15 Network Visualization and Communities

Network Visualization
James Moody
Duke Network Analysis Center (DNAC)
https://dnac.ssri.duke.edu/
Duke University
https://tinyurl.com/SNH-2019

Introduction
From the beginning, network science has been a visual science, rich with strange images
purporting to illuminate our understanding of the world.

A Little network Visualization History
Euler’s treatment of the “Seven Bridges of Kronigsberg” problem is one of the
first moments of graph theory, where he contrasted the observed map….
Euler, 1741
The study of networks has depended on a visual thinking since the
beginning:
Promising Foundations

… to an alternative to help think through what would became the first theorem
in graph theory, and the development of elements (land masses/vertices)
linked as pairs (edges/bridges)
Euler, 1741
beginning:

… and abstracted from the observed elements (land masses/bridges) to
abstract connections (Vertices/edges)
Euler, 1741
beginning:

Early kinship diagrams by Morgan
(1871)
Diagram of
consanguinity:
Seneca-Iroquois
(lineal & 1st collateral
lines, ego is male)
The study of networks has
depended on a visual thinking
since the beginning:

Or early representations of organizational relations (1921)
beginning:

..but Moreno’s sociograms from Who Shall Survive (1934) were something
special. They ignited a wave of research that was to fundamentally transform
social science.
beginning:

With a full write-up of the 1934 medical conference in the New York Times*, his
work sparked wide interest….
beginning:
*He claims it was covered in “all the major papers” but I can’t find any other clips…

Lundberg & Steel 1938 – Using a “Social Atom” representation
Moreno’s idea was quickly taken up in community studies, as the social analog
to “atoms” in physics….

Charles Loomis – 1948
The sophistication included layering of information…here using size, position,
and a pie-chart to tap multiple variables in addition to network structure.

Northaway’s – “Target Sociograms”
Researchers increasingly sought ways move from artistic production to
science -- The “target” sociogram was an early example.
From Art to Science…

..complete with “hardware” to help in the construction!

Another attempt at
regularization: add
meaning to the y and x
axes (here social status
and “group” respectively).
Attempts at generalizing dimensional meaning start to get muddy as the
figures no longer carry an intuitive connectivity pattern.
Loomis & McKinney, 1956, AJS

The flow of images continued over time, marking a wide range of potential
styles.
The space-bending
challenge is made clear
in modern attempts at
mapping large-scale
networks…
Walrus
(Tamara Munzer & Caida)

Sadly, we are now starting to see caricatures of “network” images everywhere:
From Science to Silly…

A New York Times graphic on links
between wall-street executives and the
business school they attended…

From silly, to dangerous: the “causal model” network for the Afghan conflict

…or downright spoofs of the real thing…

Lest we think only journalist do
things with marginal scientific
/ information value….many
(most?) published network
images are information thin.
Such images often provide
extremely little information;
and the information one can
derive from the image is
often wrongly-weighted.
Our challenge today is two-fold:
a) What is it about visual
representations that seem so
important to network
studies?
b) How do we do it well?
Science, Art or Craft?

The historic reliance on imagery is clear in Moreno’s work:
"If we ever get to the point of charting a whole city or a whole nation,
we would have … a picture of a vast solar system of intangible
structures, powerfully influencing conduct, as gravitation does in
space. Such an invisible structure underlies society and has its
influence in determining the conduct of society as a whole."
J.L. Moreno, New York Times, April 13, 1933
We literally make the invisible visible. Part of the captivation of network science
is the ability to see into a world that is otherwise extremely difficult to wrap our
heads around.
Lessons from history?

While the history is deeply rooted in visual analysis, why bother? If we have
good metrics, why not use them instead?
Why Visualize Network at all?
Insights from scatter plots
X y1 y2 y3
4 4.26 3.1 5.39
5 5.68 4.74 5.73
6 7.24 6.13 6.08
7 4.82 7.26 6.42
8 6.95 8.14 6.77
9 8.81 8.77 7.11
10 8.04 9.14 7.46
11 8.33 9.26 7.81
12 10.84 9.13 8.15
13 7.58 8.74 12.74
14 9.96 8.1 8.84
N=11
Mean of Y = 7.5
Regression Equation: Y = 3 + .5(X)
SE of slope estimate: 0.118, T=4.24
Sum of Squares (X-X): 110
Regression SS: 27.5
Correlation Coeff: 0.82
These 3 series seem very similar, when
viewed statistically:

0
5
10
15
0 5 10 15
0
5
10
15
0 5 10 15
And given these
statistics, we expect
a relation something
like this – a strong
correlation with
“random” error.

0
5
10
15
0 5 10 15
..but this would also
fit…

0
5
10
15
0 5 10 15
…or this…
Or many more.

Visualization allows you to see the relations among elements “in the whole” – a
complete macro-vision of your data in ways that summary statistics cannot.
This is largely because a good summary statistic captures a single dimension,
while visualization allows us to layer dimensionality and relations among them.
0
5
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0 5 10 15
0
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15
0 5 10 15
0
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15
0 5 10 15

Permuted View
0
1
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6
7
8
9
10
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14
15
12 6 0 112 1 13 7 4 3 15 10 14 9 58
Technically, all the information is retained - one could reconstruct the data
pairs from both images – but the re-ordered panel provides no additional
information.
But consider changing a key assumption of the scatter-plot: the scaled ordering
of the axes.
Standard View
0
1
2
3
4
5
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0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Original White & Harary, 2001
The exact same data, presented in press in distinct ways. We’d never see
this with a scatter plot.
Kolaczyk, Eric D., Chua, David B.,
Barthélemy, Marc (2009)
3 representations of the same data

Scatter plots are good models
for network imagery:
•Multiple dimensions
•Layered information
•Global patterns with
local detail
•Shape matters
Fails as a model in a key
respect: The coordinate space
is rigid.
The reason to visualize is that
we discover elements we
didn’t already know, and can
communicate it effectively.
Gapminder

Benefits to network graphics
• Make visible the invisible
 Give a sense of reality to unobserved features
 Can be truly beautiful (when well done), capturing audience imaginations
 Can communicate complex features quickly
• Provide multi-dimensional insights into setting processes
 Metrics capture a single dimension
 We care about the shape of related entities
 Help us contextualize and make sense of the metrics we calculate
• Help us think by organizing, arranging and abstracting generals from particulars
 Networks are already massive abstractions – removing qualitative micro-
detail to capture interconnectivity
 ..but we often need to abstract further to identify elements we care about.
Problem summary

Why are network visualizations difficult? Too much information
•Network Specific graphic problems:
•Model for social space
•Resolution (local or global)
•Multiple relations
•Dynamics
•Density
•Node-level attributes
•Edge-level attributes
•Hierarchical ordering
•Diffusion Potential
•Exploration or communication
Communication Challenges in Network Visualization
Types of problems
Visualization
Strategy
Knowledge
problem
Data
Fidelity
There is a set of basic tradeoffs made with every visualization between data, the
research problem, and the final image, which can challenge our basic instincts
as scientists, since we may have to make stuff up or throw away data.

These problems feed an entire field of graph-visualization heuristics; guides to tell
computers how “best” to arrange points, which focus on:
• Even node distribution
• Consistent edge lengths
• Avoid line crossing
• Emphasize symmetry
• Maximize edge-edge angles
• Avoid lines passing over nodes
• Avoid node overlaps
• And many many more…
Auto layouts have two conflicting problems to solve:
(a) finding a good layout and
(b) finding it quickly.
What makes a good visualization?
Solutions

Unlike a scatter-plot, the default layout styles of most off-the-shelf programs will lead to
very different layouts:

The simplest answer is that an image should clearly communicate something that we
would have difficulty knowing any other way:
This includes:
Information & Communication:
• Helping build intuition about the social process generating the network
• Succinctly capturing high-dimensional properties of the network
• Being worth the space– the information content of the image needs to reward
deeper inspection
• Beauty – powerful graphs are mesmerizing
What makes a good (data) visualization?

The simplest answer is that an image should clearly communicate something that we
would have difficulty knowing any other way:
This includes:
Science:
• Ability to replicate results – same data should produce same picture
• Quantification – most features evident from a graph should be translatable to
a measurement of the graph (though this may not be initially evident)
• Theory-relevant: either gives us something new to theorize about or is useful
as a theory-building device itself.
This probably implies a move toward problem-specific families of visualizations.
What makes a good (scientific) visualization?

So what distinguishes a scientifically effective visualization?
•Basic quantitative visualization craft: (“style” or “rhetoric”)
AfterBefore
Communication Challenges in Network Visualization
Types of problems

Visualization
Strategy
Knowledge
problem
Data
Fidelity
Visualization as craft: My instinct is that hard-and-fast rules will be difficult to
find, craft production is thus a better model than either art (too expressive) or
technical drawing (too rigid).
Let’s work through some exemplars and see how they balanced these trades
Unlike a scatter-plot, the default layout styles of most off-the-shelf programs will
lead to very different layouts:

Network visualization helps build intuition, but you have to keep the drawing
heuristic. Here we show the same graphs with two different techniques:
Tree-Based layouts
Most effective for very sparse,
regular graphs. Very useful
when relations are strongly
directed, such as organization
charts, cluster tress or internet
connections.
“Force” layouts
Most effective with graphs that have a strong
community structure (clustering, etc). Provides a very
clear correspondence between social distance and
plotted distance
Two images of the same network
(good) (Fair - poor)
Basic Layout Heuristics

Tree-Based layouts Spring embedder layouts
Two layouts of the same network
(poor)
(good)
“good” = high correlation between spatial distance and
network distance

Fixed Coordinate Layouts
Fit: 0.528 Fit: .682

Fit=0.57Fit=0.26

Chord diagrams
are the network
equivalent of pie
charts

Use maps judiciously
Does this network map of Facebook tell us anything more than population density?

Use maps judiciously
Hear, goal was to show that network distance spanned vast geographic distance

Levels of distortion?
Shrink each cluster to accent separation
Fit=0.75
Fit=0.81

Fit=0.81
Center fisheye on dense
cluster
Fit=0.74

Secondary style elements
Some seemingly innocuous features can shape the effect of network diagrams
Use curves sparingly…they are usually useless – just extra ink – it’s
a hallmark of the default Gephi style...and in Gephi is used to signal
direction (out-ties curve to the left)…but else doesn’t add much.

3d is rarely useful…almost never in 2d presentations, sometimes
interactively

Based on work supported by R21-HD072810 (NICHD, Moody PI), R01 HD068523-01 (NICHD, Moody PI), R01 DA012831-05 (NIDA Morris, Martina PI),
Small multiples?

C:45%, B: 8.5%
Network Diffusion & Peer Influence
A closer look at emerging connectivity

C:83%, B: 36%

C:99%, B: 86%

Use color & size to reinforce positional elements
Node shapes are almost impossible to discern

Static, Dynamic & Interactive
Lots of new tools for interactive network visualization. Consider:
http://bl.ocks.org/eyaler/10586116
https://kieranhealy.org/philcites/
https://graphcommons.com/graphs/ee4a43a2-3189-4f82-879c-960344332ea6
Trump
Philosophy

SVG: Fixed
layout, but with
embedded info
http://www.soc.duke.edu/~jmoody77/scimaps/DukePhdComm/comm2.htm

The scientists first rule is to never
interfere with data – but this is
probably exactly what is needed
for (social?) network science.
Consider as a good example, Ken
Frank’s drawing program:
The “raw” network is distorted by
emphasizing within-group ties.
This is then highlighted by edge-
patterns (solid or dotted) and
group boundaries.
Guiding Ideas:
Build theory into the visualization
Group-weighted MDS

The scientists first rule is to never
interfere with data – but this is
probably exactly what is needed
for (social?) network science.
Or the dynamic visualizations of
McFarland’s school classrooms.
Source: Moody, James, Daniel A. McFarland and Skye Bender-DeMoll (2005) "Dynamic Network Visualization: Methods for Meaning with Longitudinal Network
Movies” American Journal of Sociology 110:1206-1241
Black ties: Teaching relevant communication
Blue ties: Positive social communications
Red ties: Negative social communication
Guiding Ideas:

Source: Bender-deMoll & McFarland “The Art and Science of Dynamic Network Visualization” JoSS 2006
The same data produce different impressions if you change the observation window.
Guiding Ideas:

The scientists second rule has to be to look for regularity and exploit that for
theory. Consider as a good example, Harrison White’s Kinship model:
Guiding Ideas:

The scientists second rule has to be to look for regularity and exploit that for
theory. Consider as a good example, Harrison White’s Kinship model:
A powerful reduction of complexity; but at the cost of a particular perspective: Mom =
Father’s Wife, for example.
Guiding Ideas:

Abstraction
helps –
consider larger
networks
Basic Problem 1: Density/Scale

2009 Social Science Journal co-citation similarity

2009 Physical Science Journal co-citation similarity

Borrett, Stuart R., James Moody & Achim Edelmann. 2014. “The Rise of Network Ecology: Maps of the topic diversity and scientific
collaboration” Ecological Modeling (DOI: 10.1016/j.ecolmodel.2014.02.019)
Network Ecology Topic Map

http://www.soc.duke.edu/~jmoody77/scimaps/DukePhdComm/comm2.htm

Abstraction
helps –
consider dense
networks
Co-voting similarity, 109th senate

Abstraction
helps –
consider dense
networks –
Co-voting similarity, 109th senate
See also: https://bost.ocks.org/mike/miserables/

The traditional network diffusion image
is the logistic curve. Consider
Coleman, Katz and Menzel (1957):
These curves count the cumulative
number of “adopters” by time, but
don’t express much about network
structure, because they aggregate
across all transmissions.
That is, they show an aggregate
outcome without really identifying
a social process.
Basic Problem 2: Spread over a dynamic network

An alternative is to think of a network trace as the likely number reached from any given
node, where “likely” is determined either by an edge transmission p(transfer|dist) or
simple distance (geodesic), and follow each starting node.
Trace Curves:
Number reachable at
each step
The collection of curves is
useful, to either compare to
a null hypothesis or to
contextualize an observed
epidemic. Curves are
simple to use, as we have
good statistical measures of
their shape.
But they are still one-step
removed from the network
itself, so how might we
incorporate this information
into the network?

But is hard when the graph is
not simple.
How might we capture the
relevant aspects of diffusion in
a network of >10,000 nodes?
Non-adopter
Source
If your goal is to map an observed transmission process across a fixed network,
node coloring can be effective.

Start with Context: Next a snapshot of a single day (limited to time-relevant)

Space-Based layout
of the transmission
flow; shows diffusion
penetrates the full
space, but little
else…
Start with Context: Now follow only the diffusion paths

Tree Based
Layout.
Since concurrency
is an edge
property, we color
the edges by the
concurrency status
of the tie…

Tree Based
Layout.
..but since the path
carries the
infection, we
highlight the
cumulative effect
of concurrency by
noting any place
where a
transmission would
have been
impossible were it
not for an earlier
concurrent edge.
This is one way to
deal with the
importance of
network dynamics.

An alternative
version, here
including non-
transmission
edges amongst the
transmission set.

Dynamics complicate the standard point-and-line representation, since you cannot
really follow all “possible” paths:
Basic Problem 3: Display Dynamic Networks?

Temporal projections of “net-time”
Time-Space graph representations
“Stack” a dynamic network in time,
compiling all “node-time” and “edge-
time” events (similar to an event-history
compilation of individual level data).
Consider an example:
a) Repeat contemporary ties
at each time observation,
linked by relational edges
as they happen.
b) Between time slices, link
nodes to later selves
“identity” edges
Basic Problem 3: Display Dynamic Networks?

Example that combines many: Political Polarization
Consider again our senate voting network:
Network is
simultaneously dense,
(since every pair has
some score) and
dynamic, as the
network evolves over
time.

Network is dense, since
every cell has some
score and dynamic the
pattern changes over
time.
Example that combines many: Political Polarization

Political Polarization
every cell has some
time.
One problem is that
many nodes are
structurally equivalent,
generating “duplicate”
information.

every cell has some
time.
Color by structural
equivalence…

every cell has some
time.
Adjust position to
collapse SE positions.

every cell has some
time.
And then adjust color,
line width, etc. for
clarity.
While we’ve gone some
distance with identifying
relevant information
from the mass, how do
we account for time?

The extent of political polarization has been increasing recently:
Party polarization in Congress: a social networks approach,
A. Waugh, L. Pei, J. H. Fowler, P. J. Mucha and M. A. Porter,

Movie is swamped by global density. So let’s
combine a time-space projection with the block
model.

Polarization
 Time 

Conclusions: Developing a visual language of networks
The simplicity of Moreno’s
sociograms was balanced
against a determined
consistency in
presentation style that
allowed one to compare
across settings.
The aim of solid scientific
visualization should be to
(re-) develop such
conventions.

“Nouns” are the easy --
identifying symbols to
represent known node/edge
types should be easy to do.
Shape, color, size-for-
magnitude and usually be
made pretty intuitive.
The tradeoff is clutter; use
shapes, in particularly, very
sparingly.

“Style” is always evident; we
can (almost) as easily
recognize the signature of a
particular approach as one
can the voice of an author.
This is both a characteristic
of authors and the programs
the use; but is typically done
without reflection.
A review of elements
suggests some simple
features to examine for style.
For my eye, for example,
most graphs use lines that
are too thick and colors that
are too harsh.

The real challenge is to identify the
active grammar underlying a
language of networks. We’re
looking for implied rules that link
visual representations to social
characteristics. For example:
proximity-as-social-distance.
The key value of a grammar, is that
dictionaries (or “pattern books”)
collapse under the weight of
observed diversity, while grammars
admit many new utterances.
The current body of graph-heuristics
are a place to start for this grammar
-- they provide aesthetic “parts of
speech” – but not style.

Conclusions
We are not there yet, nor are we usually “at our best” – thoughtless
application of canned package visualizations often create goopy messes
that convey little substantive information.
The solution is thoughtful application of a well-honed graphical style – the
classic elements laid out by Tufte over 20 years ago for statistical
visualization –tailored to the theoretical challenges of networks.

15 Network Visualization and Communities

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