Graph Visualization and Navigation in Information Visualization: a Survey

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Graph Visualization and
Navigation in Information
Visualization: a Survey

Ivan Herman, Guy Melan
ç
on, 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


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
K
önigsberger 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 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(N
3
)


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:


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 Poincar
é 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 P
1
, P
2
, and P
3

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


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