borgatti dagstuhl 2008 presentation 2c

some notes on graph drawing in the social sciences

steve borgattiLINKS 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


factor Loadings

0.60.50.40.30.20.10-0.1

0.650.6

0.550.5

0.450.4

0.350.3

0.250.2

0.150.1

0.050

-0.05-0.1

-0.15-0.2

-0.25-0.3

-0.35-0.4

-0.45-0.5

-0.55-0.6

-0.65-0.7

-0.75-0.8

Advancement

HighPay

MeritPay

Training JobSecurityDevelopment

Support

Advancement

HighPay

MeritPay

Training

JobSecurity

Development Support

Overtime

LoyaltyExtraroleBehavior

NoticeTransfers

NoCompetitorSupport

ProprietaryProtection

MinimumStay

Overtime

LoyaltyExtraroleBehavior

NoticeTransfers

NoCompetitorSupportProprietaryProtectionMinimumStay

Violation

Factor 1

Factor 2


taxonomic display of an ultrametric distance derived via hierarchical clustering


Advancement1

HighPay1

MeritPay1

Training1

JobSecurity1

Development1

Support1

Advancement2

HighPay2

MeritPay2

Training2

JobSecurity2

Development2

Support2

Overtime1

Loyalty1ExtraroleBehavior1

Notice1

Transfers1

NoCompetitorSupp

ProprietaryProtection1

MinimumStay1

Overtime2

Loyalty2

ExtraroleBehavior2

Notice2

Transfers2

NoCompetitorSupport2

ProprietaryProtection2MinimumStay2

Violation2significant correlationsAlternative approach: graph representation


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 0.2103 -0.46203 0.02135 -0.80212 -0.79797 -0.72376 -0.81113 -0.80978(c) 2008 Stephen P. Borgatti. All rights reserved.

10.80.60.40.20-0.2-0.4-0.6-0.8-1

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

-0.1

-0.2

-0.3

-0.4

-0.5

-0.6

-0.7

-0.8

-0.9

19751976

19771978

1979

1980

1981

198219831984

1985

1986

1987

1988

1989

199019911992 1993

1994

1995

1996

1997

19981999

2000

2001

2002

20032004

2005


19751976

1977

1978

1979 19801981

1982

1983

1984

1985

19861987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999 2000

20012002 2003

2004

2005


causes of Breast Cancer


Causes of Breast Cancer

BLOWS

PROBPRODMILK

IMPLANTS

WILDLIFE

FONDLING SMOKING

NEVERBREASTFEED

LACKHYGIENE

FAMILYHISTORY

ABORTIONS

ILLEGALDRUGS

DIRTYWORK

CHEMICALSINFOOD

BIRTHCONTROL

BREAST-FEEDING

LACKMEDICALATTN

ALCOHOL

NOCHILDREN

POLLUTION

FATDIET

LARGEBREASTS

CAFFEINE

RADIATION

DIET

JUSTHAPPENS

FIBROCYSTIC

OBESITY

HORMONESUPPS

LATECHILDREN

CANCERHISTO

AGE

ETHNICITY

EARLYMENSES

SALVADOR

MEXICAN

CHICANASANGLO

PHYSICIANS


Causes of Breast Cancer

BLOWS2BREAST

PROBLEMSMILK

IMPLANTS

BREAST FONDLING

SMOKINGNEVERBREASTFEED

FAMILYHISTORY

CHEMICALSINFOOD

BIRTHCONTROLLACKMEDICALATTN

NOCHILDREN

POLLUTION

FATDIET

RADIATION

DIET

OBESITY

HORMONESUPPS

LATECHILDREN

CANCERHISTORY

AGE

SALVADOR

MEXICAN

CHICANASANGLO

PHYSICIANS

(Frequencies > 18%)


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


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

FROGSALAMANDER

FLAMINGO

WOODTHRUSH TURKEYROBIN BEAVER

RACCOON RABBIT

FROG 1.00 0.96 0.00 0.00 0.00 0.02 0.06 0.02 0.02

SALAMANDER 0.96 1.00 0.00 0.00 0.00 0.00 0.04 0.00 0.00

FLAMINGO 0.00 0.00 1.00 0.81 0.79 0.81 0.00 0.00 0.00

WOODTHRUSH 0.00 0.00 0.81 1.00 0.90 0.92 0.02 0.02 0.02TURKEY 0.00 0.00 0.79 0.90 1.00 0.87 0.02 0.02 0.02ROBIN 0.02 0.00 0.81 0.92 0.87 1.00 0.02 0.02 0.02BEAVER 0.06 0.04 0.00 0.02 0.02 0.02 1.00 0.62 0.65

RACCOON 0.02 0.00 0.00 0.02 0.02 0.02 0.62 1.00 0.71RABBIT 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

FROGSALAMANDER

FLAMINGOWOODTHRUSH

TURKEYROBIN

BEAVER

RACCOONRABBIT

MOUSE

DOLPHIN

COYOTEDEER

MOOSEELK

BEAR

WHALE

LION

SNAKESTARFISH

HYENALEOPARDGORILLA

FOX

BABOONELEPHANT

KANGAROOANTELOPE

SQUIRRELGROUNDHOG

Stress = 0.12


MDS of land animals only


Graph representation

ANTELOPE

BABOON

BEAR

BEAVER

COYOTE

DEER

DOLPHIN

ELEPHANT

ELKFLAMINGO

FOX

FROG

GORILLA

GROUNDHOG

HYENA

KANGAROO

LEOPARD

LION

MOOSE

MOUSERABBIT

RACCOON

ROBIN

SALAMANDERSNAKE

SQUIRREL

STARFISH

TURKEY

WHALE

WOODTHRUSH

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


Buy recycled prods.

}

Tell others not to do bad thingsSupport world population organizations

Save wetlands

Teach kids to preserve planetTeach about gains from environment

Teach kids about endangered speciesJoin environmental groups

Show kids by example

Write congresspersonPolitical activities

Teach kids about recycling

“Save the Earth” t-shirts

Encourage recycled products Organize drives for recyclables

Encourage others to recycle

Dolphin safe tuna

Don’t litter

Plant trees

Copper & brass

Put bins in officeRedeem cans

Pick up litter

Overpackaged foods

Restore buildings

Compost

Paper bags

Recylce toxic prods.

Recyling bins

Both sides paper

Salvation Army

No aerosol

Use own grocery bags

Reduce meat consumption

Use things longer

Plant garden

Cloth diapers

Plant shrubs

Reuse towels

Cut grass high

Use ethanol

Mulch grass clippings

Dishwasher w/ built-in heater

Frig. seal

Freezers on top

Dryer with moisture sensor

Insulate home

Oven door seal

Photocells

Automatic timers for house temp.

Insulate heating ducts

Dishwasher w/ airdry

Convection oven

Low-watt bulbs

Air off when leaveFans

Close shades

Weatherstrip

Fluorescent bulbs

Clothes line

Furnace tune-up

Turn off lights

Wear sweaters

Regulate thermostat

Clean lint filter

Cool leftovers

Gas heat Double-pane windows

Water-saving toilets

Inflate tires properlyGas mileage on new car

Assure car runs well

Buy Electric Car

Walk or bikeCarpool

Public transport

Water lawn in morning/evening

Ride Motorcycle

Remove CFC in old refrig.*A

*A

Lowflow shower

Full loads in dishwasherCold-water detergent

Water off while shaving

Rinse w/ cold waterShort dishwasher cycles

}*B

*B


U.S. Holidays

April_Fools

Christmas

Columbus Easter Fathers Flag

4th_Of_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

April_FoolsChristmasColumbusEasterFathersFlag4th_Of_JulyGroundhogHalloweenHanukkah

Kwanza

LaborMLKMemorialMothersNew_YearsPassoverPresidentsRamadan

Rosh_Hashanah

St_Patrickt_ValentinesThanksgivingVeteransYom_KippurPatriots

Cinco_de_Mayo

Secretaries

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

after removing “strange” holidays

April_Fools

Christmas

Columbus

Easter

Fathers

Flag

4th_Of_July

Groundhog

Halloween

Hanukkah

Labor

MLK

Memorial

MothersNew_Years

Passover

Presidents

St_Patrick

St_Valentines

Thanksgiving

Veterans

Yom_Kippur

Patriots

Secretari


April_Fools

Christmas

Columbus

Easter

Fathers

Flag

4th_Of_July

Groundhog

Halloween

Hanukkah

Labor

MLK

Memorial

Mothers

New_Years

Passover

Presidents

St_Patrick

St_Valentines

Thanksgiving

Veterans

Yom_Kippur

Patriots

Secretaries

graph representation


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

1960s paper by Michael Burton(c) 2008 Stephen P. Borgatti. All rights reserved.

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

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


Moreno & Sociometry 1930s

Moreno 1934

Friendship Choices Among Fourth Graders (from Moreno, 1934, p. 38).

Positive and Negative Choices in a Football Team (Moreno, 1934, p. 213).(c) 2008 Stephen P. Borgatti. All rights reserved.

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


graph drawings for concept illustration

L. Coromina et al. / Social Networks 30 (2008) 49–59(c) 2008 Stephen P. Borgatti. All rights reserved.

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

Qual XOR Quant perspective

Comic bookunderstanding of

science‐deductive‐quantitative

Legitimacy of pictures

Media limitations &

“costs”

Inability to switch toelectronicmedia

Print journals permit only simplest graphics

Habit of verbal vsvisual thinking

Lack of prestige of strange journals

+


Other issues

Lack of quality tools‐ Power & ease of use

Algorithms

Imagination & effort?

Insufficient attention to substantive issues


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


Automating Legends

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

Tool features


Smart Labeling

VERNE

MYRNA

KATHERINESYLVIANORA

HELEN

VERNE

MYRNA

KATHERINESYLVIANORA

HELEN

Computer science applications often ignore labels(c) 2008 Stephen P. Borgatti. All rights reserved.

Coding: highlighting, marking-up, cutting-up, classifying, graph elements

HLM outputannotating outputs


statistics printed on chart

A

B

C

D

E

F

G

H

I

Geary’s C: 0.333Significance: 0.000


Collapsing / expanding nodes

• Easily collapsing nodes into super nodes and then expanding back– Current tools handle by creating separate image graphs

HOLLY

BRAZEY

CAROL

PAM

PAT

JENNIE

PAULINE

ANN

MICHAEL

BILL

LEE

DON

JOHN

HARRY

GERY

ST EVE

BERT

RUSS

0.4

0.0

0.1

0.1

0.3

0.2

0.1

0.8

1

2

3

Density / Average value within blocks

1 2 3------ ------ ------

1 0.3571 0.0417 0.06252 0.1042 0.3000 0.16673 0.0000 0.1250 0.7500


convex hulls to represent categorical node attributes

‐‐ not complex algorithmically but few offer itAn

thropacsoftware


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

EVELYN

LAURA

THERESA

BRENDA

CHARLOTTE

FRANCES

ELEANOR

PEARL

RUTH

VERNE

MYRNA

KATHERINE

SYLVIA

NORA

HELEN

DOROTHYOLIVIA

FLORA

E1

E2

E3

E4

E5

E6

E7

E8

E9

E10

E11

E12

E13

E14

Davis, Gardner and Gardner data. Which women attended which social events.


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’

EVELYN

LAURA

THERESA

BRENDA

CHARLOTTE

FRANCES

ELEANOR

PEARL

RUTH

VERNE

MYRNA

KATHERINE

SYLVIA

NORA

HELEN

DOROTHY

OLIVIA

FLORA

EVELYN 8 6 7 6 3 4 3 3 3 2 2 2 2 2 1 2 1 1LAURA 6 7 6 6 3 4 4 2 3 2 1 1 2 2 2 1 0 0THERESA 7 6 8 6 4 4 4 3 4 3 2 2 3 3 2 2 1 1BRENDA 6 6 6 7 4 4 4 2 3 2 1 1 2 2 2 1 0 0CHARLOTTE 3 3 4 4 4 2 2 0 2 1 0 0 1 1 1 0 0 0FRANCES 4 4 4 4 2 4 3 2 2 1 1 1 1 1 1 1 0 0ELEANOR 3 4 4 4 2 3 4 2 3 2 1 1 2 2 2 1 0 0PEARL 3 2 3 2 0 2 2 3 2 2 2 2 2 2 1 2 1 1RUTH 3 3 4 3 2 2 3 2 4 3 2 2 3 2 2 2 1 1VERNE 2 2 3 2 1 1 2 2 3 4 3 3 4 3 3 2 1 1MYRNA 2 1 2 1 0 1 1 2 2 3 4 4 4 3 3 2 1 1KATHERINE 2 1 2 1 0 1 1 2 2 3 4 6 6 5 3 2 1 1SYLVIA 2 2 3 2 1 1 2 2 3 4 4 6 7 6 4 2 1 1NORA 2 2 3 2 1 1 2 2 2 3 3 5 6 8 4 1 2 2HELEN 1 2 2 2 1 1 2 1 2 3 3 3 4 4 5 1 1 1DOROTHY 2 1 2 1 0 1 1 2 2 2 2 2 2 1 1 2 1 1OLIVIA 1 0 1 0 0 0 0 1 1 1 1 1 1 2 1 1 2 2FLORA 1 0 1 0 0 0 0 1 1 1 1 1 1 2 1 1 2 2(c) 2008 Stephen P. Borgatti. All rights reserved.

X’X

E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11 E12 E13 E14E1 3 2 3 2 3 3 2 3 1 0 0 0 0 0E2 2 3 3 2 3 3 2 3 2 0 0 0 0 0E3 3 3 6 4 6 5 4 5 2 0 0 0 0 0E4 2 2 4 4 4 3 3 3 2 0 0 0 0 0E5 3 3 6 4 8 6 6 7 3 0 0 0 0 0E6 3 3 5 3 6 8 5 7 4 1 1 1 1 1E7 2 2 4 3 6 5 10 8 5 3 2 4 2 2E8 3 3 5 3 7 7 8 14 9 4 1 5 2 2E9 1 2 2 2 3 4 5 9 12 4 3 5 3 3E10 0 0 0 0 0 1 3 4 4 5 2 5 3 3E11 0 0 0 0 0 1 2 1 3 2 4 2 1 1E12 0 0 0 0 0 1 4 5 5 5 2 6 3 3E13 0 0 0 0 0 1 2 2 3 3 1 3 3 3E14 0 0 0 0 0 1 2 2 3 3 1 3 3 3


E1

E2

E3

E4

E5

E6

E7

E8

E9

E10

E11

E12

E13

E14

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


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

EVELYN

LAURA

THERESA

BRENDA

CHARLOTTE

FRANCES

ELEANOR

PEARL

RUTH

VERNE

MYRNA

KATHERINE

SYLVIA

NORA

HELEN

DOROTHYOLIVIA

FLORA

E1

E2

E3

E4

E5

E6

E7

E8

E9

E10

E11

E12

E13

E14


commonality of multimode data

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


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. BloomSource: PubMed, BCG Analysis

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. BloomSource: 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


ab

cd

ef

gh

ij

substance issues: What theoretical concepts to represent?

Social distance / cohesion / connectedness Structural similarity/isomorphism

Default representations e.g. kamada‐kawai Spectral / principal components / svd(c) 2008 Stephen P. Borgatti. All rights reserved.

substantive alternatives• Brandes: centrality graphs


conditions under which centrality displays should be used

0.20%

25.00%

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Interaction of network structure with choice of display(c) 2008 Stephen P. Borgatti. All rights reserved.

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 improvement

Anthony Dekker. 200?. Conceptual Distance in 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.


simpler side by side displays still have advantage of comparability

ROMUL_10BONAVEN_5

AMBROSE_9

BERTH_6

PETER_4

LOUIS_11

VICTOR_8

WINF_12JOHN_1

GREG_2

HUGH_14 BONI_15

MARK_7

ALBERT_16

AMAND_13

BASIL_3ELIAS_17

SIMP_18

ROMUL_10BONAVEN_5

AMBROSE_9

BERTH_6

PETER_4

LOUIS_11

VICTOR_8

WINF_12JOHN_1

GREG_2

HUGH_14 BONI_15

MARK_7

ALBERT_16

AMAND_13

BASIL_3ELIAS_17

SIMP_18

ROMUL_10BONAVEN_5

AMBROSE_9

BERTH_6

PETER_4

LOUIS_11

VICTOR_8

WINF_12JOHN_1

GREG_2

HUGH_14 BONI_15

MARK_7

ALBERT_16

AMAND_13

BASIL_3ELIAS_17

SIMP_18

Time 1

Time 2

Time 3


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

Krem

pel


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

1984

1997

19931996

2000

20071982

19881979

1994

1996

19691978

19902001

1994

1995

2001

2006

1971

19721989

1979

1980

1982

1984

1985

1988

2007

marist

rhode_island

boston_college

coloradocollege

cornell

chaminade

binghamtonout

nba

howardmorgan_state

south_alabama

uab

cincinnati

mississippi

uteppro

cal_poly

san_diego_state

tulsasouthern

oklahoma_state

arkansas

jackson_state

Each color indicates a different person’s career(c) 2008 Stephen P. Borgatti. All rights reserved.

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

Static representation of trajectories


Over time representation

out out

2006 2007

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

(this can animated, of course, instead of spatial comparison)


multigraphs representing multiple social relations

ROMUL_10

BONAVEN_5

AMBROSE_9

BERTH_6

PETER_4

LOUIS_11VICTOR_8

WINF_12

JOHN_1

GREG_2 HUGH_14

ALBERT_16

AMAND_13

BASIL_3

ELIAS_17

SIMP_18 Very hard to understand results


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

Film1

Film10

Film11Film12

Film13

Film2

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Film4Film5

Film6Film7

Film8

Film9


Director: Almodovar

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ALFernandez

AVGomez

AfBeato

AgAlcazar

AgAlmodovar

AlaskaPegam

AlIglesias

AlAngulo

AlCasanovaAlMayoAnLizaranAnAlonso

AnSantana

AALopez

AnMolina

ASJuan

AnBanderasAnLlorens

AsSerna

AuGirard

BeBonezi

BiAndersen

CaPena

CaElias

CaMaura

CeRoth

ChLampreave

CoGregori

CrMarcos

CrPascual

EnMorricone

EnPosner

EsGarcia

EsRambal

EuPoncela

EvCobo

EvSilvaFeRotaeta

FeAtkine

FFGomezFeGuillen

FeVivancoFrNeri

FrFemenias

GoSuarez

GuMontesinos

HeLine

ImArias

JaBardem

JeFerrero

JLAlcaine

JoSalcedo

JoSancho

JuEchanove

JuMArtinez

JuSerrano

KiManver

LiRabal

LiCanalejas

LoCardonaLoLeonLuBriales

LuCalvo

LuHostalot

MAPCAmpos

MaZarzo

MaVargas

MaVelasco

MaCarillo

maBarranco

MaParedes

MaMuro

MaOWisiedo

MiRuben

MiGomez

MiMolinaMGRomero

NaMartinez

OfAngelica

OGAlaskaPaPochPaDelgado

PeAlmodovar

PeCruz

PeCoromina

PeCoyote

Pibardem

RMSarda

RdPalma

RySakamotoSaLajusticia

TaVillalba

VeForqueViAbril

Film13

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Film10Film9

Film8Film7Film6

Film5

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Film1


Director: Garci

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JLGarci

JGCaba

LBosch

LMDelgadoVPanero

HValcarcel

RPCubero

MBalboa

MGSinde

FFGomezRAlonsoCGCuervo

AGonzalez

CCruzARozas

FGuillen

FGuillenCuervoFPiquer

MMassip

JCarideJCarideFAlgora

ECohen

JCalot

CGCondeAValero

NRodriguezJLMerino

MSampietroBSantanaEAsensiMEFlores

NGarci

MRMartinezLdOrdunaDAguadoABSanchezRVillascastinACarbonellECerezo

FFaltoyanoALarranaga

VMataix

DPenalverMLPonte

MVerdu

CGomez

ALanda

CJimenez OLorenteRTebar

MRojas

MMorales

JGluck

CPorterJPachelbelALlorente

JPuente

TGimperaVVeraEHoyoPSerrador

MLorenzo

PHoyo

SAmonJCuetoSCanadaJMFernandezPInfanzon

JCarballino

AMarsillach

MCasanova

JBodalo

EPaso

VValverdePCalotESuarezRHernandezYRiosDSalcedo

MRellanRdPenagosAFernandezJMCervino

MMerchanteJYepesFBilbao

AFerrandisAGonzalez

MMFernandez

MTejadaMRellanRFraileFVidalMBlascoMoWisiedoEFornet

CLarranagaAPicazo

ICGutierrez

FArribas

JSacristanFFaltoyano

GCobosCRodriguez

AGameroSTortosaSAndreuHAlterioCCadenasBerta

MFraguas

Film12 Film11

Film10

Film9

Film8

Film7

Film6

Film5

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Film3

Film2Film1


Types of Ties & Types of Visualization

(roads)Relations

(processes)Interactions

(traffic)Flows

Role Affective Perceptual

Sex with,Talked to,Advice to,Helped,Hurt, etc

Information,Beliefs, Personnel,Resources,Goods, etc

Mother of,Friend of,boss of,student ofCompetitor

Likes,Hates,etc

Knows,Knows ofetc

(terrain)Proximities

Membership Attribute

Same groupsSame eventsDistanceetc

Same genderSame attitudeetc

Location

Physical distance

StatesContinuous & enduring

EventsDiscrete & transitory

Spatial distance edges and arcs animation ???

Attending more to substance issues


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


borgatti dagstuhl 2008 presentation 2c

Education