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Graphs and Networks

CS 7450 - Information VisualizationMarch 2, 2004John Stasko

Spring 2004 CS 7450 2

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

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Spring 2004 CS 7450 3

What is a Graph?

• Vertices (nodes)connected by

• Edges (links)

1 2 30 1 01 0 10 1 0

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1: 22: 1, 33: 2 1

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Adjacency matrix

Adjacency list

Drawing

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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)

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Trees are Different

• Subcase of general graph• No cycles• Typically directed edges• Special designated root vertex

• Already examined them

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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

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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

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Layout Algorithms

• Entire research community’s focus• Good references:

− Tutorial (talk slides)www.cs.brown.edu/people/rt/papers/gd-tutorial/gd-constraints.pdf

− G. diBattista, P. Eades, R. Tamassia, and I. Tollis, Graph Drawing: Algorithms for the Visualization of Graphs, Prentice Hall, 1999.

− Article by Herman et al

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Vertex Issues

• Shape• Color• Size• Location• Label

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General GD Information

• Good web links− www.cs.brown.edu/people/rt/gd.html− www.research.att.com/sw/tools/graphviz/− rw4.cs.uni-sb.de/users/sander/html/gstools.html

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Edge Issues

• Color• Size• Label• Form

− Polyline, straight line, orthogonal, grid, curved, planar, upward/downward, ...

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Aesthetic Considerations

•• CrossingsCrossings -- minimize towards planar•• Total Edge LengthTotal Edge Length -- minimize towards proper

scale•• AreaArea -- minimize towards efficiency•• Maximum Edge LengthMaximum Edge Length -- minimize longest

edge•• Uniform Edge LengthsUniform Edge Lengths -- minimize variances•• Total BendsTotal Bends -- minimize orthogonal towards

straight-line

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Layout Heuristics

• Layout algorithms can be− planar− grid-based− orthogonal− curved lines− hierarchies− circular− ...

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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

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Layout Examples

• Homework assignment• Let’s judge!

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Layout Examples

• Cool java applethttp://java.sun.com/applets/jdk/1.2/demo/applets/GraphLayout/example1.html

• Examples of dynamic graph layout algorithms

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Graph Uses

• Facilitate understanding of complex socio-economic patterns

• Social Science visualization gallery (LotharKrempel):− http://www.mpi-fg-koeln.mpg.de/~lk/netvis.html

• Next slides: Krempel & Plumper’s study of World Trade between OECD countries, 1981 and 1992

1981http://www.mpi-fg-koeln.mpg.de/~lk/netvis/trade/WorldTrade.html

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1992

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Graph Uses

• Facilitate understanding of network flows, relations

• Even information with a ‘geographical’ content can best appear as a ‘network’ rail maps

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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 graphsgraphs than maps!

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Social Network Visualization

• Social Network Analysis (Linton Freeman)− http://www.sfu.ca/~insna

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People connections

Charles Isbell, Cobot

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Case Study

• SeeNet− Visualizing network data (phone traffic)

R. Becker, S. Eick and A. WilksAT&T

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Domain

• AT&T long distance phone network− 110 Nodes (switches)

Geographical location

− Connected by 12,000 linksDirected, almost completely connected

• Data every 5 minutes•• EARTHQUAKE!!!EARTHQUAKE!!!

− Oct. 17, 1989

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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?

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Edge Drawing Strategies

116Label

Thickness

Color

116

29Directed

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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

Earthquake data

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More Help

• Shorten all lines so as to de-emphasize transcontinental links

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Other Applications

• Email• How would you visualize all email traffic in

CoC between pairs of people?• Solutions???

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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

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More Email

• How about visualizing internet traffic?

http://www.ncsa.uiuc.edu/SCMS/DigLib/text/technology/Visualization-Study-NSFNET-Cox.html

Byte traffic into the ANS/NSFnet T3 backbone for the month of November, 1993

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Inbound traffic measured in billions of bytes on the NSFNET T1 backbone for September 1991

Spring 2004 CS 7450 40

Linux kernel

http://perso.wanadoo.fr/pascal.brisset/kernel3d/kernel3d.html

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TouchGraph

www.touchgraph.com

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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

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Spring 2004 CS 7450 43

Focus Change Animation

Straight linear interpolationof focus changes not as appealing as changes alongpolar coordinates

Yee, Fisher, Dhamija, Hearst InfoVis ‘01

Video

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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

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Spring 2004 CS 7450 45

MoireGraphs

• Visual nodes (ie, images)• Smooth interactions• Multiple foci• Versatile

Jankun-Kelly & MaInfoVis ‘03 Video

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Case Study

• NicheWorks− Interactive Visualization of Very Large Graphs

Graham WillsLucent

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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

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Features

• Typical interactive operations• Sophisticated graph layout algorithm

− 3 LayoutsCircularHexagonalTree

− 3 Incremental AlgorithmsSteepest DescentSwappingRepelling

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Interface: Web Site Example

Circle layout Hexagonal layout Tree layout

Interface

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Interface

Interface: Fraud Example

40,000 calls35,000 callers

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Interface: Fraud Example

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More Neat Stuff

• http://willsfamily.org/gwills/• Lots of interesting application areas• More details on NicheWorks

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More Resources

• Network visualization resources− http://www.caida.org/projects/internetatlas/viz/

• Good article on graph layout− http://www.csi.uottawa.ca/ordal/papers/sander/main.html

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More to Come...

• Topic of WWW/InfoSphere (next) will touch on graphs and networks too

• Lots of example visualizations

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Upcoming

• WWW/Internet visualization− Reading

Chi et al

• Spring Break

Spring 2004 CS 7450 58

References

• Spence and CMS texts• All referred to papers and web sites• Dagon and Leahy, F ‘99 slides

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• 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

Graph Uses

Spring 2004 CS 7450 60http://www.mpi-fg-koeln.mpg.de/~lk/netvis/zoo1.html

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