Graph Visualization and Navigation in Information Visualization: a Survey

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  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: http://www.smartmoney.com/marketmap  Size represents market share  Color represents performance  More information available through clicking  Problem: Tree structure less clear

13. Layout of Directed Graphs  Layering (http://www.csus,yk,ue/staff/NikolaNikolov/#phd)

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  “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 http://industry.ebi.ac.uk/~alan/components/examples/example1.html http://www.inxight.com/map  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 http://touchgraph.sourceforge.net/ (Force-directed? Note how animation helps adjusting to new layout)

31. 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

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 101-112, 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  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