Graph Visualization and Navigation in Information Visualization: a Survey Ivan Herman, Guy Melançon, 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 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 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

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

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(N3) 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 Problems “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 Poincaré 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 P1, P2, and P3 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 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

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 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