Graphs and Networks

Graphs and Networks

CS 7450 - Information Visualization March 2, 2004

John 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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What is a Graph?

• Vertices (nodes) connected by

• Edges (links)

1 2 3 0 1 0 1 0 1 0 1 0 1

23

1: 2 2: 1, 3

3: 2 ₁

2 3 Adjacency matrix

Adjacency list

Drawing

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

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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

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

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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, ...

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

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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!

Layout Examples

• Cool java applet

http://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 & Plumper’s study of World Trade between OECD countries, 1981 and 1992

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

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. Wilks

AT&T

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

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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

116 Label

Thickness Color

116

29 Directed

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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

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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???

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

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

Linux kernel

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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

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 Wills

Lucent

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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

Features

• Typical interactive operations

• Sophisticated graph layout algorithm

− 3 Layouts Circular Hexagonal Tree

− 3 Incremental Algorithms

Interface: Web Site Example

Circle layout Hexagonal layout Tree layout

Interface

Interface

Interface: Fraud Example

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

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

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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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• 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

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