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Lecture 19:
Graphs and Networks
April 18, 2013
COMP
150

2
Visualization
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Definition
•
Graphs represent connections or relationships
•
Social network
•
Software execution (call graph)
•
Gene expression
•
Financial transactions
•
WWW
•
US telephone system
•
One of the oldest and most studied areas of
information visualization
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What Makes a Graph?
•
Vertices (nodes)
•
Edges (links)
•
Adjacency list:
1: 2
2: 1, 3
3: 2
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Comparing Representations
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Terminology
•
Directed vs. Undirected
•
Cyclic vs. Acyclic
•
Degree of a vertex
•
In

degree
•
Out

degree
•
Weights on edges
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More Terminology
•
Centrality Measures:
•
Degree Centrality
•
How many neighbors does a vertex have?
•
Betweenness
Centrality
•
How often does a vertex appear in paths between other
nodes?
•
Closeness Centrality
•
How quickly can a node reach all other nodes in the graph?
•
Eigenvector Centrality
•
Google PageRank (assumes directed graph)
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Graphs vs. Trees
•
Tree is a special case of a general graph
•
There are no cycles in a tree
•
Edges are (usually) directed or are implicitly
directed
•
Special designations for root, leaves, etc.
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Challenges in Graph Visualization
•
Graph layout and position
•
Related to your assignment!
•
Navigation / Interaction
•
How to support a user in understanding all the
relationships in the graph
•
Scale
•
What happens if the graph has 10 nodes? 1,000
nodes? 1,000,000 nodes?
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Graph Drawing Conference
•
The problem of graph layout remains
unsolved…
•
Question: what are we trying to optimize?
•
http://www.graphdrawing.org/gd2010
/
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What Makes a Good Layout?
•
Total Edge Length
–
minimize towards proper
scale
•
Area
–
minimize for efficiency (
Tufte
!)
•
Maximum Edge Length
–
minimize longest edge
•
Uniform Edge Lengths
–
minimize variances
•
Total Bends
–
minimize orthogonal towards
straight lines
•
Crossings
–
minimize towards planar
•
http://
www.youtube.com/watch?v=EiS

W9aeG0s
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Let People Decide!
•
Paper by Frank van Ham and Bernice
Rogowitz
from IBM Research (published in
InfoVis
2008)
•
http://www.research.ibm.com/visual/papers/
IEEEViz_VanHam%20and%20Rogowitz_final.p
df
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Not An Exact Set of Criteria
Image from
Kamada
and Kawai (1988)
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NetViz
Nirvana
•
Proposed by Ben
Shneiderman
•
Every node is visible
•
Every node’s degree is countable
•
Every edge can be followed from source to
destination
•
Clusters and outliers
are identifiable
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15
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Questions?
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Common Layout Techniques
•
Hierarchical
•
Force

directed
•
Circular
•
Geographic
•
Clustered
•
Attribute

based
•
Matrix
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Layout + Scale
•
Many of these layout algorithms are constrained
by scale.
•
For example, (naive) force directed layout is
O(n^2). When n becomes large, computation
slows down.
•
Even without computation, when n becomes
large, it is difficult (impossible?) to guarantee
visibility for every vertex.
•
Solutions?
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Navigation / Interaction
•
Give a large, dense graph, how do we use
interaction to help the user query, visit,
traverse, and analyze the graph?
•
Such navigation / interaction aides can utilize
other visualization techniques
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Examples
•
http://
www.nytimes.com/interactive/2008/0
5/05/science/20080506_DISEASE.html
•
http://
mibi.deviantart.com/art/Death

and

Taxes

2007

39894058
•
http://
perlitalabs.files.wordpress.com/2010/0
6/social

graphs

to

visualize

political

factions1.png
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More Examples
•
http://www

958.ibm.com/software/data/cognos/manyeyes/visuali
zations/co

occurrences

of

names

in

the

new

3
•
http://conceptmodeler.wordpress.com/
•
http://www.visualcomplexity.com/vc/project_details.c
fm?id=392&index=392&domain
=
•
http
://blog.kobayashi.eu/wp

content/uploads/2010/09/poster_rappers_1300.jpg
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Social Networks
•
Facilitate understanding of complex socio

economic
patterns
•
Social Science visualization gallery (
Lothar
Krempel
):
•
http://www.mpi

fg

koeln.mpg.de/~lk/netvis.html
•
Social Network Analysis (
www.insna.org
)
•
http://www.slate.com/id/2180392/
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Geography
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Examples
•
http://
www.nsf.gov/news/special_reports/sci
vis/follow_money.jsp
•
http://
www.facebook.com/notes/facebook

engineering/visualizing

friendships/469716398919
•
http://www.aaronkoblin.com/work/flightpatt
erns/
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Subway Maps
London Tube
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Boston T
•
http://
www.google.com/images?q=Boston+T
&um=1&ie=UTF

8&source=og&sa=N&hl=en&tab=wi&biw=10
31&bih=1376
•
http://www.mbta.com/schedules_and_maps
/subway/
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Questions?
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Circular Layout
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Circular Layout + Edge Bundling
•
http://flare.prefuse.or
g/apps/dependency_g
raph
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Tree Layout
•
Forcing a graph into a tree
layout
•
Spanning tree
•
Hierarchical Layout
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Sugiyama Method
Images from van Dalen and
Spaans
(2001)
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Force

Directed Layout
•
Common Spring Model
•
Edges
–
springs that attract
•
Vertices
–
charged particles that repel
•
Iteratively computes new positions of the vertices
based on the lengths of the edges
•
Seeks to minimize the total energy of the system
down to 0
•
http://jung.sourceforge.net/applet/showlayouts.html
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Force Directed Layout
•
Naïve
Spring network (
assignment
5)
•
Optimized Spring network (Barnes

Hut)
•
http://
en.wikipedia.org/wiki/Barnes%E2%80%93Hut_simulatio
n
•
Frauchterman

Reingold
•
Adds global temperature (simulated annealing)
•
http://
citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.13.8
444
•
Kamada

Kawai
•
Computes the derivative of the overall energy function
•
Iteratively improves the search for global layout
•
http://cs.wellesley.edu/~cs315/Papers/Kamada

Graph%20Drawing.pdf
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Questions?
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Recent Trends in Graph Visualization
•
Attributes of nodes influence the layout
•
Not just arbitrary layout
•
Utilize graph statistics
•
Driven by interests in social network analysis
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PivotGraph
•
Cluster on common node attributes
•
Put all A’s together into a node, all B’s together
into a node
•
“Roll up” the nodes
•
Draw edge from A to B depending on how many
edges go from some A to some B
•
Position nodes on a grid based on data
attributes
Wattenberg CHI 06
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PivotGraph
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Semantic Substrates
•
Group nodes into regions
•
According to an attribute
•
Categorical, ordinal, or binned numerical
•
In each region:
•
Position nodes according to some other attributes
•
Give users control of link visibility
•
http://www.cs.umd.edu/hcil/nvss/
Shneiderman
InfoVis
06
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Semantic Substrates
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Vizster
•
Visualize social networking sites (Friendster,
MySpace, Facebook).
•
Think 2005 when social network is just starting!
•
http://hci.stanford.edu/jheer/projects/vizster/
Heer
InfoVis
05
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SocialAction
•
Combines graph structure analysis with
interactive visual exploration
•
Multiple coordinated views
•
Lists by ranking for analysis data
•
Force

directed layout for graph
•
http://www.cs.umd.edu/hcil/socialaction/
Perer
InfoVis
06
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Social Network Attributes
•
Barycenter
•
total shortest path of a node to all other nodes
•
Betweenness
Centrality
•
How often a node appears on the shortest paths between all other
nodes
•
Closeness Centrality
•
How close a node is compared to all other nodes
•
Min

cut
•
If the removal of a node creates disconnected
subgraph
(s)
•
Degree
•
Number of neighbors
•
HITS (Hyperlink

Induced Topic Search), also known as “Hubs and
Authorities”
•
Precursor to Google PageRank
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Attribute Ranking
•
Run these measures on all nodes and rank
them
•
Use secondary visualizations to display them
(lists, scatterplots,
etc
)
•
Allow the user to interact with both the graph
and the secondary visualizations
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PNNL’s Graph Vis
•
Graph “Signature”
Wong TVCG 06
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Graph Signature
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Graph Signature
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Graphs as Maps
http://www2.research.att.com/~yifanhu/MAPS/imap.html
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Matrix Representation
•
An obvious alternative visualization of graphs
is a matrix…
Ghoniem
InfoVis
04
50
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Matrix Representation
How does one
read a Matrix
visualization?
Importance of
sorting…
Henry
InfoVis
06
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Matrix Representation
Liiv
, BELIV 2010
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NodeTrix
Hybrid of matrix and
node

link
Best of both worlds?
Worst of both
methods?
Henry
InfoVis
07
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Questions?
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Interaction
•
Interaction can be used as an alternative (or a
Band

Aid) to visualizing:
•
Difficult graphs using existing layout algorithms
•
Graphs that are significantly larger than what can
be displayed on screen
•
Challenges:
•
What types of interactions make sense?
•
How to make graphs interactive?
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MoireGraph
•
Uses radial layout
•
Takes a hierarchical data as input (much like a tree)
•
If no hierarchy is available, impose levels of the graph by
performing minimum spanning tree
•
Put root at the center, children are further out
towards the edge of the circle, with decreasing
emphasis (similar to hyperbolic trees)
•
Like hyperbolic trees, interaction is key
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MoireGraph
Jankun

Kelly
InfoVis
03
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MoireGraph
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MoireGraph
Layout
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Interactive Big Graphs
Van Ham
InfoVis
2010
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Interactive Big Graphs
•
Similar to
SocialAction
•
Use additional attributes (graph characteristics)
to assist in the analysis
•
Allow users to focus on particular nodes
•
Apply Degree

of

Interest (DOI) methods
•
Rely heavily on interaction
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Animating Change of Focus
Yee
InfoVis
01
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Animating Change of Focus
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Questions?
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