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Visualization

MGT 780 SPRING 2022

STEVE BORGATTI

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15 FEB

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Agenda

Ordination
Graph layout algorithms
Using Netdraw
Inducing hypotheses

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Problem statement

Lay out nodes in a 2-dim representation in such a way that:

communicates structure of network

including features of nodes such as centrality

facilitates drawing inferences/hypothesizing about the network

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Campnet

Week 3 of a summer course

Nodes colored by gender

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Four basic approaches

Scaling/ordination/spectral analysis

Multidimensional scaling, Principal components, Correspondence analysis
Singular value decomposition (SVD); eigenvectors of laplacians

Graph layout algorithms (GLAs)

Specifically designed for graphs
Often borrow from physical metaphors such as balls connected by springs

Property-preserving optimization algorithms

Special purpose algorithms designed to reveal specific graph properties
E.g., put more central people in the middle

Scatterplots using node attributes as axes

E.g., x-axis is age, y-axis is status

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Scaling & Ordination

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MDS approach

Data driving distances between US cities

Objective: place points on map such that distances in map correspond as well as possible to distances in input matrix

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	BOSTON	NY	DC	MIAMI	CHICAGO	SEATTLE	SF	LA	DENVER
BOSTON	0	206	429	1504	963	2976	3095	2979	1949
NY	206	0	233	1308	802	2815	2934	2786	1771
DC	429	233	0	1075	671	2684	2799	2631	1616
MIAMI	1504	1308	1075	0	1329	3273	3053	2687	2037
CHICAGO	963	802	671	1329	0	2013	2142	2054	996
SEATTLE	2976	2815	2684	3273	2013	0	808	1131	1307
SF	3095	2934	2799	3053	2142	808	0	379	1235
LA	2979	2786	2631	2687	2054	1131	379	0	1059
DENVER	1949	1771	1616	2037	996	1307	1235	1059	0

->dsp cities

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Multidimensional scaling (MDS)

Metric MDS

Linear relationship between input proximities and map distances

Non-metric MDS

Monotonic relationship: closest pair in data should be closest pair in map, same with 2^nd closest, and so on

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BOSTON

NY

DC

MIAMI

CHICAGO

SEATTLE

SF

LA

DENVER

Tools|Scaling|MDS|non-metric ~cities

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MDS on network

Steps

Symmetrize the data
Compute geodesic �distances

Or alters in common

Run MDS

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

HO BR CA PA PA JE PA AN MI BI LE DO JO HA GE ST BE RU

LL AZ RO M T NN UL N CH LL E N HN RR RY EV RT SS

Y EY L IE IN AE Y E

E L

-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --

1 HOLLY 0 4 2 1 1 2 2 2 1 2 4 1 3 1 2 3 4 3

2 BRAZEY 4 0 5 5 5 6 4 5 3 4 1 4 3 4 2 1 1 2

3 CAROL 2 5 0 1 1 2 1 2 3 4 5 3 2 3 3 4 4 3

4 PAM 1 5 1 0 2 1 1 1 2 3 5 2 2 2 3 4 4 3

5 PAT 1 5 1 2 0 1 1 2 2 3 5 2 2 2 3 4 4 3

6 JENNIE 2 6 2 1 1 0 2 1 3 4 6 3 3 3 4 5 5 4

7 PAULINE 2 4 1 1 1 2 0 1 3 4 4 3 1 3 2 3 3 2

8 ANN 2 5 2 1 2 1 1 0 3 4 5 3 2 3 3 4 4 3

9 MICHAEL 1 3 3 2 2 3 3 3 0 1 3 1 2 1 1 2 3 2

10 BILL 2 4 4 3 3 4 4 4 1 0 4 1 3 1 2 3 4 3

11 LEE 4 1 5 5 5 6 4 5 3 4 0 4 3 4 2 1 1 2

12 DON 1 4 3 2 2 3 3 3 1 1 4 0 3 1 2 3 4 3

13 JOHN 3 3 2 2 2 3 1 2 2 3 3 3 0 3 1 2 2 1

14 HARRY 1 4 3 2 2 3 3 3 1 1 4 1 3 0 2 3 4 3

15 GERY 2 2 3 3 3 4 2 3 1 2 2 2 1 2 0 1 2 1

16 STEVE 3 1 4 4 4 5 3 4 2 3 1 3 2 3 1 0 1 1

17 BERT 4 1 4 4 4 5 3 4 3 4 1 4 2 4 2 1 0 1

18 RUSS 3 2 3 3 3 4 2 3 2 3 2 3 1 3 1 1 1 0

Geodesic distance of symmetrized campnet dataset

->csym = symmet(campnet)

->geo = geodesic(csym)

Tools|Scaling|MDS|nonmetric ~geo

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MDS results

Geodesic distances of symmetrized campnet dataset
Non-metric MDS

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HOLLY

BRAZEY

CAROL

PAM

PAT

JENNIE

PAULINE

ANN

MICHAEL

BILL

LEE

DON

JOHN

HARRY

GERY

STEVE

BERT

RUSS

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MDS with network ties drawn on top

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In netdraw, open campnet dataset, then import MDS coordinates

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Friends in common

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->csym = symmet(campnet)

Method = 1

Missings = 0

->f = fic(csym)

->draw campnet

Rendered by printing to pdf

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Saving images from netdraw

Standard quality

In netdraw, press ctrl-C and copy to clipboard
Paste into word or ppt

Publication quality

In NetDraw, save as Metafile

Import into powerpoint and edit as need

In NetDraw, print to pdf

Copy and paste

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Graph layout algorithms

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Force-directed layouts

Draw analogy with physical systems such as springs or electrical forces
Attractive force can be modeled as springs between connected nodes: force increases with distance

Can also be gravity model, magnetic model, etc.

Optionally can add simultaneous repulsive force like those of electrically charged particles based on Coulomb's law
Kamada-Kawai uses only spring-based attractive force where ideal spring length is geodesic distance between nodes

Results resemble metric MDS

Fructerman-Reingold uses attractive plus repulsive

This tends to make length of drawn lines be somewhat homogeneous

Many variations

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None of these are always better than the others – depends on the network

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NetDraw

Netdraw uses multidimensional scaling as a base, (i.e., matching physical distance to geodesic distance) but then adds an optimization layer that adds additional aesthetic criteria
Results should maximize three criteria

correspondence between physical distance on screen with geodesic distance between nodes
Avoid nodes being displayed on top of each other
Try to make each line (representing a tie) approximately the same length

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Netdraw layout of campnet

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Cf. MDS with network ties added

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In netdraw, open campnet dataset, then import MDS coordinates

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Directly representing graph properties

E.g., radial graphs in which equally central nodes are placed equally closed to center

Can be any node attribute, such as age

Given that constraint, place nodes �tied to each other near each other
Drawn using

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https://visone.info/html/download.html

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Attribute-based scatterplots

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Socio-demographic (or “Blau”) space

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Attribute-based approach – “Blau space”

Network data

Krack-high-tec (21 managers)
Who seeks advice from whom (lines between nodes)

Attribute data

High-tec-attributes
Age of each person (x-axis)
Rank in the organization (y-axis)
Teams (reporting to same supervisor)

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age

rank

Try x=tenure, y=level, tie = reports to

Netdraw: Layouts|Attribs as coordinates

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Network: Krack-high-tec

Attribs: High-tec-attributes

Layout: Try x=tenure, y=level, tie = reports to

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Three broad approaches

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Attribute-based scatterplot	Scaling / Ordination	Graph Layout Algorithms
E.g., x-axis corresponds to age, y-axis corresponds to status	E.g., multidimensional scaling (MDS), principal components, correspondence analysis	Force-directed/spring embedders E.g., Kamada-Kuwai, Rheingold-Fruchterman
Axes are meaningful	Axes not meaningful	Axes not meaningful
Network data can be 1/0	Network data must be valued (or converted into valued data)	Network data can be 1/0
Distances in space are meaningful	Distances meaningful and correspond to input values	Distances loosely related to geodesic distance
Unique solutions up to rotation	Unique solutions up to rotation	Many equally valid solutions Careful not to over-interpret
Cannot move nodes by hand	Cannot move nodes by hand	Can move nodes by hand

->x = makeclique(10)

->draw x

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2-mode data

Two approaches
1-mode projection

Convert the data to 1-mode by constructing person-person network or event-event network, then drawing these separately

2-mode bipartite graph

Draw a single network that connects row-nodes to column-nodes
No ties will exist within modes

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X

Women by events

XX’

Women by women

X’X

Event by Event

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Bipartite representation

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->draw davis

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Visualizing tie change

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Visualizing �tie-level changes

Side-by-side display

Static representation
Nodes don’t change positions

Requires small networks, few time periods
Works well in print

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SAMPSON Liking T2

SAMPSON Liking T3

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Newcomb data over time

Node positions change over time
But beware the Brownian motion of the graph layout algorithm

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Newcomb data over time

Changes in tie strength (and centrality) over time
Node positions fixed

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(animation)

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EIES data

Collected by Freeman and Freeman in 1978

32 researchers who participated in an early study on the effects of electronic information exchange, a precursor of email communication

4 different slopes of movement over time

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https://sites.google.com/site/ucinetsoftware/datasets/freemanseiesdata

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EIES data

After identifying 4 groups with similar slopes the nodes are colored by group
Movement of each group is made sequential so we can see pattern
Analysis

Top left -> INSNA
Bottom coalesce -> socy
Fall down 🡪 left the field
No move 🡪 didn’t play

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Uses of motion as design element

Nodes maintain fixed positions, ties appear and disappear

Ignores changes in centrality etc.
Traces help maintain memory but this is still issue

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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.

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simpler side by side displays still have advantage of comparability

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Time 1

Time 2

Time 3

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US Supreme Court – Rehnquist years

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Supreme Court Data

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How often judges were together on the majority across all 10 years

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How often judges were together on the majority across all 10 years

Supreme Court Data�-- all years, all judges

Stacked Correspondence analysis

Supreme Court Data

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Supreme Court Data�-- all years, selected judges

Stacked Correspondence analysis

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Week_2-HOLLY

Week_2-BRAZEY

Week_2-CAROL

Week_2-PAM

Week_2-PAT

Week_2-JENNIE

Week_2-PAULINE

Week_2-ANN

Week_2-MICHAEL

Week_2-BILL

Week_2-LEE

Week_2-DON

Week_2-JOHN

Week_2-HARRY

Week_2-GERY

Week_2-STEVE

Week_2-BERT

Week_2-RUSS

Week_3-HOLLY

Week_3-BRAZEY

Week_3-CAROL

Week_3-PAM

Week_3-PAT

Week_3-JENNIE

Week_3-PAULINE

Week_3-ANN

Week_3-MICHAEL

Week_3-BILL

Week_3-LEE

Week_3-DON

Week_3-JOHN

Week_3-HARRY

Week_3-GERY

Week_3-STEVE

Week_3-BERT

Week_3-RUSS

Generate this in netdraw with camp92 data

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A different take on visualizing change

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Multi-Relational Approach

Each time point is a slice of a multidimensional actor-by-actor-by-time matrix

Just like multiple relations on the same nodes

Sample datasets

SAMPSON dataset includes who likes whom at points in time

SAMPLK1 SAMPLK2 SAMPLK3

NEWFRAT dataset includes weekly esteem rankings for about 13 weeks

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Correlations among matrices – Sampson data

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id	SampLK1	SampLK2	SampLK3
ROMUALD-BONAVENTURE	0	1	1
ROMUALD-AMBROSE	0	0	1
ROMUALD-BERTHOLD	0	0	0
ROMUALD-PETER	3	3	3
ROMUALD-LOUIS	0	0	0
ROMUALD-VICTOR	1	0	0
ROMUALD-WINFRID	0	0	0
ROMUALD-JOHN_BOSCO	0	0	0
ROMUALD-GREGORY	0	0	0
ROMUALD-HUGH	2	0	0
ROMUALD-BONIFACE	0	0	0
ROMUALD-MARK	0	0	0
ROMUALD-ALBERT	0	0	0
ROMUALD-AMAND	0	2	2
ROMUALD-BASIL	0	0	0
ROMUALD-ELIAS	0	0	0
ROMUALD-SIMPLICIUS	0	0	0
BONAVENTURE-ROMUALD	0	0	0
BONAVENTURE-AMBROSE	0	0	1
BONAVENTURE-BERTHOLD	0	0	0

SAMPLK1 SAMPLK2 SAMPLK3

--------- --------- ---------

SAMPLK1 1.000 0.645 0.638

SAMPLK2 0.645 1.000 0.768

SAMPLK3 0.638 0.768 1.000

After T1, social structure changes little

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Correlations among matrices (NEWFRAT dataset)

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	0	1	2	3	4	5	6	7	8	10	11	12	13	14	15
0	1.00	0.65	0.60	0.55	0.46	0.40	0.36	0.32	0.36	0.35	0.36	0.34	0.30	0.33	0.31
1	0.65	1.00	0.81	0.74	0.60	0.59	0.53	0.49	0.51	0.49	0.49	0.50	0.50	0.51	0.45
2	0.60	0.81	1.00	0.85	0.75	0.69	0.67	0.60	0.63	0.61	0.61	0.62	0.61	0.62	0.58
3	0.55	0.74	0.85	1.00	0.84	0.79	0.74	0.69	0.70	0.70	0.70	0.69	0.68	0.70	0.65
4	0.46	0.60	0.75	0.84	1.00	0.88	0.84	0.81	0.78	0.77	0.79	0.74	0.75	0.75	0.72
5	0.40	0.59	0.69	0.79	0.88	1.00	0.91	0.88	0.82	0.82	0.82	0.79	0.80	0.80	0.78
6	0.36	0.53	0.67	0.74	0.84	0.91	1.00	0.92	0.88	0.86	0.84	0.81	0.80	0.81	0.80
7	0.32	0.49	0.60	0.69	0.81	0.88	0.92	1.00	0.90	0.87	0.86	0.82	0.81	0.82	0.80
8	0.36	0.51	0.63	0.70	0.78	0.82	0.88	0.90	1.00	0.89	0.85	0.83	0.81	0.81	0.80
10	0.35	0.49	0.61	0.70	0.77	0.82	0.86	0.87	0.89	1.00	0.89	0.87	0.84	0.84	0.85
11	0.36	0.49	0.61	0.70	0.79	0.82	0.84	0.86	0.85	0.89	1.00	0.89	0.86	0.85	0.84
12	0.34	0.50	0.62	0.69	0.74	0.79	0.81	0.82	0.83	0.87	0.89	1.00	0.92	0.88	0.83
13	0.30	0.50	0.61	0.68	0.75	0.80	0.80	0.81	0.81	0.84	0.86	0.92	1.00	0.91	0.85
14	0.33	0.51	0.62	0.70	0.75	0.80	0.81	0.82	0.81	0.84	0.85	0.88	0.91	1.00	0.90
15	0.31	0.45	0.58	0.65	0.72	0.78	0.80	0.80	0.80	0.85	0.84	0.83	0.85	0.90	1.00

Decline away from T1

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Correlations among matrices�(NEWFRAT dataset)

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Correlations drop off as time difference increases
Correlations drop faster at the early time points

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Correlations among matrices (NEWFRAT dataset)

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Multidimensional scaling representation of correlations among time periods

-- arrows added to indicate flow of time

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Correlations among matrices�(NEWFRAT dataset)

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NEWC1

NEWC2

NEWC3

NEWC4

NEWC5

NEWC6

NEWC7

NEWC8

NEWC10

NEWC11

NEWC12

NEWC13

NEWC14

NEWC15

Network representation. A line is drawn between two time periods if the correlation between them is greater than 0.8

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Change in 2-mode data

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Director: Almodovar

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-2.00

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ALFernandez

AVGomez

AfBeato

AgAlcazar

AgAlmodovar

AlaskaPegam

AlIglesias

AlAngulo

AlCasanova

AlMayo

AnLizaran

AnAlonso

AnSantana

AALopez

AnMolina

ASJuan

AnBanderas

AnLlorens

AsSerna

AuGirard

BeBonezi

BiAndersen

CaPena

CaElias

CaMaura

CeRoth

ChLampreave

CoGregori

CrMarcos

CrPascual

EnMorricone

EnPosner

EsGarcia

EsRambal

EuPoncela

EvCobo

EvSilva

FeRotaeta

FeAtkine

FFGomez

FeGuillen

FeVivanco

FrNeri

FrFemenias

GoSuarez

GuMontesinos

HeLine

ImArias

JaBardem

JeFerrero

JLAlcaine

JoSalcedo

JoSancho

JuEchanove

JuMArtinez

JuSerrano

KiManver

LiRabal

LiCanalejas

LoCardona

LoLeon

LuBriales

LuCalvo

LuHostalot

MAPCAmpos

MaZarzo

MaVargas

MaVelasco

MaCarillo

maBarranco

MaParedes

MaMuro

MaOWisiedo

MiRuben

MiGomez

MiMolina

MGRomero

NaMartinez

OfAngelica

OGAlaska

PaPoch

PaDelgado

PeAlmodovar

PeCruz

PeCoromina

PeCoyote

Pibardem

RMSarda

RdPalma

RySakamoto

SaLajusticia

TaVillalba

VeForque

ViAbril

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Correspondence analysis

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Director: 2

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JLGarci

JGCaba

LBosch

LMDelgado

VPanero

HValcarcel

RPCubero

MBalboa

MGSinde

FFGomez

RAlonso

CGCuervo

AGonzalez

CCruz

ARozas

FGuillen

FGuillenCuervo

FPiquer

MMassip

JCaride

JCarideFAlgora

ECohen

JCalot

CGConde

AValero

NRodriguez

JLMerino

MSampietro

BSantana

EAsensi

MEFlores

NGarci

MRMartinez

LdOrduna

DAguado

ABSanchez

RVillascastin

ACarbonell

ECerezo

FFaltoyano

ALarranaga

VMataix

DPenalver

MLPonte

MVerdu

CGomez

ALanda

CJimenez

OLorente

RTebar

MRojas

MMorales

JGluck

CPorter

JPachelbel

ALlorente

JPuente

TGimpera

VVera

EHoyo

PSerrador

MLorenzo

PHoyo

SAmon

JCueto

SCanada

JMFernandez

PInfanzon

JCarballino

AMarsillach

MCasanova

JBodalo

EPaso

VValverde

PCalot

ESuarez

RHernandez

YRios

DSalcedo

MRellan

RdPenagos

AFernandez

JMCervino

MMerchante

JYepes

FBilbao

AFerrandis

AGonzalez

MMFernandez

MTejada

MRellan

RFraile

FVidal

MBlasco

MoWisiedo

EFornet

CLarranaga

APicazo

ICGutierrez

FArribas

JSacristan

FFaltoyano

GCobos

CRodriguez

AGamero

STortosa

SAndreu

HAlterio

CCadenas

Berta

MFraguas

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Director 2

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