Graph Visualization and
Navigation in Information
Visualization: a Survey
Ivan Herman, Guy Melan
ç
on, and
M. Scott Marshall
(Presentation: Anne Denton
March 6, 2003)
Outline
Graph drawing and graph visualization
Graph layout
Navigation of large graphs
Reorganization of data: Clustering
Information Visualization
vs. Graph Drawing
Graph Drawing
Old topic, many books, etc.
May have other goals than visualization
E.g. VLSI design
Graph Visualization
Size key issue
Usability requires nodes to be discernable
Navigation considered
Node Information?
Sometimes a “size” or “importance” is
represented
Navigational systems may have links to data
Glyphs?
Mentioned as representation of higher levels in
hierarchical clustering
Focus on structure

based properties
Application independent
Examples
Class browsers
Entity relationship diagrams
Real

time systems (state transition diagrams)
VLSI circuit design (circuit schematics rather
than actual design)
Document management system
Web

navigation
Virtual Reality (scene graph)
History of Graph Drawing
Euler used a drawing to solve the
K
önigsberger Brückenproblem (1736)
Symposia on Graph Drawing initiated 1992
Issues
Planarity
No edges cross in 2D
Aesthetic rules
Edges should have same length
Edges should be straight lines
Isomorphic substructures displayed equivalently
Note: Isomorphic subtrees laid out in
same way
Problem: High Density of nodes
Reingold and Tilford algorithm
for Trees
Tasks Related to Graph
Drawing
Layering a graph
Turning graph into directed acyclic graph
Planarizing (achieve that no edges cross)
Minimizing area
Minimizing number of bends in edges
But
Algorithms too complex for large graphs
Problem: Size
Previous example: few hundred nodes
How about thousands of nodes?
Solutions
3D
Non

Euclidean geometry (e.g., hyperbolic
geometry)
Reduce size
Show part only / blow up part
Other problems related to
Navigation
Predictability
Two different runs on similar trees should
lead to similar results
Traditional layouts next page are
predicatable
Time Complexity
Real time interaction
Traditional Tree Layouts
Classical layout on earlier slide
H

tree layout: best for balanced trees
Radial view
Balloon view: related to 3

d cone tree
Tree

Map
Useful for information visualization
because area is meaningful
Example:
http://www.smartmoney.com/marketmap
Size represents market share
Color represents performance
More information available through clicking
Problem: Tree structure less clear
Layout of Directed Graphs
Layering
(
http://www.csus,yk,ue/staff/NikolaNikolov/#phd
)
Spring Layout
Force directed
Nodes are modeled as physical bodies
that are connected through springs
(edges)
High time complexity: > O(N
3
)
Not predictable
Spanning Trees
Further conclusions from size
Don’t insist on planarity
Don’t worry about edge crossings
Graph can be visualized through minimum
spanning tree
Additional edges added later
Very common technique
Helps with predictability
Visualization depends on starting point
3D Techniques
Benefits
“Gaining more space”
Human familiarity with 3D
Problems
2D displays
Missing motion and stereo cues
May be solved by better technology
Examples of 3D Techniques
3D version of a radial tree
Info cube
Cone Tree
Developed directly for 3D
Interactiveness important:
Nodes can be rotated
Fly

Through of 2D
Representation
SGI File System Navigator
Size represents file size
Similar:
Perspective
wall
Hyperbolic Layout
Mainly used for trees
E.g. web

content viewers
2D or 3D
Similar to fish

eye lense
Possibility of interacting with large trees
EBI Hyperbolic Viewers
2D example applets
http://industry.ebi.ac.uk/~alan/components/examples/example1.html
http://www.inxight.com/map
3D image
Hyperbolic Viewer Concepts
For a given point and non

intersecting line: many
parallel lines through point
Segments that are congruent in the hyperbolic sense
are exponentially smaller in the Euclidean sense
when approaching the perimeter
Projective Klein model
Straight lines
Suitable for 4x4 matrix

based graphics
Conformal or Poincar
é model
Straight lines drawn as arcs
Angles are drawn correctly in Euclidean sense
Computationally more demanding
Klein Model vs. Poincare Model
T. Munzner, P. Burchard, “Visualizing the structure of the World
Wide Web in 3D Hyperbolic Space,” Proceedings of the VRML
Symposium, pp 33

38, 1995.
Klein Model
Poincare Model
Simple Tree Construction
Algorithm
Node P with with wedge QPR
Subtrees start at P
1
, P
2
, and P
3
Euclidean
Hyperbolic
Navigation and Interaction
Zoom and pan
Zoom for graphs exact, not pixel

based
(adjustment of screen transformations)
Geometric zooming
Simple blow

up
Semantic zooming
Content changes
Clustering
Problem with Combination of
Zoom and Pan
Assume zoom and pan independent
Objects may
temporarily
move away
Solution: Space

scale diagram
(Semantic zoom:
picture differs
for each level)
Focus + Context Techniques
Zooming looses contextual information
Focus + context keeps context
Example
Fisheye
distortion
Fisheye Distortion
Process
Pick focus point
Map points within radius using a concave
monotonic function
Example: Sarkar

Brown distortion function
Problem with Fisheye
Distortion should also be applied to links
Prohibitively slow (polyline)
Alternative
Continue using lines
Can result in unintended line crossings
Other Alternative
Combine layout with focus+context
Hyperbolic viewer
Other combinations possible (e.g. balloon view
with focus

dependent radii) but not yet done
Incremental Exploration and
Navigation
For very large graphs (e.g. Internet)
Small portion displayed
Other parts displayed as needed
Displayed graph small
Layout and interaction times may be small
Example not from the paper
http://touchgraph.sourceforge.net/
(Force

directed? Note how animation helps
adjusting to new layout)
Clustering
Structure

based clustering
Most common in graph visualization
Often retain structure of graph
Useful for user orientation
Content

based clustering
Application specific
Can be used for
Filtering: de

emphasis or removal of elements from view
Search: emphasis of an element or group of elements
Clustering continued
Common goal
Finding disjoint clusters
Clumping
Finding overlapping clusters
Common technique
Least number of edges between neighbors
(Ratio Cut technique in VLSI design)
Hierarchical Clustering
From successive application
of clustering process
Can be navigated
as tree
Visualization of higher levels
Herman et al. say
glyphs are used (?)
P. Eades, Q. Feng, “Multilevel
Visualization of Clustered Graphs,
” Lecture Notes in Computer
Science”, 1190, pp 101

112,
1997
Node Metrics
Measure abstract feature
Give ranking
Edge metrics also possible
Structure

based or content

based
Examples
Application

specific weight
Degree of the node
“Degree of Interest” (Furnas)
Methods of representing
unselected nodes
Ghosting
De

emphasizing or
relegating nodes
to background
Hiding
Not displaying at all
Grouping
Grouping under super

node representation
Summary
Graph drawing and graph visualization
Overlap but different goals and problems
Graph layout
Much is known from graph drawing
Navigation of large graphs
Key tool in dealing with size
Reorganization of data: Clustering
Still much to be done
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