Borgatti dagstuhl 2008 presentation 2c

some notes on graph drawing in
the social sciences
steve borgatti
LINKS center, U of Kentucky
http://linkscenter.org

(c) 2008 Stephen P. Borgatti. All rights reserved.

informal review of three areas
• Three areas that routinely use relational
concepts/data
– Multivariate/correlational analysis
– Cultural domain analysis (CDA)
– Social network analysis
• I will briefly review each area
– Bottom line: Graph drawing capabilities
underutilized
– Note: how many social scientists are here today?


MULTIVARIATE CORRELATION
ANALYSIS
(c) 2008 Stephen P. Borgatti. All rights
reserved.

Robinson and Kraatz and Rousseau. 1993. Changing oblgations and the psychological contract. AMJ

factor Loadings
0.65 Violation
0.6
0.55
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1 Development Training
Development Support
Support
0.05 Training
MinimumStay JobSecurity
Factor 2

0
-0.05 NoCompetitorSupport Advancement
-0.1 JobSecurity
Transfers
-0.15 Notice Transfers Advancement
ProprietaryProtection NoCompetitorSupport MeritPay
-0.2 Notice HighPay
-0.25 ProprietaryProtectionMinimumStay
-0.3
MeritPay
-0.35 HighPay
-0.4 Overtime
-0.45
-0.5 Loyalty
Overtime
-0.55 ExtraroleBehavior
-0.6
-0.65 ExtraroleBehavior Loyalty
-0.7
-0.75
-0.8
-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6

Factor 1

taxonomic display of an ultrametric distance
derived via hierarchical clustering


ProprietaryProtection1
Development1
Violation2 Alternative approach: graph representation
Training2 significant correlations
Training1
NoCompetitorSupp
Development2
JobSecurity2 NoCompetitorSupport2
Support1
ProprietaryProtection2
JobSecurity1 MinimumStay2
Transfers2

MinimumStay1 Advancement1
Loyalty2
Support2 Notice2

HighPay1
Transfers1
Overtime2
Loyalty1
ExtraroleBehavior1
HighPay2 ExtraroleBehavior2

Notice1
Overtime1

MeritPay1 MeritPay2
Advancement2

significant correlations


correlations across NBA basketball
statistics by year
1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985
1975 1 0.928279 0.927808 0.928896 0.838372 0.783556 0.206393 -0.32018 0.536656 -0.5205 -0.42529
1976 0.928279 1 0.984528 0.958696 0.741861 0.600266 0.122462 -0.35468 0.34183 -0.56261 -0.48742
1977 0.927808 0.984528 1 0.970976 0.712434 0.620917 0.138264 -0.43971 0.316522 -0.6341 -0.57314
1978 0.928896 0.958696 0.970976 1 0.67141 0.679082 -0.04106 -0.54299 0.239347 -0.70144 -0.60623
1979 0.838372 0.741861 0.712434 0.67141 1 0.795042 0.570848 0.206046 0.847329 -0.03545 0.079793
1980 0.783556 0.600266 0.620917 0.679082 0.795042 1 0.204282 -0.11971 0.568092 -0.38493 -0.23208
1981 0.206393 0.122462 0.138264 -0.04106 0.570848 0.204282 1 0.63392 0.818101 0.493733 0.442857
1982 -0.32018 -0.35468 -0.43971 -0.54299 0.206046 -0.11971 0.63392 1 0.524133 0.891949 0.892671
1983 0.536656 0.34183 0.316522 0.239347 0.847329 0.568092 0.818101 0.524133 1 0.377666 0.4359
1984 -0.5205 -0.56261 -0.6341 -0.70144 -0.03545 -0.38493 0.493733 0.891949 0.377666 1 0.975475
1985 -0.42529 -0.48742 -0.57314 -0.60623 0.079793 -0.23208 0.442857 0.892671 0.4359 0.975475 1
1986 -0.6864 -0.6194 -0.68456 -0.71887 -0.29893 -0.63231 0.206989 0.677066 0.031823 0.904912 0.866002
1987 -0.67597 -0.57798 -0.6613 -0.61884 -0.42873 -0.65514 -0.16858 0.427463 -0.2146 0.715316 0.714919
1988 -0.69299 -0.71588 -0.79897 -0.75789 -0.3393 -0.49831 -0.00088 0.63753 -0.00032 0.859792 0.873478
1989 -0.41757 -0.41191 -0.4616 -0.28054 -0.27803 -0.04923 -0.54372 0.083636 -0.3312 0.222508 0.354378
1990 -0.75627 -0.70969 -0.80302 -0.73685 -0.45177 -0.48624 -0.23059 0.557054 -0.24396 0.693496 0.727823
1991 -0.63945 -0.64977 -0.74498 -0.6365 -0.3661 -0.27912 -0.32179 0.491066 -0.21383 0.57259 0.650299
1992 -0.32965 -0.4241 -0.50457 -0.35256 -0.16175 0.135144 -0.41186 0.297327 -0.14119 0.235618 0.369358
1993 -0.79797 -0.85057 -0.9089 -0.82198 -0.52997 -0.39879 -0.25553 0.491591 -0.2573 0.618981 0.645245
1994 -0.28033 -0.46061 -0.37743 -0.25087 -0.53085 0.046788 -0.51087 -0.43987 -0.45693 -0.38011 -0.39308
1995 -0.78403 -0.76537 -0.68581 -0.79119 -0.62392 -0.6389 0.241243 0.28223 -0.26043 0.424438 0.259308
1996 -0.5761 -0.56068 -0.48055 -0.6393 -0.39881 -0.56247 0.475357 0.330645 -0.03839 0.434513 0.253553
1997 -0.16402 -0.1849 -0.04059 -0.1543 -0.31074 -0.14648 0.213941 -0.25982 -0.20245 -0.2935 -0.45213
1998 -0.21206 -0.1275 -0.00827 -0.06616 -0.57853 -0.39612 -0.22095 -0.59048 -0.58721 -0.50781 -0.67561
1999 0.054955 0.177395 0.283975 0.232268 -0.38889 -0.24898 -0.25953 -0.73364 -0.53808 -0.69069 -0.82948
2000 0.55283 0.519177 0.584801 0.605677 0.070271 0.15764 -0.25315 -0.81688 -0.11711 -0.72829 -0.76058
2001 -0.16506 -0.13719 -0.09461 -0.01211 -0.6672 -0.35674 -0.74175 -0.75262 -0.74584 -0.58994 -0.66516
2002 -0.10462 -0.25898 -0.28209 -0.10424 -0.29863 0.204661 -0.68097 -0.27067 -0.35702 -0.3069 -0.21413
2003 0.020001 0.048715 0.096185(c) 2008 Stephen P. Borgatti. All rights reserved.
0.2103 -0.46203 0.02135 -0.80212 -0.79797 -0.72376 -0.81113 -0.80978

1 2004
2003 2001
0.9
1999 1998
0.8
1994
0.7

0.6 2000 1997
0.5
2002
0.4

0.3
1995
0.2
2005
0.1 1996
1978
0 1977
1976 1989 1993
-0.1 1992
1975
-0.2
1980 1991
1990
1987
-0.3

-0.4 1988
1986
-0.5

-0.6 1981
1979 1984
-0.7
1983 1982 1985
-0.8

-0.9
-1 -0.8 -0.6
(c) 2008 Stephen P. Borgatti. All rights reserved.0.4
-0.4 -0.2 0 0.2 0.6 0.8 1

1981 1979 1980

1983

1984
1975
1982 1976

1990 1985 1977

1987 1986 1996
1978
1988
1995

1991 1993
1999
2000
2005
1998
1989
1992 1997

2004
1994

2002
(c) 2008 Stephen P. Borgatti. All rights reserved. 2003
2001

causes of Breast Cancer


Causes of Breast Cancer
ABORTIONS WILDLIFE LATECHILDREN
DIRTYWORK
ETHNICITY
IMPLANTS
EARLYMENSES
AGE

LACKHYGIENE
NOCHILDREN OBESITY
PROBPRODMILK SALVADOR CANCERHISTO
PHYSICIANS
FONDLING SMOKING
ILLEGALDRUGS
HORMONESUPPS
FAMILYHISTORY
MEXICAN
BIRTHCONTROL FIBROCYSTIC
BLOWS FATDIET
BREAST-FEEDING
NEVERBREASTFEED

ALCOHOL ANGLO
CHICANAS
LACKMEDICALATTN DIET
CHEMICALSINFOOD
RADIATION
POLLUTION
CAFFEINE JUSTHAPPENS
LARGEBREASTS

Causes of Breast Cancer
(Frequencies > 18%)
OBESITY
NOCHILDREN
AGE

LATECHILDREN FATDIET

IMPLANTS PHYSICIANSCANCERHISTORY

HORMONESUPPS

SALVADOR
PROBLEMSMILK FAMILYHISTORY

BLOWS2BREAST

CHICANAS
CHEMICALSINFOOD ANGLO
POLLUTION DIET

MEXICAN
NEVERBREASTFEED SMOKING
RADIATION

LACKMEDICALATTN BIRTHCONTROL
BREAST FONDLING

Quick summary of multivariate
visualization
• Visualization dominated by tables or principal
components / vector spaces and taxonomic
displays
• Even the simplest graph representations are a
contribution


CULTURAL DOMAIN ANALYSIS

reserved.

Perceived Similarities
• Direct ratings
– ‘How similar are “rabies” and “lupus” on a 1 to 5 scale?’
• Pilesorts
– (given cards, each with name of a fruit) “Please sort these fruits
into piles according to how similar they are …”
– For each pair of items, count proportion of respondents that
place them in same pile
• Triad tests
– ‘In each group of three below, which is the most different?’
• SHARK DOLPHIN SEAL
• DOG SEAL CAT
– Each time an item is chosen, give a point towards similarity of
the other two


Aggregated Pilesort Data
SALAMA FLAMIN WOODT RACCO
FROG NDER GO HRUSH TURKEY ROBIN BEAVER ON RABBIT
FROG 1.00 0.96 0.00 0.00 0.00 0.02 0.06 0.02 0.02
SALAMA
NDER 0.96 1.00 0.00 0.00 0.00 0.00 0.04 0.00 0.00
FLAMIN
GO 0.00 0.00 1.00 0.81 0.79 0.81 0.00 0.00 0.00
WOODT
HRUSH 0.00 0.00 0.81 1.00 0.90 0.92 0.02 0.02 0.02
TURKEY 0.00 0.00 0.79 0.90 1.00 0.87 0.02 0.02 0.02
ROBIN 0.02 0.00 0.81 0.92 0.87 1.00 0.02 0.02 0.02
BEAVER 0.06 0.04 0.00 0.02 0.02 0.02 1.00 0.62 0.65
RACCO
ON 0.02 0.00 0.00 0.02 0.02 0.02 0.62 1.00 0.71
RABBIT 0.02 0.00 0.00 0.02 0.02 0.02 0.65 0.71 1.00

Nonmetric multidimensional scaling (MDS) of
similarity matrix
TURKEY
ROBIN
WOODTHRUSH
FLAMINGO

WHALE
DOLPHIN SALAMANDER
FROG SNAKE
STARFISH

KANGAROO
ANTELOPE GORILLA
BABOON
ELK ELEPHANT
BEAVER MOOSE LION
LEOPARD
DEER
RABBIT BEAR
SQUIRREL HYENA
GROUNDHOGRACCOON COYOTE
FOX
MOUSE

Stress = 0.12

MDS of land animals only


Graph representation
A link indicates that more than 50% of respondents placed the two items in the same pile

ELEPHANT
KANGAROO

SNAKE
BABOON SALAMANDER

FROG

GORILLA

LION

LEOPARD
HYENA DOLPHIN
STARFISH

FOX WHALE
COYOTE

RACCOON
BEAR
DEER SQUIRREL
BEAVER
GROUNDHOG
ANTELOPE MOUSE WOODTHRUSH
RABBIT
ROBIN
MOOSE TURKEY
ELK
(c) 2008 Stephen P. Borgatti. All rights reserved. FLAMINGO

*B
Water off while shaving
Cut grass high Full loads in dishwasher
Plant shrubs Cold-water detergent
Mulch grass clippings Lowflow shower
Plant garden Rinse w/ cold water
Compost Short dishwasher cycles
Plant trees Water lawn in morning/evening

Close shades
Restore buildings Recyling bins Water-saving toilets
Salvation Army Turn off lights
Pick up litter Use things longer *B Air off when leave

}
Paper bags Cloth diapers
Encourage others to recycle Fans
Don’t litter Reuse towels
Organize drives for recyclables Dishwasher w/ built-in heater
Encourage recycled products Cool leftovers
Wear sweaters Insulate home
Teach kids about recycling Clothes line Weatherstrip
Save wetlands Double-pane windows Automatic timers for house temp.
Gas heat Frig. seal
Insulate heating ducts
Convection oven Dryer with moisture sensor
Copper & brass Both sides paper Clean lint filter Oven door seal
Redeem cans Use own grocery bags Freezers on top
}

Put bins in office Recylce toxic prods. Fluorescent bulbs
Buy recycled prods.
Overpackaged foods Low-watt bulbs
*A No aerosol Remove CFC in old refrig. Dishwasher w/ airdry
Reduce meat consumption Photocells
Political activities Walk or bike Furnace tune-up
Write congressperson Dolphin safe tuna Carpool Regulate thermostat
Inflate tires properly
“Save the Earth” t-shirts
Public transport Gas mileage on new car
Use ethanol Assure car runs well
*A
Join environmental groups
Teach kids about endangered species Buy Electric Car
Ride Motorcycle
Show kids by example
Teach about gains from environment
Teach kids to preserve planet
Support world population organizations
Tell others not to do bad things


U.S. Holidays

April_F Christm Columb 4th_Of
ools as us Easter Fathers Flag _July
April_Fools 0 0 0.185 0.148 0.222 0.407 0.111
Christmas 0 0 0 0.741 0.111 0.037 0.111
Columbus 0.185 0 0 0 0.222 0.444 0.296
Easter 0.148 0.741 0 0 0.148 0.037 0.148
Fathers 0.222 0.111 0.222 0.148 0 0.148 0.185
Flag 0.407 0.037 0.444 0.037 0.148 0 0.37
4th_Of_July 0.111 0.111 0.296 0.148 0.185 0.37 0


non‐metric MDS representation

Rosh_Hashanah

Kwanza
Ramadan Cinco_de_Mayo
Thanksgiving
Yom_Kippur
4th_Of_July
New_Years
April_Fools
Groundhog
Presidents
Christmas
Halloween
Columbus
Hanukkah
Passover
Memorial
Veterans
Mothers
Patriots
Fathers
Easter
Labor
Flag
t_Valentines
St_Patrick
Secretaries
MLK

(Degenerate solution)

after removing “strange” holidays
4th_Of_July
Veterans
Labor
MemorialPatriots
Flag
Yom_Kippur Thanksgiving Columbus
Presidents
Passover
MLK
Hanukkah

Easter
Christmas Secretari
St_Patrick
Groundhog
April_Fools

St_Valentines
New_Years
Halloween
Mothers
Fathers


Yom_Kippur
Hanukkah
Passover graph
Christmas representation
Easter

MLK Thanksgiving

Presidents Halloween
Veterans
Columbus New_Years
4th_Of_July
Patriots St_Valentines
Labor Flag
Memorial April_Fools

Groundhog St_Patrick
Fathers
Secretaries
Mothers

PROFIT – property fitting
Given a spatial representation, multiple
regression of a node attribute on the X
Y coordinates
‐‐ testing for perceptual dimensions

1960s paper by Michael Burton

Graph representation
• Obviously can represent personality traits as
nodes, strong similarities as links
• Dimensions such as good/bad or
active/passive are just node attributes
– Typically represented by node size or dark‐to‐light
coloration
• How to present multiple attributes at the
same time?


Contagion (Guatemala)

Susan C. Weller. 1984. Cross‐Cultural Concepts of Illness: Variation and Validation, American Anthropologist

Severity (Guatemala)


Age of the Infirm (Guatemala)


Perhaps vectors of this type could be
used in graph representations as well
• Certainly if node coordinates are obtained in
such a way that distances in the map
correspond to, say, input proximities
– Or perhaps located so as to maximize
correspondence of all node attributes to the map
vectors


Brief summary of CDA visualization
• Similar to multivariate area in that graph
representations are useful but virtually
unknown
• Notion of fitting vectors to represent gradients
along node dimensions might be useful to
apply to some graph representations


SOCIAL NETWORK ANALYSIS

reserved.

Moreno & Sociometry 1930s
Friendship Choices
Among Fourth
Graders (from
Moreno, 1934, p.
38).

Positive and Negative Choices in a Football
Moreno 1934 Team (Moreno, 1934, p. 213).

Fast‐forward 60 years ..
• Huge advances
in computing
• But small
advances in
graph
visualization (in
mainstream
social science)

Kilduff, Martin, and David Krackhardt 1994. "Bringing the Individual Back In: A
Structural Analysis of the Internal Market for Reputation in Organizations." Academy
of Management Journal, 37: 87‐108.

McGrath, Cathleen, David Krackhardt, and Jim Blythe. 2003 "Visualizing Complexity in
Networks: Seeing Both the Forest and the Trees." Connections, 25(1): 37‐47

J.H. Fowler, S. Jeon / Social Networks 30 (2008) 16–30

graph drawings for concept illustration

L. Coromina et al. / Social Networks 30 (2008) 49–59

frequency of usage of graph drawing in
organizational studies
• Examined all articles in the last 3* years in two
top journals
– Administrative Science Quarterly (*all 3 years)
– Organization Science (*2 years only)
• Of 23 empirical papers focusing on social
networks
– Only 3 had drawings of graphs
– Only 1 depicted actual data (as opposed to an
illustration of a structural idea)


in short …
• In organizational studies at least, graph
drawings are
– Rare
– Hardly different from nearly a century ago
• Few design elements
• Largely the same substantive concepts
• Of course, more use in presentations
– And even more in private exploration of data


many of the reasons are institutional
rather than technical

Print journals Inability to Legitimacy of Habit of verbal vs
permit only + switch to pictures visual thinking
simplest electronic
graphics media
Qual XOR Quant
perspective
Media Lack of
limitations & prestige of
“costs” strange
Comic book
journals
understanding of
science
‐deductive
‐quantitative


Other issues

Lack of quality tools Insufficient attention
‐ Power & ease of use to substantive issues

Imagination
& effort?

Algorithms


User Interfaces
• Netdraw
– “userly” but pathetically programmed. Fat, buggy,
quirky and inconsistent in its conception of the data
• Pajek
– Elegantly programmed and powerful, but frightening
to mainstream social scientists
• Only a command‐line interface could create more fear
• Visone
– In a way, a blend of netdraw and pajek, but almost
ascetically lean: prefers economy to convenience


Tool features

Automating Legends
• Automatically
generate
legends when
using design
elements like
color, size,
shape, etc
– Guess


Smart Labeling
NORA SYLVIA
KATHERINE
HELEN VERNE

MYRNA
KATHERINE
NORA SYLVIA

VERNE
HELEN

MYRNA
Computer science applications often ignore labels

annotating outputs
HLM output

Coding: highlighting,(c) 2008 Stephen P. Borgatti. All rights reserved.
marking-up, cutting-up, classifying, graph elements

statistics printed on chart

A

Geary’s C: 0.333
B
Significance: 0.000
D

C

E

G

F

H

I


Collapsing / expanding nodes
• Easily collapsing nodes into super nodes and
then expanding back
– Current tools handle by creating separate image
graphs Density / Average value within blocks

1 2 3
------ ------ ------
BILL 1 0.3571 0.0417 0.0625
0.8
3
HARRY
DO N
2 0.1042 0.3000 0.1667 0.1

MICHAEL
3 0.0000 0.1250 0.7500
HOLLY
0.2

PAT
0.3
GERY
2
LEE
ST EVE
0.1
JEN N IE
0.1
BRAZEY PAM

RUSS
0.0

AN N
BERT JO HN
PAULIN E 0.4
CARO L 1

convex hulls to represent categorical
node attributes
‐‐ not complex algorithmically but few offer it
Anthropac software


hyperedges
• Graphml allows for them but do any software
tools use them?


Multi‐mode data
• D

Davis, Gardner and Gardner (published in the 1941 book Deep South)


Implicit handling of modality
Davis, Gardner and Gardner OLIVIA
E2
data. Which women DOROTHY
FLORA
attended which social events.
PEARL

E1 E9
E11
MY RNA
RUTH
EVELY N

THERESA

E8
E4 LAURA
KATHERINE E10
E6

NORA E12
E3
BRENDA

E5 SY LVIA

E7 VERNE HELEN

FRANCES E14

ELEANOR
CHARLOTTE E13

reducing modality
• Current approach:
– Analysis programs provide a tool for constructing
new graph, based on number of ties in common,
then allows you to draw that graph
• E.g., if X is 2‐mode data matrix in which xij = 1 means
that woman I attended event j, then X’X gives the
number of women who co‐occurred at each pair of
events and XX’ gives the number of events in common
for each pair of women
– X’X and XX’ induce new graphs that can be visualized
• Separate drawing step from data construction step


XX’
THE CHA FRA ELE KAT DOR
EVE LAU RES BRE RLO NCE AN PEA RUT VER MY HER SYL NOR HEL OTH OLI FLO
LYN RA A NDA TTE S OR RL H NE RNA INE VIA A EN Y VIA RA
EVELYN 8 6 7 6 3 4 3 3 3 2 2 2 2 2 1 2 1 1
LAURA 6 7 6 6 3 4 4 2 3 2 1 1 2 2 2 1 0 0
THERESA 7 6 8 6 4 4 4 3 4 3 2 2 3 3 2 2 1 1
BRENDA 6 6 6 7 4 4 4 2 3 2 1 1 2 2 2 1 0 0
CHARLOTTE 3 3 4 4 4 2 2 0 2 1 0 0 1 1 1 0 0 0
FRANCES 4 4 4 4 2 4 3 2 2 1 1 1 1 1 1 1 0 0
ELEANOR 3 4 4 4 2 3 4 2 3 2 1 1 2 2 2 1 0 0
PEARL 3 2 3 2 0 2 2 3 2 2 2 2 2 2 1 2 1 1
RUTH 3 3 4 3 2 2 3 2 4 3 2 2 3 2 2 2 1 1
VERNE 2 2 3 2 1 1 2 2 3 4 3 3 4 3 3 2 1 1
MYRNA 2 1 2 1 0 1 1 2 2 3 4 4 4 3 3 2 1 1
KATHERINE 2 1 2 1 0 1 1 2 2 3 4 6 6 5 3 2 1 1
SYLVIA 2 2 3 2 1 1 2 2 3 4 4 6 7 6 4 2 1 1
NORA 2 2 3 2 1 1 2 2 2 3 3 5 6 8 4 1 2 2
HELEN 1 2 2 2 1 1 2 1 2 3 3 3 4 4 5 1 1 1
DOROTHY 2 1 2 1 0 1 1 2 2 2 2 2 2 1 1 2 1 1
OLIVIA 1 0 1 0 0 0 0 1 1 1 1 1 1 2 1 1 2 2
FLORA 1 0 1 0 0 0 0 1 1 1 1 1 1 2 1 1 2 2

X’X
E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11 E12 E13 E14
E1 3 2 3 2 3 3 2 3 1 0 0 0 0 0
E2 2 3 3 2 3 3 2 3 2 0 0 0 0 0
E3 3 3 6 4 6 5 4 5 2 0 0 0 0 0
E4 2 2 4 4 4 3 3 3 2 0 0 0 0 0
E5 3 3 6 4 8 6 6 7 3 0 0 0 0 0
E6 3 3 5 3 6 8 5 7 4 1 1 1 1 1
E7 2 2 4 3 6 5 10 8 5 3 2 4 2 2
E8 3 3 5 3 7 7 8 14 9 4 1 5 2 2
E9 1 2 2 2 3 4 5 9 12 4 3 5 3 3
E10 0 0 0 0 0 1 3 4 4 5 2 5 3 3
E11 0 0 0 0 0 1 2 1 3 2 4 2 1 1
E12 0 0 0 0 0 1 4 5 5 5 2 6 3 3
E13 0 0 0 0 0 1 2 2 3 3 1 3 3 3
E14 0 0 0 0 0 1 2 2 3 3 1 3 3 3


visualization of X’X
(event by event overlap matrix)
E2

E1 E9
E11

E8
E4
E10
E6

E3 E12

E5

E7

E14

E13


but users don’t see it in terms of the
operations needed to get there
E2 OLIVIA
DOROTHY
FLORA

PEARL

E1 E9
E11
MY RNA
RUTH
EVELY N

THERESA

E8
E4 LAURA
KATHERINE E10
E6

NORA E12
E3
BRENDA

E5 SYLVIA

E7 VERNE HELEN

FRANCES E14

ELEANOR
CHARLOTTE E13

commonality of multimode data
• E.g. Publications. Each article is a hyper‐edge
relating authors, topics, years, journals etc.


As far as I know, only
TouchGraph does this
well , and there is room
for improvement

Note: Bloom BR[au] and Harvard[ad] 1/1/90‐11/27/04 All A1, AA1, M1, MM1, MA1, J1, JAJM1, deg sep1 from author Barry L. Bloom
Source: PubMed, BCG Analysis (c) 2008 Stephen P. Borgatti. All rights reserved.

Note: Bloom BR[au] and Harvard[ad] 1/1/90‐11/27/04 All A1, AA1, M1, MM1, MA1, J1, JAJM1, deg sep1 from author Barry L. Bloom
Source: PubMed, BCG Analysis (c) 2008 Stephen P. Borgatti. All rights reserved.

visualizing relational algebra via
implicit multimode reductions
• Suppose we have multimodal data represented as
series of interlinked tables:
– AD = author by document
– TD = keywords by document
• AD*AD’ = author by author co‐authorships
• AD*TD’ = authors by their topics
• TD*TD’ = topic by topic co‐occurrences in documents
• Y = AT*TD*TD’*AT’ = author by author linkage of their
topics, i.e., yij > 0 if author i writes about topics that co‐
occur with the topics that author j writes about


integrating better with data sources
• Currently user is responsible for constructing a
graph of interest to be visualized
– Users think that should be part of the visualization
program
• Ability to directly access a database of tables
relating multiple kinds of entities and
construct graphs on the fly
– With filtering


substance issues: What theoretical
concepts to represent?

d c
i
j
e
f
a
b
h
g

Social distance / cohesion / connectedness Structural similarity/
isomorphism

Default representations e.g. kamada‐kawai Spectral / principal components / svd

substantive alternatives
• Brandes: centrality
graphs


conditions under which centrality
displays should be used
31
19
15
12 5
27

13

29

30
10
33
4 30
33 34
28
22
21
24
32

25
8 24
23
28

16

18
2 1 25 20
26

25.00% 8

34
6 2
32 26 17
18

11 27 7 1 4
6 20 22
11

7 31

17 0.20% 5
13

29
23
21
19
16
15
10
12

Interaction of network structure with choice of display

representing social processes
• Brokerage, social catalysis

• A kind of hypergraph?


What else would we want to
represent?
• Robustness of measures
– Jackknifing and bootstrapping results

• Multiple centrality
measures
• Ergm models …
– Space of possible networks


uses of motion as design element
• Case I
– Motion reveals static
structure from multiple
points of view
– I don’t think we do a
good job with this

Anthony Dekker. 200?. Conceptual Distance in Social Network
Analysis. Journal of Social Structure. (Vol. 6, No. 3 )

• Case II
– Motion reveals change
in network structure
and position over time
– Maintaining the
meaning of the
motion/position link
• Brownian motion of the
spring embedder
– But see visone for
algorithmic Anthony Dekker. 200?. Conceptual Distance in
improvement Social Network Analysis. Journal of Social
Structure. (Vol. 6, No. 3 )


Case III
• Nodes maintain
fixed positions,
ties appear and
disappear
– Ignores changes
in centrality etc.
– Traces help
maintain
memory but this
is still issue
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.

ALBERT_16

HUGH_14 BONI_15
MARK_7
simpler side by side
GREG_2

JOHN_1
WINF_12
Time 1
displays still have
ELIAS_17 BASIL_3
advantage of
AMBROSE_9

SIMP_18
comparability
BERTH_6

AMAND_13 VICTOR_8

PETER_4 ALBERT_16
ROMUL_10
BONAVEN_5
MARK_7
LOUIS_11
HUGH_14 BONI_15

ALBERT_16 GREG_2

MARK_7

HUGH_14 BONI_15 JOHN_1 Time 3
WINF_12
GREG_2

Time 2 JOHN_1
WINF_12 ELIAS_17 BASIL_3
AMBROSE_9

ELIAS_17 BASIL_3
AMBROSE_9 SIMP_18
BERTH_6

SIMP_18 AMAND_13 VICTOR_8
BERTH_6

AMAND_13 VICTOR_8
PETER_4
PETER_4 ROMUL_10
BONAVEN_5
ROMUL_10
BONAVEN_5 LOUIS_11
LOUIS_11

representing trajectories
• Examples
– Movements of individuals from position to
position
– Movement of children, drugs, goods, etc through
locations
– Diffusion of information, beliefs, viruses through
network links


Representing trajectories
Case I
• Treating
trajectories only
dyadically, as we
often do with
trade flows

Lothar Krempel


Movement of football players

Lothar Krempel

Movement of college basketball coaches
from school to school

Nodes are schools. Arcs indicate
that a coach has moved from
one school to the other. But
*paths* through the network
are lost

Retaining the paths
mississippi
morgan_state
howard
1994
2006
cincinnati 2001
1990 cornell
2001 nba 1996
uab 1993
coloradocollege
jackson_state
1979 2000chaminade
2007 1996 1988
1989
1972
out
1969 1994
2007
binghamton
1978 1982 1995
pro 1971 south_alabama
1988 utep
arkansas marist
1984
1985 cal_poly
1979 rhode_island
oklahoma_state 1997

1984 san_diego_state boston_college
1980

southern 1982
tulsa Each color indicates a different person’s career

Static representation of trajectories

Nodes are schools. Arcs are coaches. Arrowhead points in direction of movement.
C l id ifi h i

Static representation of trajectories

Nodes are schools. Arcs are coaches. Arrowhead points in direction of movement

Over time representation
(this can animated, of course, instead of spatial comparison)

out out

2006 2007

This again loses the concept of a path through the network – can’t track any coach’s trajectory

multigraphs representing multiple
social relations
PETER_4

BERTH_6

BONAVEN_5

ROMUL_10

AMAND_13
BASIL_3 VICTOR_8 LOUIS_11

AMBROSE_9
JOHN_1

ELIAS_17

HUGH_14
GREG_2

SIMP_18
Very hard to
ALBERT_16
understand results

WINF_12

So what is the best way to represent
trajectories?
• It is the whole path to be preserved, so we can
observe things like increases in status over
time

Film13
Film1
Film12 Film11 Film2

Film3
Film9

Film7
Film10
Film8 Film6 Film4
Film5


1.50
Director: Almodovar
AlCasanova
AnAlonso
AuGirard
SaLajusticia
PeCoyote
AlMayo
MiGomez MaOWisiedo
FeAtkine
AnLizaran
CrMarcos
EnPosner
RySakamoto
JeFerrero
EvCobo
AVGomez
AsSerna ViAbril
1.00 VeForque BiAndersen Film10
NaMartinez
LuHostalot Film5 Film9
EuPoncela
JuMArtinez BeBonezi
LuBriales
GoSuarez
AALopez
AnBanderas MGRomero
LoCardona
LoLeon
EnMorricone
Film4
TaVillalba
AnLlorens
maBarranco
MiMolina
MAPCAmpos
MaVelascoJLAlcaine
GuMontesinos Film8
RdPalma
0.50 LiCanalejas ChLampreaveFilm6
MaCarillo
MaZarzo
LuCalvo
CrPascual
Film3 Film7
CaMaura
ALFernandez
EsGarcia
PeAlmodovar AgAlmodovar
PeCoromina
JuSerrano JoSalcedo MaParedes
0.00
KiManver
Film11
JuEchanove
CaElias
MaVargas
HeLine

-0.50

ImArias
AlIglesias
Film13AfBeato
-1.00
Film2 RMSarda
FFGomez
ASJuan
CaPena
MiRuben
FeGuillen
Film12
Film1OfAngelica PeCruz
AnSantana
FeVivanco
AgAlcazar
MaMuro CeRoth
JaBardem
JoSancho
LiRabal
AnMolina
AlAngulo
FrNeri
Pibardem
PaDelgado CoGregori
-1.50
AlaskaPegam
PaPoch
OGAlaska
FrFemenias
FeRotaeta
EsRambal
EvSilva

-2.00
-2.00 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 2.00

Director: Garci
1.50 JCarballino
AFerrandis
AGonzalez
MMFernandez
PInfanzon
JPachelbel
ALlorente
CPorter
JMFernandez
SCanada
JCueto
PSerrador
TGimpera
SAmon
EHoyo
VVera
EPaso
JPuente
1.00
Film5 Film8
RHernandez
DSalcedo
ESuarez
PCalot
YRios
AMarsillach
VValverde
PHoyo
NGarci
Film7 JCalot Film10 ECerezo
AGonzalez AValero FGuillen
RVillascastin
MSampietro
MRMartinez
ABSanchez
ACarbonell
LdOrduna
BSantana
MEFlores
DAguado
EAsensi
JBodalo CGCuervo
RPCubero
CGConde
ARozas
LMDelgado
VPanero
FFGomez
RAlonso
CCruz
FGuillenCuervo
JCarideFAlgora
FPiquer
JCaride
0.50 JGCaba
JGluck
MLorenzo
NRodriguez
JLMerino LBosch

Film6 ECohen Film12 Film11
MMerchante
AFernandez
RdPenagos
MRellan
FBilbao
JYepes
JMCervino HValcarcel
MRojas
0.00 Film2MoWisiedo
CRodriguez
GCobos EFornetFilm4
MBlasco
MTejada
MRellan
RFraile
FVidal MGSinde
JLGarci
Film1
FFaltoyano
JSacristan
CCadenas
AGamero
STortosa
SAndreu
HAlterio
Berta
MCasanova
MFraguas
MMassip
MBalboa
-0.50

-1.00

ALanda

-1.50

-2.00

Film9
Film3

-2.50 MMorales VMataix
FFaltoyano CGomez
CJimenez ALarranaga
FArribas OLorente
RTebar
CLarranaga DPenalver
APicazo MVerdu
MLPonte

-3.00 ICGutierrez

-1.50 -1.00
-0.50 0.00 0.50 1.00 1.50 2.00

http://vw.indiana.edu/07netsci/entries/submissions/fullsize/7Koblin.mov

Attending more to substance issues

Types of Ties & Types of Visualization
States   Events
Continuous & enduring Discrete & transitory

(terrain) (roads) (processes) (traffic)
Proximities Relations Interactions Flows

Location Membership Attribute Role Affective Perceptual

Physical Same groups Same gender Mother of, Likes, Knows, Sex with, Information,
distance Same events Same attitude Friend of, Hates, Knows of Talked to, Beliefs,
Distance etc boss of, etc etc Advice to, Personnel,
etc student of Helped, Resources,
Competitor Hurt, etc Goods,
etc

Spatial distance edges and arcs animation ???

Conclusion
• Underutilization of graph drawing in the social sciences
– Reasons are institutional & technical but not so much algorithmic
• Publication needs dominate …
• Some design possibilities not yet used well
– Motion / animation
• Some tool needs not yet well met
– Especially integration with databases
– Separation of graph from data
• Insufficient attention to substance issues
– Closeness & structural equivalence & centrality have been addressed
– Representing processes, mechanisms
• One (personal) challenge: how to best represent graph traversals ‐‐
trajectories


krempel

Borgatti dagstuhl 2008 presentation 2c

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