1. Graph Visualization and Navigation in Information Visualization: a Survey
Ivan Herman, Guy Melançon, and M. Scott Marshall
(Presentation: Anne Denton
March 6, 2003)

2. Outline Graph drawing and graph visualization Graph layout
Navigation of large graphs
Reorganization of data: Clustering

3. Information Visualization vs. 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

4. 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

5. 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)

6. History of Graph Drawing
Euler used a drawing to solve the Königsberger 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

7. Reingold and Tilford algorithm for Trees
Note: Isomorphic subtrees laid out in same way
Problem: High Density of nodes

8. 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

9. 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

10. 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

11. 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

12. Tree-Map
Useful for information visualization because area is meaningful
Example:
Size represents market share
Color represents performance
More information available through clicking
Problem: Tree structure less clear

13. Layout of Directed Graphs
Layering (

14. Spring Layout Force directed
Nodes are modeled as physical bodies that are connected through springs (edges)
High time complexity: > O(N3)
Not predictable

15. 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

16. 3D Techniques Benefits Problems “Gaining more space”
Human familiarity with 3D
Problems
2D displays
Missing motion and stereo cues
May be solved by better technology

17. Examples of 3D Techniques
3D version of a radial tree
Info cube

18. Cone Tree Developed directly for 3D Interactiveness important:
Nodes can be rotated

19. Fly-Through of 2D Representation
SGI File System Navigator
Size represents file size
Similar:
Perspective
wall

20. 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

21. EBI Hyperbolic Viewers
2D example applets
3D image

22. 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 Poincaré model
Straight lines drawn as arcs
Angles are drawn correctly in Euclidean sense
Computationally more demanding

23. 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

24. Simple Tree Construction Algorithm
Node P with with wedge QPR
Subtrees start at P1, P2, and P3
Euclidean Hyperbolic

25. 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

26. 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)

27. Focus + Context Techniques
Zooming looses contextual information
Focus + context keeps context
Example
Fisheye
distortion

28. Fisheye Distortion Process Pick focus point
Map points within radius using a concave monotonic function
Example: Sarkar-Brown distortion function

29. 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

30. 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
(Force-directed? Note how animation helps adjusting to new layout)

31. Clustering Structure-based clustering Content-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

32. 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)

33. Hierarchical Clustering
From successive application
of clustering process
Can be navigated
as tree

34. 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 ,
1997

35. 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)

36. Methods of representing unselected nodes
Ghosting
De-emphasizing or
relegating nodes
to background
Hiding
Not displaying at all
Grouping
Grouping under super
-node representation

37. Summary Graph drawing and graph visualization Graph layout
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