# Graph Visualization and Navigation in Information Visualization: a Survey

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15 Νοε 2013 (πριν από 4 χρόνια και 4 μήνες)

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Graph Visualization and
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

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

Node Information?

Sometimes a “size” or “importance” is
represented

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
-

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

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

Solutions

3D

Non
-
Euclidean geometry (e.g., hyperbolic
geometry)

Reduce size

Show part only / blow up part

Other problems related to

Predictability

Two different runs on similar trees should

predicatable

Time Complexity

Real time interaction

Classical layout on earlier slide

H
-
tree layout: best for balanced trees

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

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

Graph can be visualized through minimum
spanning tree

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

Zoom and pan

Zoom for graphs exact, not pixel
-
based

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

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

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 (?)

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