Graphs and Networks

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Graphs and Networks

• CS 7450 - Information Visualization
• March 1, 2005
• John Stasko

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Connections

• Spences chapter 8 is called Connectivity
• Connections throughout our lives and the world
• Circle of friends
• Deltas flight plans
• Model connected set as a Graph

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What is a Graph?

• Vertices (nodes)connected by
• Edges (links)

Adjacency list
1 2 2 1, 3 3 2
1 2 3 0 1 0 1 0 1 0 1 0
1
1 2 3
2
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Drawing
Adjacency matrix
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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

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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 communitys 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

• 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

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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
• Lets 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 (Lothar
  Krempel)
• http//www.mpi-fg-koeln.mpg.de/lk/netvis.html
• Next slides Krempel Plumpers study of World
  Trade between OECD countries, 1981 and 1992

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1981
http//www.mpi-fg-koeln.mpg.de/lk/netvis/trade/Wo
rldTrade.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 graphs 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. WilksATT

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Domain

• ATT 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

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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
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Label
Thickness
Color
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Directed
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Problems

• Too many lines!
• Occlusion
• Long lines become more important
• Cant see what happens in Midwest
• Solutions
• Use half/half technique out/out
• Draw most important last
• Use thickness color for traffic

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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?

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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/technolo
gy/Visualization-Study-NSFNET-Cox.html
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Inbound traffic measured in billions of bytes on
the NSFNET T1 backbone for September 1991
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Linux kernel
http//perso.wanadoo.fr/pascal.brisset/kernel3d/ke
rnel3d.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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Focus Change Animation
Straight linear interpolation of focus changes
not as appealing as changes along polar
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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MoireGraphs

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

Jankun-Kelly Ma InfoVis 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 Layouts
• Circular
• Hexagonal
• Tree
• 3 Incremental Algorithms
• Steepest Descent
• Swapping
• Repelling

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Interface Web Site Example
Hexagonal layout
Tree layout
Circle layout
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Interface
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Interface
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Interface Fraud Example
40,000 calls 35,000 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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HW6

• Work with two hierarchy visualizers SequoiaView
  and Grokker
• Understand and critique visualizations and user
  interfaces
• Shorter evaluation lt5 pages

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Upcoming

• WWW/Internet visualization
• Reading
• Chi et al
• Hierarchies Trees

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References

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

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Graph Uses

• Track flows and movements of individuals in
  society
• Next slides Krempels map of Duisburg zoo
  visitors
• Physical coordinates yields ball of string
  merely reflecting the autobahn division of zoo
• Gravity solution to graph shows flow

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http//www.mpi-fg-koeln.mpg.de/lk/netvis/zoo1.htm
l
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