Title: Graph Visualization and Navigation in Information Visualization: a Survey
1Graph Visualization and Navigation in Information
Visualization a Survey
- Ivan Herman, Guy Melançon, and M. Scott Marshall
- (Presentation Anne Denton
- March 6, 2003)
2Outline
- Graph drawing and graph visualization
- Graph layout
- Navigation of large graphs
- Reorganization of data Clustering
3Information Visualizationvs. 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
4Node 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
5Examples
- 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)
6History 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
7Reingold and Tilford algorithm for Trees
- Note Isomorphic subtrees laid out in same way
- Problem High Density of nodes
8Tasks 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
9Problem 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
10Other 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
11Traditional Tree Layouts
- Classical layout on earlier slide
- H-tree layout best for balanced trees
- Radial view
- Balloon view related to 3-d cone tree
12Tree-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
13Layout of Directed Graphs
- Layering (http//www.csus,yk,ue/staff/NikolaNikolo
v/phd)
14Spring Layout
- Force directed
- Nodes are modeled as physical bodies that are
connected through springs (edges) - High time complexity gt O(N3)
- Not predictable
15Spanning Trees
- Further conclusions from size
- Dont insist on planarity
- Dont 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
163D Techniques
- Benefits
- Gaining more space
- Human familiarity with 3D
- Problems
- 2D displays
- Missing motion and stereo cues
- May be solved by better technology
17Examples of 3D Techniques
- 3D version of a radial tree
- Info cube
18Cone Tree
- Developed directly for 3D
- Interactiveness important
- Nodes can be rotated
19Fly-Through of 2D Representation
- SGI File System Navigator
- Size represents file size
- Similar
- Perspective
- wall
20Hyperbolic Layout
- Mainly used for trees
- E.g. web-content viewers
- 2D or 3D
- Similar to fish-eye lense
- Possibility of interacting with large trees
21EBI Hyperbolic Viewers
- 2D example applets
- http//industry.ebi.ac.uk/alan/components/example
s/example1.html - http//www.inxight.com/map
- 3D image
22Hyperbolic 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
23Klein 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
24Simple Tree Construction Algorithm
- Node P with with wedge QPR
- Subtrees start at P1, P2, and P3
- Euclidean Hyperbolic
25Navigation 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
26Problem 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)
27Focus Context Techniques
- Zooming looses contextual information
- Focus context keeps context
- Example
- Fisheye
- distortion
28Fisheye Distortion
- Process
- Pick focus point
- Map points within radius using a concave
monotonic function - Example Sarkar-Brown distortion function
29Problem 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 focuscontext
- Hyperbolic viewer
- Other combinations possible (e.g. balloon view
with focus-dependent radii) but not yet done
30Incremental 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)
31Clustering
- 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
32Clustering continued
- Common goal
- Finding disjoint clusters
- Clumping
- Finding overlapping clusters
- Common technique
- Least number of edges between neighbors
- (Ratio Cut technique in VLSI design)
33Hierarchical Clustering
- From successive application
- of clustering process
- Can be navigated
- as tree
34Visualization 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
35Node 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)
36Methods of representing unselected nodes
- Ghosting
- De-emphasizing or
- relegating nodes
- to background
- Hiding
- Not displaying at all
- Grouping
- Grouping under super
- -node representation
37Summary
- 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