In765 Knowledge Networks:In765 Knowledge Networks:A Structural Study of NetworksA Structural Study of Networks

Judith Molka-DanielsenJudith Molka-DanielsenMolde University CollegeMolde University College

j.molka-danielsen@himolde.noj.molka-danielsen@himolde.nohttp://home.himolde.no/~molkahttp://home.himolde.no/~molka

20052005

Types of Networks..Types of Networks..

Social Social NetworksNetworks

Friends, families, Friends, families,

colleagues colleagues Logical Logical ResourcesResources

web-pages, web-pages,

P2P-GnutellaP2P-Gnutella

TelephoneTelephone Wireline, mobileWireline, mobile

TransportTransport Roads, railroads, Roads, railroads,

airline, electricityairline, electricity

EconomicEconomic Firms, markets, Firms, markets,

organizationorganization

Physical Physical ResourcesResources

Internet Internet

IP routersIP routers

Why Study Networks? Why Study Networks? Research AreasResearch Areas

Availability and vulnerability of services: Availability and vulnerability of services: electric, telephone, air connections, etc.electric, telephone, air connections, etc.

Preventing or stopping of viruses on data Preventing or stopping of viruses on data networks. networks.

The importance of weak ties: connectivness The importance of weak ties: connectivness to the core, finding a job, finding a web to the core, finding a job, finding a web page. page.

The characterization of network structure The characterization of network structure and the role of hubs in the spreading an and the role of hubs in the spreading an idea, or proliferation of a product, and idea, or proliferation of a product, and managing organizations.managing organizations.

Former ResearchFormer Research

Random Network Theory –Erdös & Rényi (1960)Random Network Theory –Erdös & Rényi (1960) Six Degrees of Separation –S.Milgram (1967)Six Degrees of Separation –S.Milgram (1967) Cluster Coefficient –Small Worlds – Watts & Cluster Coefficient –Small Worlds – Watts &

Strogatz (1998)Strogatz (1998) Hubs and Scale Free Networks – Albert, Jeong, & Hubs and Scale Free Networks – Albert, Jeong, &

BarabBarabáási (1999)si (1999) Hubs in Social Networks – Malcolm Gladwell Hubs in Social Networks – Malcolm Gladwell

(2000)(2000)

Random Networks

Erdös-Rényi model (1960)

- Democratic

- Random

Pál ErdösPál Erdös (1913-1996)(1913-1996)

Connect with probability p

p=1/6 N=10

k ~ 1.5 Poisson distribution

Six Degrees of Separation

Nodes: individuals

Links: social relationship (family/work/friendship/etc.)

S. Milgram (1967)

Social networks: Many individuals with diverse social interactions between them.

John Guare (1980) Six Degrees of Separation

Cluster CoefficientClustering: My friends will likely know each other!

Probability to be connected C » p

C =# of links between 1,2,…n neighbors

n(n-1)/2

Network C Crand L N

WWW 0.1078 0.00023 3.1 153127

Internet 0.18-0.3 0.001 3.7-3.763015-6209

Actor 0.79 0.00027 3.65 225226

Coauthorship 0.43 0.00018 5.9 52909

Metabolic 0.32 0.026 2.9 282

Foodweb 0.22 0.06 2.43 134

C. elegance 0.28 0.05 2.65 282

Cfriends= 15/ [6(5)/2] = 100%

Hubs in NetworksHubs in Networks

200 million 200 million searches each daysearches each day

More than 2300 More than 2300 searches per searches per secondsecond

In 88 languagesIn 88 languages 3.2 billion web 3.2 billion web

pages indexed. pages indexed. 10 000 super 10 000 super

computers perform computers perform the searches. the searches.

Do we find Hubs in Social Networks? Yes.Do we find Hubs in Social Networks? Yes.

Most influencialMost influencial Access to the most informationAccess to the most information Impacts others decisions most Impacts others decisions most Have the most powerHave the most power

Who do you know?Who do you know?(similar to a study by Malcolm Gladwell, 2000)(similar to a study by Malcolm Gladwell, 2000)

Bjørnstjerne Bjørnsons VeiBjørnstjerne Bjørnsons Vei

Alme Jørund Alme Jørund Andenes Aud Andenes Aud Andestad Reidar Andestad Reidar Bakke Gerd Inger Bakke Gerd Inger Bergseth Egil Bergseth Egil Bergtun Lill Eldrid Bergtun Lill Eldrid Bjøringsøy Karl Magnar Bjøringsøy Karl Magnar Bjørkly Jorunn Bjørkly Jorunn Bjørkly Åsa Bjordal Bjørkly Åsa Bjordal Bjørnebo Solveig Randi Midtbø Bjørnebo Solveig Randi Midtbø Broks Vivi-Annie Broks Vivi-Annie Brokstad Jon Brokstad Jon Drageseth Dagfinn Drageseth Dagfinn Dyrli Janne Merete Dyrli Janne Merete Døving Ellen Døving Ellen Eilertsen Gudny Eilertsen Gudny Flø Jorunn Marie Flø Jorunn Marie Fylling Lars Kristen Tovan Fylling Lars Kristen Tovan

Gjære Arne Gjære Arne Gjære Guro Wiersholm Gjære Guro Wiersholm Gjære Vibeke Wiersholm Gjære Vibeke Wiersholm Grønbugt Rutt Grønbugt Rutt Grønset Erling Rune Grønset Erling Rune Gudbrandsen Åste Einbu Gudbrandsen Åste Einbu Gøncz Geir Janos Gøncz Geir Janos Göncz Arne Göncz Arne Hansen Helge Hansen Helge Hansen Sissel Hansen Sissel Helde Marit Illøkken Helde Marit Illøkken Henriksen Line Henriksen Line Hjelmsøt Maria Hjelmsøt Maria Hoem Jermund Hoem Jermund Hofset Siv Hofset Siv Jenset Grete Jenset Grete Jenset Torbjørn Jenset Torbjørn Jordet Birgit Jordet Birgit Kanestrøm Andreas Julshamn Kanestrøm Andreas Julshamn ……

12-12-1515 11

8-118-11 33

4-74-7 55

0-30-3 1313

1515 11

1010 11

99 11

88 11

66 22

55 22

33 11

22 44

11 66

00 33

A = number of persons known on the list.

B = number of persons (nodes) that person A knows.

A B

A B

Who do you know?: survey to faculty

gruppert

22

Power Law Distribution of Node Linkages

0

2

4

6

8

10

12

14

12-158-114-70-3

Number of Links

Nu

mb

er o

f N

od

es

No of nodes

15-15-2323 11

7-147-14 11

5-65-6 22

2-42-4 88

0-10-1 3636

2323 11

1414 11

66 11

55 11

44 44

33 11

22 33

11 1616

00 2020

A B

A B

Who do you know?: survey to students

gruppert48

Power Law Distribution of Node Linkages

0

5

10

15

20

25

30

35

40

15-237-145-62-4 0-1

Number of Links

Nu

mb

er o

f N

od

es

A = number of persons known on the list.

B = number of persons (nodes) that person A knows.

Scale Free Networks and Power LawsScale Free Networks and Power Lawsby Albert, Jeong, Barabasi.by Albert, Jeong, Barabasi.

Collaboration Among ResearchersNetworks have diverse nodes and links are

-computers

-routers

-satellites

-researchers

-phone lines

-TV cables

-EM waves

-co-authorship

Unique co-author link distribution – Unique co-author link distribution – researchers represented individuallyresearchers represented individually

Unique Co-authors Distribution

0

2

4

6

8

10

12

14

0 20 40 60 80

#Unique Co-author Links

#Res

earc

her

s -

with

exa

ctly

thi

s co

unt

Unique Co-Authors versus PublicationsUnique Co-Authors versus Publications

Unique Co-Authors vs. Publications

0

1020

3040

5060

70

0 50 100 150 200 250

Number of Publications

# U

niq

ue

Co

-Au

tho

rs

Average # of Co-Authors versus PublicationsAverage # of Co-Authors versus Publications

Average #Co-Authors vs # Publication

0,000,501,001,502,002,503,003,504,004,50

0 50 100 150 200 250

Number of Publications

Ave

rag

e #

of

Co

-Au

tho

rs

15

K. Danielsen

25 26

15

17

7

47

5

1

1

1

P. Sætre

J.Molka-Danielsen B. Jæger

K.A. Olsen

M.Spring

D. Tipper

O. OhrenO. Bø

R. Hveberg

K.Borgen

Informatics

17

8 4

6 6

10

4

1

77

A. Løkketangen

K.Haugen J.Odeck

K.Jörnsten

Ø.Halskau

5 2

4

2

F.Løbersli

2

NJ.Berland

11

K.Haugen

2S.W

allace7

M.Risnes

14

10

A-K Wallace

1S.

Wal

lace

6

LM Hvattum

1

HF Nordhaug

17

D. Woodruff

1

2

1

16

K.Haugen

J.Odeck

4

3

H. Arntzen

2

2

2

T.Crainic2

S.Wall

aceAG

Liu

m

2

6

5 Olstad1

1O.Larsen

A.Olstad2

Informatics Institute Cluster: researchers and co-author links

20

52

S. Vatne S. Bjørkly

Helsefag

G-U.Stavik

4

4

R. Michaelsen

4

J. Berg

12

3

1

H. Gammelsæter

E. R

ekd

al

11

HK.Aass1

AM.Botslangen

1

K.Dahl2

E.Braute4

I.Kamsvåg2

K.Westad Hauge

22

E.Lykkeslet Strømskag

5

M.Løvlien

4

E.Jørgensen3

AJ.Orøy2

A.Ødegård2

T.Skrondal2

2

H.Bakken

T.Aarseth

I.Gjerde

1

1

30

D.M.Berge

S.Brå

then

3

H. Gammelsæter

T.Aarseth

I.Gjerde

5

6

O.Hauge1

4

L.Rønhovd

e 2

1

1

Å.Brekk1

A.Hervi

k1

H.Sundal3

1

1

Health Institute Cluster: researchers and co-author links

80

H. Gammelsæter

31

T. Aarseth

28

K. Tornes

3

9

I. Gjerde

11

L.Rønhovde

16

B.Jákupsstovu

5A.Brekk

H.Bakken1

1 4

2

1

4

2

12

3

2

A. Hervik

1

S. Vatne

1E.Rekdal

1

Samfunnsfag

3

Ø.Opdal

E.Rekdal A. Hervik

1

3

3N.Rudi

EG.Standal1

H.Bakken

D.M.BergeD.M.Berge

D.M.Berge

D.M.Berge

5

6

6

4

2

DM Berge 1

Social Sciences Institute: researchers and co-author links

237

S. Wallace

39

K. Haugen

Ø. Halskau

30

I.Gribkovskaia9

A.Buvik

69

NJ.Berland7

2

A.H

ervi

k

1

AK.Wallace 1

7

3

AG.Lium

1

1

3

A.Løkketangen2

1

A.H

ervi

k

1

O.Larsen

20 2

Økonomi/Logistikk

NJ.Berland 2

A.Hervik

11

A.Løkketangen5

2

Dauzère-Pérès

K.Jörnsten

98

A.Løkketangen4

4

2

2

A.Hervik

2

2

A.Olstad7

2

2

5

1

A.Løkketangen

A.H

erv

ik

2

S.Brå

then

2

D.Woodruff

4

A.Løkketangen

1

2T.Crainic

2

D.Woodruff1

T.Crainic2

Economics/Logistics Cluster: researchers and co-author links

154

A.Hervik

S. Bråthen

88

B. Foss

13

O.L

arse

n

J.Odeck

19

H.Hjelle

26

K.Bedringås

11

H.Bremnes

12

O.Hauge

9

E.Rekdal2

P. Solibakke

19

B.Guvag5

A.Dedekam6

O.Sættem4

R.Rasmussen2

14

3

3

A.Olstad2

1

A.Buvik

1

H.Gammelsæter1

S.Wallace

1

2

K.Haugen

11

5

13

A.Løkketangen2

2

4

1-H.Gammelsæter

1-Ø.Opdal

1-S.Vatne

8

2

Økonomi DM-Berge 3

1DM-Berge

1

DM-Berge 1

1

K.Jörnsten

2

Ø.Opdal 3

D. Woodruff 3

1

1

Economics Institute Cluster: researchers and co-author links

154A.Hervik

S. Bråthen

88

B. Foss13

J.Odeck19

H.Hjelle26

K.Bedringås11

H.Bremnes12

O.Hauge9

E.Rekdal2

14

3

3 1

2

5

13

24

8

Økonomi

1

11

237S. Wallace

39

K. Haugen

Ø. Halskau30

I.Gribkovskaia9

A.Buvik69

2

7

3AG.Lium

11

3

1

O.Larsen

20 2

Økonomi/Logistikk

K.Jörnsten98

42

2

A.Olstad7

2

5

1

2

80

H.

Gam

me

lsæ

ter

31T

. Aar

seth 28

K. T

orn

es3

9I.

Gje

rde

11L.

Rø

nho

vde

16B

.Ják

upss

tovu

5

A.B

rekk

4

2

1

4

2

12

3

2

Sam

funn

sfag

3Ø

.Op

dal

6

20S. Vatne

Helsefag

G-U.Stavik4

4R. Michaelsen

4J. Berg

123

1

2H.Bakken

30D.M.Berge

1

1

H.Sundal3

1

15K

. Da

nielsen

2526

15

17

7

47

51

1

P. S

ætre

J.Molka-

Da

nielsen

B. Jæ

ger

K.A

. Olsen

M.S

pring

D. T

ipper

O.O

hren

O. B

ø

K.B

orgen

Informatics

17

84

66

10

4

1

77

A. L

økke

tangen

NJ.B

erland11

10

A-K

Wallace

6LM

Hva

ttum

17D

. Wo

odruff

1

2

1

16

H. A

rntzen

2

2

2T

.Crainic

65

1

3

1

4

2

2

1

2

7

5

1

2

2

4

2

1

1

61

5

4

1

2

11

1

3

1

1

11

1

1

2

2

1

3

1

Connected Network Tree of researchers and co-author links

ConclusionsConclusions Network of researchers at HSM is a Network of researchers at HSM is a Scale FreeScale Free

network. (existance of hubs, clustering network. (existance of hubs, clustering coeffiencient)coeffiencient)

Co-authors are not chosen randomlyCo-authors are not chosen randomly.. Co-authorship & Publication count: Co-authorship & Publication count: (cannot claim (cannot claim

causality)causality)– Average # of co-author per paperAverage # of co-author per paper is the is the

same regardless of the total # of publications same regardless of the total # of publications per author. per author. (does not help)(does not help)

– Average # of unique associationsAverage # of unique associations is related is related to a total # of publications per author. to a total # of publications per author. (helps)(helps)

Role of Role of ““connectors” (nodes with a high # of connectors” (nodes with a high # of external links) are importantexternal links) are important– They often have high publication counts. They often have high publication counts. – They have more external contacts.They have more external contacts.– They are more likely to hold a joint appointment They are more likely to hold a joint appointment

(again not causal).(again not causal).