Graph Visualization and Navigation in Information Visualization: a Survey

Ivan Herman, Guy Melançon, and M. Scott Marshall

(Presentation: Anne DentonMarch 6, 2003)

Outline Graph drawing and graph

visualization Graph layout Navigation of large graphs Reorganization of data: Clustering

Information 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

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

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 edgesBut 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

“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:

Perspectivewall

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 appletshttp://industry.ebi.ac.uk/~alan/components/examples/example1.htmlhttp://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 ModelT. 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 differsfor 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 smallExample not from the paperhttp://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