1. Networks from
data bases
V. Batagelj
Two mode
networks
Big data
Multiplication Networks from data bases
Derived
networks
Pajek
Vladimir Batagelj
University of Ljubljana
Undicesima conferenza nazionale di statistica
Rome, February 20-21, 2013
V. Batagelj Networks from data bases

2. Outline
Networks from
data bases
V. Batagelj
Two mode
networks
Multiplication
Derived
1 Two mode networks
networks 2 Multiplication
Pajek
3 Derived networks
4 Pajek
V. Batagelj Networks from data bases

3. Example: Internet Movie Data Base
Networks from
data bases
V. Batagelj
Lee Tamahori
Two mode
networks Pierce Brosnan
Halle Berry
Multiplication
Paul Haggis
Derived Neal Purvis
networks Die Another Day Robert Wade
Ian Fleming
Pajek
Martin Campbell
Judi Dench
Casino Royale
Daniel Craig
Mads Mikkelsen
Eva Green
Skyfall Sam Mendes
John Logan
Ralph Fiennes
Javier Bardem
On February 17, 2013 IMDB (Internet Movie Data Base) contained 2,262,638 titles and 4,745,392 names.
Web of Science, Scopus, Zentralblatt Math, Google Scholar, DBLP, Amazon, etc.
V. Batagelj Networks from data bases

4. Two mode networks from data bases
Networks from
data bases A simple data base B is a set of records B = {Rk : k ∈ K}, where K is the
V. Batagelj set of keys. A record has the form Rk = (k, q1 (k), q2 (k), . . . , qr (k)) where
qi (k) is the description of the property (attribute) qi for the key k.
Two mode
networks
Suppose that the description q(k) takes values in a finite set Q. It can
always be transformed into such set by partitioning the set Q and recoding
Multiplication
the values. Then we can assign to the property q a two-mode network
Derived
networks K × q = (K, Q, L, w ) where (k, v ) ∈ L iff v ∈ q(k). w (k, v ) is the weight
Pajek
of the link (k, v ); often w (k, v ) = 1.
Single-valued properties can be represented by a partition.
Examples:
(papers, authors, was written by),
(papers, keywords, is described by),
(parlamentarians, problems, positive vote),
(persons, journals, is reading),
(persons, societies, is member of, years of membership),
(buyers/consumers, goods, bought, quantity), etc.
V. Batagelj Networks from data bases

5. Methods: degree distributions
Networks from
data bases
V. Batagelj
Two mode
networks In a network (V, L) the degree deg(v ) of vertex v ∈ V is equal
Multiplication to the number of links that have vertex v as their end-vertex.
Derived The indegree / outdegree is equal to the number of incoming /
networks
outgoing links.
Pajek
Usually one of the first analyses of a network is to look at its
degree distribution(s). Are there isolated nodes (deg(v ) = 0)?
Which are the nodes with the largest degrees? What is the
average degree? What is the shape of degree distribution?
V. Batagelj Networks from data bases

6. Methods: two-mode cores and 4-rings weights
Networks from The subset of vertices C ⊆ V is a (p, q)-core in a two-mode network
data bases
N = (V1 , V2 ; L), V = V1 ∪ V2 iff
V. Batagelj
a. in the induced subnetwork K = (C1 , C2 ; L(C )), C1 = C ∩ V1 ,
Two mode
networks
C2 = C ∩ V2 it holds ∀v ∈ C1 : degK (v ) ≥ p and
Multiplication
∀v ∈ C2 : degK (v ) ≥ q ;
Derived b. C is the maximal subset of V satisfying condition a.
networks
Pajek
A k-ring is a simple closed chain of length k. Using k-rings we can
define a weight of edges as
wk (e) = # of different k-rings containing the edge e ∈ E
In two-mode network there are no 3-
rings. The densest substructures are
complete bipartite subgraphs Kp,q .
They contain many 4-rings. There-
fore these weights can be used to
identify the dense parts of a network.
V. Batagelj Networks from data bases

7. Example: (247,2)-core and (27,22)-core in IMDB
Networks from Zhukov, Boris (I)
Wright, Charles (II)
Wilson, Al (III)
Wight, Paul
Wickens, Brian
White, Leon
data bases
Warrior
Warrington, Chaz
Ware, David (II)
Waltman, Sean
Walker, P.J.
von Erich, Kerry
Vaziri, Kazrow
Van Dam, Rob
Valentine, Greg
Vailahi, Sione
Tunney, Jack
Traylor, Raymond
Tenta, John
Taylor, Terry (IV)
’WWF Smackdown!’ Taylor, Scott (IX)
Taylor, Scott (IX)
Tanaka, Pat
Tajiri, Yoshihiro
Van Dam, Rob
V. Batagelj
Szopinski, Terry
Storm, Lance
Steiner, Scott
Steiner, Rick (I) ’WWE Velocity’
Solis, Mercid
Snow, Al
Smith, Davey Boy
Slaughter, Sgt.
Matthews, Darren (II)
Simmons, Ron (I)
Shinzaki, Kensuke
Shamrock, Ken
Senerca, Pete
Scaggs, Charles
’Sunday Night Heat’ LoMonaco, Mark
Savage, Randy
Saturn, Perry
Sags, Jerry
Ruth, Glen
Runnels, Dustin
Rude, Rick
Rougeau, Raymond
Rougeau Jr., Jacques
’Raw Is War’ Hughes, Devon
Rotunda, Mike
Ross, Jim (III)
Rock, The
Roberts, Jake (II)
Rivera, Juan (II)
Rhodes, Dusty (I) WWF Vengeance Huffman, Booker
Two mode
Reso, Jason
Reiher, Jim
Reed, Bruce (II)
Race, Harley
Prichard, Tom
Powers, Jim (IV)
Poffo, Lanny WWF Unforgiven Heyman, Paul
Plotcheck, Michael
Piper, Roddy
Pfohl, Lawrence
Hebner, Earl
networks
Pettengill, Todd
Peruzovic, Josip
Palumbo, Chuck (I)
Page, Dallas
Ottman, Fred WWF Rebellion
Orton, Randy
Okerlund, Gene
Nowinski, Chris
Norris, Tony (I)
McMahon, Stephanie
Nord, John
Neidhart, Jim
Nash, Kevin (I)
Muraco, Don
Morris, Jim (VII)
WWF No Way Out Keibler, Stacy
Morley, Sean
Morgan, Matt (III)
Mooney, Sean (I)
Moody, William (I)
WWF No Mercy Wight, Paul
Multiplication
Miller, Butch
Mero, Marc
Survivor Series McMahon, Vince
McMahon, Shane
Matthews, Darren (II)
Martin, Andrew (II)
Martel, Rick
Marella, Robert
Marella, Joseph A.
Manna, Michael WWF Judgment Day Simmons, Ron (I)
Lothario, Jose
Senerca, Pete
Long, Teddy
LoMonaco, Mark
Lockwood, Michael
Levy, Scott (III)
Levesque, Paul Michael
Lesnar, Brock
Leslie, Ed
WWF Insurrextion
Ross, Jim (III)
Derived Leinhardt, Rodney
Layfield, John
Lawler, Jerry
Lawler, Brian (II)
Laurinaitis, Joe
Laughlin, Tom (IV)
Lauer, David (II)
Knobs, Brian
Knight, Dennis (II)
WWF Backlash Rock, The
Killings, Ron
networks Kelly, Kevin (VIII)
Keirn, Steve
Jones, Michael (XVI)
Johnson, Ken (X)
Jericho, Chris
Jarrett, Jeff (I)
Jannetty, Marty
James, Brian (II)
WWE Wrestlemania XX Reso, Jason
Jacobs, Glen
Jackson, Tiger
Hyson, Matt
Hughes, Devon
Huffman, Booker
WWE Wrestlemania X-8 McMahon, Vince
Howard, Robert William
McMahon, Shane
Howard, Jamie
Houston, Sam
Horowitz, Barry
WWE Vengeance
Pajek
Horn, Bobby
Hollie, Dan
Hogan, Hulk
Hickenbottom, Michael
Heyman, Paul
Hernandez, Ray
Henry, Mark (I) Martin, Andrew (II)
Hennig, Curt
Helms, Shane
Hegstrand, Michael WWE Unforgiven
Heenan, Bobby
Hebner, Earl
Hebner, Dave
Heath, David (I)
Levesque, Paul Michael
WWE SmackDown! Vs. Raw
Hayes, Lord Alfred
Hart, Stu
Hart, Owen
Hart, Jimmy (I)
Hart, Bret
Harris, Ron (IV)
Harris, Don (VII)
Layfield, John
Harris, Brian (IX)
Hardy, Matt
Hardy, Jeff (I)
Hall, Scott (I)
Guttierrez, Oscar
Gunn, Billy (II)
WWE No Way Out Lawler, Jerry
Guerrero, Eddie
Guerrero Jr., Chavo
Gray, George (VI)
Goldberg, Bill (I)
Gill, Duane
Gasparino, Peter WWE No Mercy Jericho, Chris
Garea, Tony
Funaki, Sho
Fujiwara, Harry
Frazier Jr., Nelson
Foley, Mick
Flair, Ric
Finkel, Howard WWE Judgment Day Jacobs, Glen
Royal Rumble Fifita, Uliuli
Fatu, Eddie
Farris, Roy
Eudy, Sid Hardy, Matt
Enos, Mike (I)
Eaton, Mark (II)
Eadie, Bill
WWE Armageddon
Duggan, Jim (II)
Douglas, Shane
DiBiase, Ted
DeMott, William
Davis, Danny (III)
Hardy, Jeff (I)
Darsow, Barry
Cornette, James E.
Copeland, Adam (I)
Constantino, Rico
Connor, A.C.
Wrestlemania X-Seven Gunn, Billy (II)
Cole, Michael (V)
Coage, Allen
Coachman, Jonathan
Clemont, Pierre
Clarke, Bryan
Chavis, Chris
Centopani, Paul
Cena, John (I)
Wrestlemania X-8 Guerrero, Eddie
Canterbury, Mark
Candido, Chris
Calaway, Mark
Bundy, King Kong
Buchanan, Barry (II)
Brunzell, Jim Wrestlemania 2000 Copeland, Adam (I)
Brisco, Gerald
Bresciano, Adolph
Bloom, Wayne
Bloom, Matt (I) Cole, Michael (V)
Blood, Richard
Blanchard, Tully
Blair, Brian (I) Survivor Series
Blackman, Steve (I)
Bischoff, Eric
Bigelow, Scott ’Bam Bam’
Benoit, Chris (I)
Batista, Dave
Calaway, Mark
Bass, Ron (II)
Barnes, Roger (II)
Backlund, Bob
Austin, Steve (IV)
Summerslam Bloom, Matt (I)
Apollo, Phil
Anoai, Solofatu
Anoai, Sam
Anoai, Rodney
Anoai, Matt
Anoai, Arthur
Angle, Kurt
AndrØ the Giant
Royal Rumble Benoit, Chris (I)
Anderson, Arn
Albano, Lou
Al-Kassi, Adnan
Ahrndt, Jason
Adams, Brian (VI)
Young, Mae (I)
Wright, Juanita
No Way Out Austin, Steve (IV)
Wilson, Torrie
Vachon, Angelle
Stratus, Trish
Runnels, Terri
Robin, Rockin’
Psaltis, Dawn Marie King of the Ring Anoai, Solofatu
Moretti, Lisa
Moore, Jacqueline (VI)
Moore, Carlene (II)
Mero, Rena
McMichael, Debra
Angle, Kurt
McMahon, Stephanie
Martin, Judy (II)
Martel, Sherri Invasion
Laurer, Joanie
Keibler, Stacy
Kai, Leilani
Hulette, Elizabeth
Stratus, Trish
Fully Loaded
Guenard, Nidia
Garca, LiliÆn
Ellison, Lillian
Dumas, Amy
Dumas, Amy
IMDB 2005: n1 = 428440, n2 = 896308, m = 3792390.
V. Batagelj Networks from data bases

8. Example: Islands for w4 / Charlie Brown and Adult
Networks from
data bases
V. Batagelj
Morgan, Jonathan (I)
Kesten, Brad
Brando, Kevin
Schoenberg, Jeremy Boy, T.T. Davis, Mark (V)
Two mode Hauer, Brent
Robbins, Peter (I)
networks Shea, Christopher (I) Charlie Brown and Snoopy Show Voyeur, Vince
Altieri, Ann
Reilly, Earl ’Rocky’
Charlie Brown Celebration
Multiplication Ornstein, Geoffrey You Don’t Look 40, Charlie Brown
He’s Your Dog, Charlie Brown
Dough, Jon
Making of ’A Charlie Brown Christmas’
You’re In Love, Charlie Brown Sanders, Alex (I)
Derived It’s the Great Pumpkin, Charlie Brown
Charlie Brown’s All Stars! Life Is a Circus, Charlie Brown
North, Peter (I)
networks Charlie Brown Christmas
Race for Your Life, Charlie Brown
Michaels, Sean
Be My Valentine, Charlie Brown
Horner, Mike
Pajek Mendelson, Karen
It’s Magic, Charlie Brown
Dryer, Sally
Stratford, Tracy Melendez, Bill You’re a Good Sport, Charlie Brown Drake, Steve (I)
Boy Named Charlie Brown It’s a Mystery, Charlie Brown
It’s an Adventure, Charlie Brown
Byron, Tom Silvera, Joey
It’s Flashbeagle, Charlie Brown
Momberger, Hilary
Play It Again, Charlie Brown
West, Randy (I)
Is This Goodbye, Charlie Brown?
Charlie Brown Thanksgiving
There’s No Time for Love, Charlie Brown
You’re Not Elected, Charlie Brown Jeremy, Ron
Snoopy Come Home
It’s the Easter Beagle, Charlie Brown
Wallice, Marc Savage, Herschel
Thomas, Paul (I)
Shea, Stephen
Pajek
Pajek
V. Batagelj Networks from data bases

9. Sparsity and Dunbar’s number
Networks from
data bases
V. Batagelj
Two mode Networks obtained from data bases are usually large – tens of
networks
thousands or millions of nodes. Large networks are usually
Multiplication
Derived
sparse – they have small average degree.
networks
Pajek
In one-mode networks describing relations among people this
can be related to Dunbar’s number with a value around 150.
See Wikipedia: Dunbar’s number.
In general, if initiator of a link wants to keep the link he should
spend / invest a certain amount of finite total ”energy” he has.
V. Batagelj Networks from data bases

10. Multiplication of networks
Networks from
data bases To a simple two-mode network N = (I, J , E, w ); where I and J are
V. Batagelj sets of vertices, E is a set of edges linking I and J , and w : E → R
(or some other semiring) is a weight; we can assign a network matrix
Two mode
networks
W = [wi,j ] with elements: wi,j = w (i, j) for (i, j) ∈ E and wi,j = 0
Multiplication
otherwise.
Given a pair of compatible networks NA = (I, K, EA , wA ) and
Derived
networks NB = (K, J , EB , wB ) with corresponding matrices AI×K and BK×J
Pajek we call a product of networks NA and NB a network
NC = (I, J , EC , wC ), where EC = {(i, j) : i ∈ I, j ∈ J , ci,j = 0} and
wC (i, j) = ci,j for (i, j) ∈ EC . The product matrix
C = [ci,j ]I×J = A ∗ B is defined in the standard way
ci,j = ai,k · bk,j
k∈K
In the case when I = K = J we are dealing with ordinary one-mode
networks (with square matrices).
V. Batagelj Networks from data bases

11. Multiplication of networks
Networks from
data bases
V. Batagelj
Two mode
networks
i
Multiplication
ai,k
j
Derived
networks bk,j
Pajek k
J
I A B
K
ci,j = ai,k · bk,j
k∈K
If all weights in networks NA and NB are equal to 1 the value of ci,j
counts the number of ways we can go from i ∈ I to j ∈ J passing
through K.
V. Batagelj Networks from data bases

12. Multiplication of networks
Networks from
data bases
V. Batagelj
The standard matrix multiplication has the complexity
Two mode
networks
O(|I| · |K| · |J |) – it is too slow to be used for large networks.
Multiplication
For sparse large networks we can multiply much faster
Derived considering only nonzero elements.
networks
In general the multiplication of large sparse networks is a
Pajek
’dangerous’ operation since the result can ’explode’ – it is not
sparse.
If for the sparse networks NA and NB there are in K only few
vertices with large degree and no one among them with large
degree in both networks then also the resulting product
network NC is sparse.
V. Batagelj Networks from data bases

13. Derived networks
Networks from
data bases From a bibliographical data base we get two-mode networks WA =
V. Batagelj Works × Authors and WK = Works × Keywords. Since they have a
common set Works the networks WAT and WK are compatible and
Two mode
networks multiplying them we obtain a derived network
Multiplication
AK = WAT ∗ WK
Derived
networks
Pajek
The entry akit = number of times author i used in his/her works
keyword t.
The dataset of EU projects on simulation (January 2006) contains
data about research groups. We obtain networks: P = Groups ×
Projects, C = Groups × Countries, and U = Groups × Institutions.
Sizes: |Groups| = 8869, |Projects| = 933, |Institutions| = 3438,
|Countries| = 60.
In the derived network W = Projects × Institutions = PT ∗ U we
determine link islands for w4 .
V. Batagelj Networks from data bases

14. Analysis of Projects × Institutions
Networks from PSI FUR PRODUKTE UND
ARMINES
TQT SRL
SYS.E DER INFORMATIONSTECH.
data bases BICC GENERAL CABLE
28283
ESI SOFTWARE SA
CHALMERS TEKNISKA HOEGSKOLA
COLOPLAST A/S MTU AERO ENGINES
25525 DAIMLER CHRYSLER AG
V. Batagelj FRAUENHOFER INST. FUER
PRODUKTIONSTECH. UND AUTOMATISIERUNG EADS DE UND RAUMFAHRT E.V.
BUURSKOV
DE ZENTRUM FUER LUFT
EA TECH. LTD
VOLKSWAGEN AG
506503
LMS UMWELTSYS.E, DIPL. ING. DR. HERBERT BACK MECALOG SARL
BAE SYSTEMS 506257
EUROCOPTER S. INST. NAT. DE RECHERCHE
SUR LES TRANSPORTS ET LEUR SCURIT
IST-2000-29207 AIRBUS UK LIMITED DASSAULT AVIATION
TESSITURA LUIGI SANTI SPA
Two mode INST. FUER TEXTIL UND
VERFAHRENSTECH. DENKENDORF
AIRBUS DEUTSCHLAND
502917
SNECMA MOTEURS SA INST. SUPERIOR TECNICO
C. R. FIAT S.C.P.A.
KBC MANUFAKTUR, KOECHLIN, 502909
networks BAUMGARTNER UND CIE. AG
NAT. TEC. UNIV. OF ATHENS NL ORG. FOR APPLIED
SCIENTIFIC RESEARCH - TNO
502842
29817 AIRBUS FRANCE SAS BARTENBACH
TRUMPF-BLUSEN-KLEIDER ALENIA AERONAUTICA SPA 501084
WALTER GIRNER UND CO. KG
Multiplication BARCO NV G4RD-CT-2002-00836
STICHTING NATIONAAL LUCHT
G4MA-CT-2002-00022
POLYMAGE SARL
MSO CONCEPT INNOVATION + SOFTWARE OFFICE NAT. DETUDES ET ROSENHEIMER GLASTECH.
DE REC. AEROSPATIALES
Derived 7210-PR/163
BRPR987001
G4RD-CT-2001-00403
502896
G4RD-CT-2000-00178 ENK6-CT-2002-30023
G4RD-CT-2002-00795 RUDOLF BRAUNS AND CO. KG
networks 7215-PP/031
CENTRE DE RECH. METALLURG. 502889 SHERPA ENGINEERING SARL
G4RD-CT-2000-00395 CATALYSE SARL
7210-PR/233 VOEST-ALPINE STAHL
Pajek INST. DE RECHERCHES
DE LA SIDERURGIE FR
THYSSENKRUPP STAHL A.G.
EVG3-CT-2002-80012
T3.2/99 DISENO DE SISTEMAS EN SILICIO
CENTRE FOR EUROP. ECONOMIC
SMT4982223 ILEVO AB
FONDAZIONE ENI - ENRICO MATTEI
7210-PR/095
CSTB IST-2001-35358
JERNKONTORET HPSE-CT-2002-00108
UNIV. DER BUNDESWEHR MUENCHEN
BUILDING RESEARCH CHIPIDEA - MICROELECTRONICA, S.A.
ENEL.IT UNIV. PANTHEON-ASSAS - PARIS II
LANDIS & GYR - EUROPE AG
OESTERREICHISCHER BERGRETTUNGSDIENST SSAB TUNNPL¯T
IFEN GES. FUER SATELLITENNAVIGATION 7215-PP/034 RESEARCH INST. OF THE FINNISH ECONOMY
JOE3980089
WYKES ENGINEERING COMPANY LH AGRO EAST S.R.O. QLK6-CT-2002-02292
IST-2000-30158
TECHNOFARMING S.R.L. T3.5/99 THE AARHUS SCHOOL OF BUSINESS
MEFOS, FOUNDATION FOR
CINAR LTD. HELP SERVICE REMOTE SENSING METALLURGICAL RESEARCH
INST. CARTOGRAFIC DE CATALUNYA
HPSE-CT-2002-00143
LESPROJEKT SLUZBY S.R.O.
BAYER. ROTES KREUZ ENERGY RESEARCH CENTRE NL
IST-2000-28177 BRITISH STEEL UNIV. OF MACEDONIA
7210-PR/142
JOR3980200
FRAUENHOFER INST. FUER AGRO-SAT CONSULTING
MATERIALFLUSS UND LOGISTIK DATASYS S.R.O.
ENK5-CT-2000-00335 UNIV. OF ABERDEEN
ORAD HI TEC SYS. POLAND CENTRE DE ROBOTIQUE
CRE GROUP LTD. MJM GROUP, A.S. FRIMEKO INT. AB
BBL INOX PNEUMATIC AS
DFA DE FERNSEHNACHRICHTEN AGENTUR
TPS TERMISKA PROCESSER AB
KOMMANDITGES. HAMBURG 1 PROLEXIA
FERNSEHEN BETEILIGUNGS & CO A.S.M. S.A. ZAMISEL D.O.O INGENIORHOJSKOLEN HELSINGOR TEKNIKUM IST-1999-56418
DPME ROBOTICS AB
GATE5 AG INDUSTRIAS ROYO
511758
LKSOFTWARE UAB LKSOFT BALTIC BRST985352
SUPERELECTRIC DI
IST-2000-30082 SVETS & TILLBEHOR AB CARLO PAGLIALUNGA & C. SAS
ALBERTSEN & HOLM AS
WISDOM TELE VISION SPORTART IST-1999-57451
OK GAMES DI ALESSANDRO CARTA
ASM - DIMATEC INGENIERIA
FFT ESPANA TECH. DE AUTOMOCION, ENERGITEKNIK HEATEX AB
UNIV. DE ZARAGOZA
YAHOO! DEOSAUHING EETRIUKSUS BROD THOMASSON
EDAG ENGINEERING + DESIGN GUNNESTORPS SMIDE & MEKANISKA AB Pajek
V. Batagelj Networks from data bases

15. Collaboration networks
Networks from
data bases Let WA be the works × authors two mode network; wapi ∈ {0, 1} is
V. Batagelj describing the authorship of author i of work p.
Two mode
networks
wapi = deg(p) = # of authors of work p
i∈A
Multiplication
Derived Let N be its normalized version, ∀p ∈ W : i∈A npi = 1, obtained
networks
from WA by npi = wapi / deg(p), or by some other rule determining
Pajek the author’s contribution.
The first collaboration network Co = WAT ∗ WA
coij = wapi wapj = 1
p∈W p∈N(i)∩N(j)
coij = the number of works that authors i and j wrote together.
Problem: The Co network is composed of complete graphs on the
set of work’s authors. Works with many authors produce large
complete subgraphs.
V. Batagelj Networks from data bases

16. Cores of orders 10–21 in Computational Geometry
Networks from
data bases
V. Batagelj C.Zelle
H.A.El-Gindy S.P.Fekete
M.E.Houle
J.Czyzowicz M.L.Demaine P.Belleville V.Sacristan
K.R.Romanik
Two mode I.Streinu H.Everett
D.H.Rappaport
F.Hurtado H.Meijer
networks A.Lubiw
D.Bremner
G.Liotta
T.C.Shermer
B.Zhu D.M.Avis
W.J.Lenhart S.S.Skiena D.M.Mount
Multiplication T.C.Biedl
P.K.Bose E.M.Arkin
M.J.vanKreveld G.T.Toussaint
S.M.Robbins J.Urrutia J.S.B.Mitchell G.T.Wilfong
M.Yvinec S.H.Whitesides O.Aichholzer
Derived J-M.Robert
E.D.Demaine
O.Devillers
M.T.deBerg Te.Asano
S.Lazard N.Katoh
networks T.Roos
D.L.Souvaine
M.H.Overmars J-R.Sack H.Alt
I.G.Tollis
M.Teillaud G.Rote H.Imai
R.Seidel J.O’Rourke M.T.Goodrich
Pajek J-D.Boissonnat J.Erickson S.Suri
D.Halperin
J.S.Vitter N.M.Amato
M.Sharir
K.Mehlhorn R.Pollack B.Chazelle D.Z.Chen
S-W.Cheng
R.Wenger J.S.Snoeyink
O.Schwarzkopf J.E.Hershberger
P.K.Agarwal R.Tamassia R.L.S.Drysdale
J.Pach F.P.Preparata Q.Huang
E.Welzl
L.J.Guibas K.Kedem S.J.Fortune
J.C.Clements J.Matousek H.S.Sawhney
D.Eppstein C-K.Yap D.G.Kirkpatrick
S.A.Mitchell B.Aronov J.Ashley
D.White E.Trimble D.P.Dobkin
H.Edelsbrunner F.Aurenhammer D.T.Lee
M.W.Bern D.Steele
W.J.Bohnhoff L.P.Chew A.Aggarwal
R.R.Lober S.R.Kosaraju
G.D.Sjaardema T.K.Dey N.Amenta P.Yanker D.Petkovic
G.Lerman
T.J.Wilson L.Lopez-Buriek P.Plassmann J.Hass
J.R.Hipp E.Sedgwick C.K.Johnson M.Gorkani
M.Flickner
W.R.Oakes J.Harer D.Letscher C.Grimm
T.J.Tautges A.Hicks
S.Parker
D.Zorin
T.L.Edwards
J.Weeks W.Niblack J.Hafner
S.E.Benzley
B.Dom
T.D.Blacker M.Whitely
V. Batagelj Networks from data bases

17. pS -core at level 46 of Computational Geometry
Networks from
data bases E.Arkin
V. Batagelj J.Mitchell I.Tollis A.Garg
M.Bern L.Vismara
D.Eppstein
G.diBattista
M.Goodrich
Two mode R.Tamassia
networks G.Liotta
D.Dobkin S.Suri J.O’Rourke
J.Vitter
Multiplication
J.Hershberger
Derived
networks B.Chazelle
R.Seidel B.Aronov L.Guibas
F.Preparata
J.Snoeyink
H.Edelsbrunner
Pajek M.Sharir P.Agarwal
R.Pollack
J.Pach D.Halperin P.Gupta
M.Smid R.Janardan
E.Welzl M.Overmars P.Bose
J.Boissonnat
M.vanKreveld O.Devillers
J.Matousek J.Majhi
M.Yvinec
C.Yap M.deBerg
J.Schwerdt
O.Schwarzkopf G.Toussaint M.Teillaud
J.Czyzowicz
J.Urrutia
C.Icking
R.Klein
V. Batagelj Networks from data bases

18. Second collaboration network
Networks from
data bases
V. Batagelj
The second collaboration network Cn = WAT ∗ N
Two mode
networks
cnij = bip npj = npj
Multiplication p∈W p∈N(i)∩N(j)
Derived
networks
cnij = contribution of author j to works, that (s)he wrote together with the
author i.
Pajek
It holds bip npj = deg(p) and cnij = deg(i)
j∈A j∈A j∈A
cnii = npi is the contribution of author i to his/her works.
p∈N(i)
cnii
Self-sufficiency: Si =
deg(i)
Collaborativness (co-authorship index): Ki = 1 − Si
V. Batagelj Networks from data bases

19. The ”best” authors in Statistics
Networks from
data bases
V. Batagelj name contrib pap self collab
1. Burt R 83.716667 96 0.872049 0.127951
2. Newman M 59.533333 87 0.684291 0.315709
3. Doreian P 59.070408 75 0.787605 0.212395
Two mode 4. Bonacich P 45.416667 59 0.769774 0.230226
5. Marsden P 41.000000 50 0.820000 0.180000
networks 6. White H 39.986111 51 0.784041 0.215959
7. Wellman B 38.754762 57 0.679908 0.320092
Multiplication 8. Friedkin N 36.333333 40 0.908333 0.091667
9. Leydesdo L 34.533333 47 0.734752 0.265248
Derived 10. Borgatti S 30.469048 57 0.534545 0.465455
11. Freeman L 30.250000 36 0.840278 0.159722
networks 12. Everett M 27.450000 45 0.610000 0.390000
13. Litwin H 26.166667 32 0.817708 0.182292
Pajek 14. Snijders T 23.920408 42 0.569534 0.430466
15. Skvoretz J 23.691667 39 0.607479 0.392521
16. Breiger R 23.520408 30 0.784014 0.215986
17. Krackhar D 22.031519 35 0.629472 0.370528
18. Valente T 21.616667 44 0.491288 0.508712
19. Barabasi A 18.755159 42 0.446551 0.553449
20. Mizruchi M 18.333333 25 0.733333 0.266667
21. Carley K 17.616667 35 0.503333 0.496667
22. Cohen C 17.111111 32 0.534722 0.465278
23. Moody J 16.916667 22 0.768939 0.231061
24. Rothenbe R 16.492063 40 0.412302 0.587698
25. Pattison P 16.483333 34 0.484804 0.515196
26. Batagelj V 16.353741 29 0.563922 0.436078
27. Lazega E 16.000000 20 0.800000 0.200000
28. Latkin C 15.896032 49 0.324409 0.675591
29. Wasserma S 15.803741 33 0.478901 0.521099
30. Berkman L 15.767857 36 0.437996 0.562004
V. Batagelj Networks from data bases

20. Third collaboration network
Networks from
data bases
V. Batagelj
Two mode
The third collaboration network Ct = NT ∗ N
networks ctij = the total contribution of collaboration of authors i and j
Multiplication
to works.
Derived
networks
It holds ctij = ctji , i∈A j∈A ctij = |W | and
Pajek
i∈A j∈A npi npj = 1 – the total contribution of a complete
subgraph corresponding to the authors of a work is 1.
ctij = npi is the total contribution of author i to works
j∈A p∈W
from W .
V. Batagelj Networks from data bases

21. Components in SN5 cut at level 0.5
Networks from
Network SN5 (2008): for "social network*" + most frequent references + around 100 social networkers;
data bases
|W | = 193376, |C | = 7950, |A| = 75930, |J| = 14651, |K | = 29267
V. Batagelj
Jackson_M Muth_S
Kogovsek_T Park_J
Mrvar_A Demeneze_M
Ferligoj_A Krackhar_D
Calvo-Ar_A
Two mode Batagelj_V Moore_C
Leinhard_
Rothenbe_R
networks Woodard_K Newman_M Kilduff_M
Doreian_P Zenou_Y
Barabasi_A Holland_P Potterat_J
Gastner_M
Watts_D
Multiplication Willer_DHummon_N Albert_R
Balkundi_P
Girvan_M Leinhard_S
Derived Fararo_T
Parker_A Jeong_H Mccarty_C
Shelley_G
Landau_R
networks Galaskie_J
Skvoretz_J Cross_R Killwort_P
Farquhar_M
Sherman_S
Faust_K Anderson_C Litwin_H
Borgatti_S
Pajek Knowlton_A Hua_W
Bernard_H Bowling_A
Wasserma_S Robins_G Teresi_J
Latkin_C Shiovitz_S
Pattison_P Sokolovs_J
Iacobucc_D Everett_M Browne_P
Cohen_C
Hopkins_N Mandell_W Grundy_E
Boyd_J Davey-Ro_M
Breiger_R
Holmes_D
Steinhau_H Bonacich_P Bjorkman_T Hawkins_J
Masuda_N Chou_K Grabowsk_A Suitor_J Braha_D
Metzke_C Bienenst_E Hansson_L Konno_N Fraser_M Bar-Yam_Y
Chi_I Kosinski_R Pillemer_K
Sundquis_J Ennett_S Wellman_B Boyack_K Ostergre_P
Johnson_C Jolly_A Laumann_E Fingerma_K
Johansso_S Bauman_K Klavans_R
Hampton_K Barer_B Marsden_P Hanson_B
Wylie_J Birditt_K
Carley_K Yang_H Farmer_T Stauffer_D Leydesdo_L
Morris_M Foster_B Carter_W
Banks_D Tang_J Weisbuch_G Vandenbe_P
Rodkin_P Kretzsch_M Seidman_S Feld_S
Gronlund_A
Vespigna_A
Bell_D Neaigus_A Keeling_M
Feiring_C
Berkman_L
Degenne_A Weisner_C Krause_N
Shaw_B
Newton_J
Wallace_D Wallace_RV. Batagelj Networks from data bases
Solomon_P Draine_J
Ohtsuki_H Lindstro_D
Lin_N Kimura_M Saito_K Holme_P
Schneide_J Borlund_P

22. Authors’ citations network
Networks from
data bases
V. Batagelj
Two mode
networks
i
Multiplication was,i s
Derived
networks
Pajek cis,t j
wat,j
t
A T
A
WA W Ci W WA
Ca = WAT ∗ Ci ∗ WA is a network of citations between
authors. The weight w (i, j) counts the number of times a work
authored by i is citing a work authored by j.
V. Batagelj Networks from data bases