Graphs and Networks

CS 7450 - Information Visualization March 1, 2005 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

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What is a Graph?

• • Vertices (nodes) connected by Edges (links) 1 2 3 1 2 3 0 1 0 1 0 1 0 1 0 Adjacency matrix Adjacency list 1: 2 2: 1, 3 3: 2 1 2 Drawing 3 Spring 2005 CS 7450 3

Graph Terminology

• • • • Graphs can have

cycles

Graph edges can be

undirected directed

or 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

them (nominal, ordinal or quantitative) ) on Spring 2005 CS 7450 4

Trees are Different

• • • • Subcase of general graph No cycles Typically directed edges Special designated root vertex Spring 2005 CS 7450 5

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 2005 CS 7450 6

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 2005 CS 7450 7

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 Spring 2005 CS 7450 8

Vertex Issues

• • • • • Shape Color Size Location Label Spring 2005 CS 7450 9

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

• • • • • •

Crossings

-- minimize towards planar

Total Edge Length

scale

Area

-- minimize towards proper -- minimize towards efficiency

Maximum Edge Length

edge -- minimize longest

Uniform Edge Lengths Total Bends

straight-line -- minimize variances -- minimize orthogonal towards Spring 2005 CS 7450 12

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 Spring 2005 CS 7450 14

Layout Examples

• • Homework assignment Let’s judge!

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Layout Examples

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

Examples of dynamic graph layout algorithms Spring 2005 CS 7450 16

Graph Uses

• • • Facilitate understanding of complex socio economic patterns Social Science visualization gallery (Lothar Krempel):  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 Spring 2005 CS 7450 17

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

1981

1992

Graph Uses

• • Facilitate understanding of network flows, relations Even information with a ‘geographical’ content can best appear as a ‘network’ rail maps Spring 2005 CS 7450 20

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!

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Social Network Visualization

• Social Network Analysis (Linton Freeman)  http://www.sfu.ca/~insna Spring 2005 CS 7450 25

People connections

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Case Study

• SeeNet  Visualizing network data (phone traffic) R. Becker, S. Eick and A. Wilks AT&T Spring 2005 CS 7450 27

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 2005 CS 7450 28

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

116 Label Thickness Color 116 Directed 29 Spring 2005 CS 7450 30

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 2005 CS 7450 31

Earthquake data

More Help

• Shorten all lines so as to de-emphasize transcontinental links Spring 2005 CS 7450 33

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 Spring 2005 CS 7450 36

More Email

• How about visualizing internet traffic?

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Byte traffic into the ANS/NSFnet T3 backbone for the month of November, 1993 http://www.ncsa.uiuc.edu/SCMS/DigLib/text/technology/Visualization-Study-NSFNET-Cox.html

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

Linux kernel

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

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TouchGraph

Spring 2005 CS 7450 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 Spring 2005 CS 7450 42

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 2005 CS 7450 43

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 2005 CS 7450 44

MoireGraphs

• • • • Visual nodes (ie, images) Smooth interactions Multiple foci Versatile Jankun-Kelly & Ma InfoVis ‘03 Spring 2005 Video CS 7450 45

Case Study

• NicheWorks  Interactive Visualization of Very Large Graphs Graham Wills Lucent Spring 2005 CS 7450 46

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 2005 CS 7450 47

Features

• • Typical interactive operations Sophisticated graph layout algorithm  3 Layouts Circular Hexagonal Tree  3 Incremental Algorithms Steepest Descent Swapping Repelling Spring 2005 CS 7450 48

Interface: Web Site Example

Circle layout Hexagonal layout Tree layout

Interface

Interface

Interface: Fraud Example

40,000 calls 35,000 callers

Interface: Fraud Example

More Neat Stuff

• • • http://willsfamily.org/gwills/ Lots of interesting application areas More details on NicheWorks Spring 2005 CS 7450 54

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 Spring 2005 CS 7450 56

HW6

• • • Work with two hierarchy visualizers: SequoiaView and Grokker Understand and critique visualizations and user interfaces Shorter evaluation: <5 pages Spring 2005 CS 7450 57

Upcoming

• • WWW/Internet visualization  Reading Chi et al Hierarchies & Trees Spring 2005 CS 7450 58

References

• • • Spence and CMS texts All referred to papers and web sites Dagon and Leahy, F ‘99 slides Spring 2005 CS 7450 59

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 2005 CS 7450 60

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