strategies 116 Label Thickness Color Directed Spring 2004 CS

16 Problems Too many lines! Occlusion Long lines become more important Can t see what happens in Midwest Solutions Use half/half technique out/out Draw most important last Use thickness & color for traffic Spring 2004 CS Earthquake data

17 More Help Shorten all lines so as to de-emphasize transcontinental links Spring 2004 CS

18 Other Applications How would you visualize all traffic in CoC between pairs of people? Solutions??? Spring 2004 CS Solutions Put everyone on circle, lines between Color or thicken line to indicate magnitude Use spring/tension model People who send a lot to each other are drawn close together Shows clusters of communications Spring 2004 CS

19 More How about visualizing internet traffic? Spring 2004 CS Byte traffic into the ANS/NSFnet T3 backbone for the month of November,

20 Inbound traffic measured in billions of bytes on the NSFNET T1 backbone for September 1991 Linux kernel Spring 2004 CS

21 TouchGraph Spring 2004 CS Focus of Graph Particular node may be focus, often placed in center for circular layout How does one build an interactive system that allows changes in focus? Use animation Intuition about changes not always right Spring 2004 CS

22 Focus Change Animation Straight linear interpolation of focus changes not as appealing as changes along polar coordinates Yee, Fisher, Dhamija, Hearst InfoVis 01 Video Spring 2004 CS Radial Display Can we combine some of the properties of the hyperbolic graphs without the hyperbolic distortion? Still use a radial technique with root/focus at center Spring 2004 CS

23 MoireGraphs Visual nodes (ie, images) Smooth interactions Multiple foci Versatile Jankun-Kelly & Ma InfoVis 03 Video Spring 2004 CS Case Study NicheWorks Interactive Visualization of Very Large Graphs Graham Wills Lucent Spring 2004 CS

24 Big Graphs 20,000-1,000,000 Nodes Works well with 50,000 Projects Software Engineering Web site analysis Large database correlation Telephone fraud detection Spring 2004 CS Features Typical interactive operations Sophisticated graph layout algorithm 3 Layouts Circular Hexagonal Tree 3 Incremental Algorithms Steepest Descent Swapping Repelling Spring 2004 CS

25 Interface: Web Site Example Circle layout Hexagonal layout Tree layout Interface

26 Interface Interface: Fraud Example 40,000 calls 35,000 callers

27 Interface: Fraud Example More Neat Stuff Lots of interesting application areas More details on NicheWorks Spring 2004 CS

28 More Resources Network visualization resources Good article on graph layout Spring 2004 CS More to Come... Topic of WWW/InfoSphere (next) will touch on graphs and networks too Lots of example visualizations Spring 2004 CS

29 Upcoming WWW/Internet visualization Reading Chi et al Spring Break Spring 2004 CS References Spence and CMS texts All referred to papers and web sites Dagon and Leahy, F 99 slides Spring 2004 CS

30 Graph Uses Track flows and movements of individuals in society Next slides: Krempel s map of Duisburg zoo visitors Physical coordinates yields ball of string merely reflecting the autobahn division of zoo Gravity solution to graph shows flow Spring 2004 CS Spring 2004 CS

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