# Two-mode networks and multiplication

## Transcription

Two-mode networks and multiplication
```Two-mode
V. Batagelj
Direct
methods
2-mode cores
Introduction to Network Analysis using Pajek
7. Two-mode networks and multiplication
4-ring weights
Multiplication
Kinship
relations
Vladimir Batagelj
Projections
Collaboration
Other derived
networks
EU projects
University of Ljubljana
Phd program on Statistics
University of Ljubljana, 2016
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Outline
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
1
2
3
4
5
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7
8
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Direct methods
2-mode cores
4-ring weights
Multiplication
Kinship relations
Projections
Collaboration
Other derived networks
EU projects
Josh On: They rule 2004
Other derived
networks
EU projects
e-mail: [email protected]
wiki: http://vladowiki.fmf.uni-lj.si/doku.php?id=pajek:ev:pde
version: March 1, 2016
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Two-mode networks
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
In a two-mode network N = (U, V, L, P, W) the set of vertices
consists of two disjoint sets of vertices U and V, and all the lines
from L have one end-vertex in U and the other in V. Often also a
weight w : L → R ∈ W is given; if not, we assume w (u, v ) = 1 for
all (u, v ) ∈ L.
A two-mode network can also be described by a rectangular matrix
A = [auv ]U ×V .
(
wuv
(u, v ) ∈ L
auv =
0
otherwise
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Examples: (persons, societies, years of membership),
(buyers/consumers, goods, quantity),
(parlamentarians, problems, positive vote),
(persons, journals, reading),
(papers, keywords, is described by), etc.
3 / 65
Deep South
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Classical example of two-mode network are the Southern women (Davis
1941).
Davis.paj. Freeman’s overview.
Multiplication
Kinship
relations
Projections
Collaboration
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networks
EU projects
4 / 65
Approaches to two-mode network analysis
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
The usual approach to analyze a two-mode network is to
transform it to a one-mode network and use standard methods
on it.
For direct analysis of two-mode networks we can use the
eigen-vector approach – a two-mode variant of Kleinberg’s
hubs and authorities. The weight vector (x, y) on U ∪ V is
determined by relations y = Ax and x = AT y.
Network/2-Mode Network/Important Vertices
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There are also special methods for clustering and
blockmodeling in two-mode networks.
In this lecture we will present two additional direct methods:
two-mode cores and 4-rings.
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Internet Movie Database http://www.imdb.com/
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
EU projects
12th Annual Graph Drawing Contest, 2005. The IMDB network is two-mode and
has 1324748 = 428440 + 896308 vertices and 3792390 arcs.
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Two-mode cores
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
EU projects
The subset of vertices C ⊆ V is a (p, q)-core in a two-mode
network N = (V1 , V2 ; L), V = V1 ∪ V2 iff
a. in the induced subnetwork K = (C1 , C2 ; L(C )),
C1 = C ∩ V1 , C2 = C ∩ V2 it holds ∀v ∈ C1 : degK (v ) ≥ p
and ∀v ∈ C2 : degK (v ) ≥ q ;
b. C is the maximal subset of V satisfying condition a.
Properties of two-mode cores:
• C (0, 0) = V
• K(p, q) is not always connected
• (p1 ≤ p2 ) ∧ (q1 ≤ q2 ) ⇒ C (p1 , q1 ) ⊆ C (p2 , q2 )
• C = {C (p, q) : p, q ∈ N}. If all nonempty elements of C
are different it is a lattice.
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Algorithm for two-mode cores
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
EU projects
To determine a (p, q)-core the procedure similar to the ordinary
core procedure can be used:
repeat
remove from the first set all vertices of degree less than p,
and from the second set all vertices of degree less than q
until no vertex was deleted
It can be implemented to run in O(m) time.
Interesting (p, q)-cores? Table of cores’ characteristics
n1 = |C1 (p, q)|, n2 = |C2 (p, q)| and k – number of components
in K(p, q):
• n1 + n2 ≤ selected threshold
• ’border line’ in the (p, q)-table.
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Table (p, q : n1 , n2 ) for Internet Movie Database
Two-mode
V. Batagelj
Network/2-Mode Network/Core/2-Mode Border
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
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networks
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1 1590: 1590
1 | 16 39:
2 516: 788
3 | 17 35:
3 212: 1705 18 | 18 32:
4 151: 4330 154 | 19 30:
5 131: 4282 209 | 20 28:
6 115: 3635 223 | 21 26:
7 101: 3224 244 | 22 24:
8
88: 2860 263 | 24 23:
9
77: 3467 393 | 27 22:
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69: 3150 428 | 29 20:
11
63: 2442 382 | 32 19:
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56: 2479 454 | 35 18:
13
50: 3330 716 | 36 17:
14
46: 2460 596 | 39 16:
15
42: 2663 739 | 42 15:
2173
2791
2684
2395
2216
1988
1854
34
31
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995
1080
1063
1087
1087
1153
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| 1334
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14:
13:
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9:
8:
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5:
4:
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1:
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95
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34 162
31 177
29 198
22 203
7 114
6 137
8 258
3 186
2 247
1 1334
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(247,2)-core and (27,22)-core
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Survivor Series
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relations
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10 / 65
(2,516)-Hard core
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
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networks
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Nasty Lovers
Naked Truth, The
Naked Ambition
Naked and Nasty
Mystic Pieces
Mystery of the Golden Lotus
Muff ’n’ Jeff
Motel Sex
More Than Friends
Moonstroked
Model Wife
Miscreants
Mirage 2
Mirage
Mind Shadows 2
Mind Shadows
Midslumber’s Night Dream
Midnight Pink
Midnight Hour, The
Megasex
Matter of Size, A
Masque
Mark of Zara
Marilyn Whips Wallstreet
Manbait 2
Manbait
Man Who Loves Women, The
Make My Wife, Please
Make My Night
Make Me Want It
Magic Shower, The
Lust in the Fast Lane
Lust College
Lust Bug, The
Lust at the Top
Luscious Lucy in Love
Lucky Break
Lovin’ USA
Lovers, The
Love Lessons
Love Ghost
Love Bites
Loose Morals
Loose Ends III
Loose Ends II
Loose Ends
Loads of Fun 4
Little Romance
Like a Virgin
Life and Loves of Nikki Charm
Let’s Play Doctor
Legend of Barbi-Q and Little Fawn, The
Laying the Ghost
Latin Lust
Last Temptation, The
Lascivious Ladies of Dr. Lipo, The
Laid Off
Lady in Red, The
KSEX 106.9
Kiss, The
Kiss My Asp
Kinky Vision 2
Kinky Couples
Kinky
Keyhole Video #114: Christy Canyon Special
Kascha and Friends
Just Another Pretty Face
Juicy Sex Scandals
Juicy Lucy
Jezebel
Jaded Love
It’s My Body
Interactive
Insatiable
Inferno
Indecent Itch
Indecent Exposures
Inches for Keisha
In Search of the Golden Bone
Immaculate Erection
Images of Desire
I Want It All
I Touch Myself
I Like to Be Watched
I Dream of Christy
Hunger, The
House On Chasey Lane
House of the Rising Sun
House of Sleeping Beauties 2
House of Sleeping Beauties
House of Blue Dreams
Hottest Ticket
Hothouse Rose Part 1
Hotel Sodom
Hotel Paradise
Hotel Fantasy
Hot Wired
Hot Tight Asses 9
Hot Tight Asses 8
Young Nurses In Lust
Young Girls in Tight Jeans
Young and Naughty
Year of the Sex Dragon, The
XTV 2
XTV 1
X-rated Bloopers and Outtakes
X-rated Blondes
X Dreams
Wrapped Up
WPINK-TV 3
Woman in Pink, The
Within and Without You
With Love from Susan
With Love from Ginger
Witching Hour, The
Wire Desire
Wings of Passion
Willing Women
Wild Women 61: Rachel Ryan
Wild Women 32: Summer Rose
Wild Women 11: Tanya Foxx
Wild Weekend
Wild in the Wilderness
Wild Buck
Wild Bananas On Butt Row
Wild and Wicked 3
Wicked Whispers
Wicked Ways #2
Wicked One
Wicked As She Seems
Whore, The
Whore of the Worlds
Whore House
Who Killed Holly Hollywood?
White Bunbusters
Whispered Lies
Where the Sun Never Shines
What Gets Me Hot!
Wet Dreams Reel Fantasies
West Coast Girls
We Love to Tease
Way They Were, The
Wacky World of X-Rated Bloopers
Voyeur, The
Voyeur’s Favorite Blowjobs and Anals 8, The
Voodoo Lust: The Possession
Visions of Desire
Virgin Dreams
Video Tramp
Victoria and Company
Vegas: Snake Eyes
Vagina Town
Up Your Ass 5
Up ’n Coming
Unforgivable
Unchain My Heart
Unbelievable Orgies
Turnabout
True Legends of Adult Cinema: The Modern Video Era
True Legends of Adult Cinema: The Erotic 80’s
Trashy Lady
Tracie Lords
Toys 4 Us 2
Touch of Mischief
Touch Me
Torrid Without a Cause
Top It Off
Top 25 Adult Stars of All Time, The
Too Good to Be True
Tomboy
To the Rear
Tits Ahoy
Tip of the Tongue
Tight Squeeze
Tight Ends in Motion
Thrill Street Blues
Three-way Lust
Three by Three
Those Lynn Girls
This Is Your Sex Life
Texas Crude
Terms of Endowment
Terminal Case of Love
Temptation Eyes
Teasers
Tease, The
Tawnee Be Good
Taste of Victoria Paris
Taste of Tawnee, A
Taste of Ariel
Tarnished Knight
Talk Dirty to Me, Part III
Talk Dirty to Me 9
Takin’ It to the Limit
Take My Wife, Please!
Take Me
Tailspin 1
Tails of Perversity 3
Tails of Perversity 2
Tails of Perversity
Tailiens 2
Tailiens
Tailhouse Rock
Tailgunners
Swedish Erotica 74
Swedish Erotica 56
Swedish Erotica 54
Surfside Sex
Superstars of Sex: Racquel Darrian
Super Tramp
Super Groupie
Sunny After Dark
Summer Break
Sugarpussy Jeans
Suburban Swingers 2
Street Walkers
Strange Sex in Strange Places
Stiff Competition 2
Stiff Competition
Starting Over
Starr
Star, The
Star Cuts 4: Ginger Lynn
Star Cuts 39: Trinity Loren
Star Cuts 37: Buffy Davis
Star 85
Splendor in the Ass
Splash Shots
Spies
Spermbusters
Spellbound
Spectacular Orgasms
Sorority Pink 2: The Initiation
Sophisticated Lady
Sodomania: The Baddest of the Best
Sodomania: Slop Shots 1
Sodomania 18
Sodomania 13
Snatched
Smart Ass, The
Smart Ass Returns, The
Slumber Party
Sloppy Seconds
Slip of the Tongue
Slip Into Ginger and Amber
Slightly Used
Sleeping with Everybody
Slave to Love
Sky Foxes
Skin Games
Sister Dearest
Sindy Does Anal Again
Simply Kia
Simply Blue
Shot From Behind
Sheila’s Deep Desires
Shayla’s Gang
Shaved Pink
Shane’s World
Sexy Secrets N 1
Sexy and 18
Sexual Fantasies
Sextectives
Sexpertease
Sex Toys
Sex Stories
Sex Sluts in the Slammer
Sex Shoot
Sex Plays
Sex Maniacs
Sex Fifth Avenue
Sex Busters
Sex Beat
Sex Appraisals
Sex Academy 2: The Art of Talking Dirty
Sex 3: After Seven
Sensual Exposure
Seeing Red
Seducers, The
Secret of Her Suckcess
Secret Life of Nina Hartley, The
Secret Fantasies 4
Secret Fantasies 3
Screaming Rage
Scarlet Woman, The
Scarlet Bride, The
Savanah Unleased
Satyr
Satin Seduction
Sabotage
Ruthless Affairs
Royals: Ginger Lynn
Roll-x Girls
Rocky Porno Video Show, The
Rising, The
Rise of the Roman Empress 2
11 / 65
IMDB cores / Pajek commands
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
See How to deal with very large networks?
Options/Read-Write/Read-Save vertices labels [Off]
Read/Network [IMDB.net] 1:40
Info/Memory
Network/2-Mode Network/Core/2-Mode Review
Network/2-Mode Network/Core/2-Mode [27 22]
Info/Partition
Operations/Network+Partition/Extract Subnetwork [Yes 1]
Network/2-Mode Network/Partition into 2 Modes
Network/Create New Network/Transform/Add/Vertex Labels/
from File(s) [IMDB.nam]
Draw/Network+First Partition
Layers/in y direction
Options/Transform/Rotate 2D [90]
EU projects
12 / 65
k-rings
Two-mode
V. Batagelj
Direct
methods
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
2-mode cores
Since for each eadge e of a complete
graph Kr , r ≥ k ≥ 3 we have wk (e) =
(r − 2)!/(r − k)! the edges belonging
to cliques have large weights. Therefore
these weights can be used to identify the
dense parts of a network.
The k-rings can be efficiently determined only for small values of k – 3,
4, 5.
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
EU projects
Complete graph K5
On the k-rings we can also base the notion of short cycle connectivity
which provides us with another decomposition of networks.
13 / 65
4-rings and analysis of two-mode networks
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
In two-mode network there are no 3-rings. The densest
substructures are complete bipartite subgraphs Kp,q . They
contain many 4-rings.
There are
p
q
1
= p(p − 1)q(q − 1)
2
2
4
4-rings in Kp,q ; and each of its edges
e has weight
w4 (e) = (p − 1)(q − 1)
EU projects
Network/Create New Network/with Ring Counts.../4-Rings/Undirected
14 / 65
Directed 4-rings
Two-mode
V. Batagelj
There are 4 types of directed 4-rings:
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
EU projects
cyclic
transitive
genealogical
diamond
In the case of transitive rings Pajek provides a special weight
counting on how many transitive rings the arc is a shortcut.
Network/Create New Network/with Ring Counts/4-Rings/Directed
15 / 65
Simple line islands in IMDB for w4
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
EU projects
We obtained 12465 simple line islands on 56086 vertices. Here
is their size distribution.
Size Freq
Size Freq
Size Freq
Size Freq
-------------------------------------------------------2 5512
20
19
38
4
59
2
3 1978
21
18
39
3
61
1
4 1639
22
15
40
2
64
1
5
968
23
9
42
2
67
1
6
666
24
13
43
3
70
1
7
394
25
12
45
3
73
1
8
257
26
6
46
4
76
1
9
209
27
6
47
5
82
1
10
148
28
5
48
1
86
1
11
118
29
6
49
2
106
1
12
87
30
3
50
2
122
1
13
55
31
6
51
1
135
1
14
62
32
5
52
2
144
1
15
46
33
3
53
1
163
1
16
39
34
1
54
2
269
1
17
27
35
5
55
1
301
1
18
28
36
4
57
1
332
2
19
29
37
7
58
1
673
1
-------------------------------------------------------16 / 65
Example: Islands for w4
Charlie Brown and Adult
Two-mode
V. Batagelj
Morgan, Jonathan (I)
Kesten, Brad
Direct
methods
Brando, Kevin
Robbins, Peter (I)
Shea, Christopher (I)
Altieri, Ann
2-mode cores
Ornstein, Geoffrey
4-ring weights
Multiplication
Kinship
relations
Dough, Jon
Sanders, Alex (I)
North, Peter (I)
Michaels, Sean
Race for Your Life, Charlie Brown
Be My Valentine, Charlie Brown
Mendelson, Karen
Horner, Mike
It’s Magic, Charlie Brown
Dryer, Sally
Melendez, Bill
You’re a Good Sport, Charlie Brown
Drake, Steve (I)
It’s a Mystery, Charlie Brown
It’s an Adventure, Charlie Brown
Byron, Tom
Silvera, Joey
It’s Flashbeagle, Charlie Brown
Play It Again, Charlie Brown
Momberger, Hilary
EU projects
Voyeur, Vince
Reilly, Earl ’Rocky’
Charlie Brown Celebration
You Don’t Look 40, Charlie Brown
He’s Your Dog, Charlie Brown
Making of ’A Charlie Brown Christmas’
You’re In Love, Charlie Brown
It’s the Great Pumpkin, Charlie Brown
Charlie Brown’s All Stars!
Life Is a Circus, Charlie Brown
Boy Named Charlie Brown
Other derived
networks
Davis, Mark (V)
Hauer, Brent
Projections
Collaboration
Boy, T.T.
Charlie Brown and Snoopy Show
Charlie Brown Christmas
Stratford, Tracy
Schoenberg, Jeremy
West, Randy (I)
Is This Goodbye, Charlie Brown?
Charlie Brown Thanksgiving
There’s No Time for Love, Charlie Brown
Jeremy, Ron
You’re Not Elected, Charlie Brown
Snoopy Come Home
It’s the Easter Beagle, Charlie Brown
Wallice, Marc
Savage, Herschel
Thomas, Paul (I)
Shea, Stephen
Pajek
Pajek
17 / 65
Example: Islands for w4
Mark Twain and Abid
Two-mode
Sergeant Madden
V. Batagelj
Honky Tonk
Sawak nus el lail
Hoodlum Saint, The
Roaring Twenties, The
Direct
methods
2-mode cores
Soltan, Hoda
Malak el zalem, El
Rostom, Hind
Unconquered
Union Pacific
Phelps, Lee (I)
Flavin, James
Big City
Star Is Born, A
4-ring weights
Dunn, Ralph
Multiplication
Tarik el saada
Hub fil zalam
San Quentin
You Can’t Take It with You
Vogan, Emmett
Chandler, Eddy
Flowers, Bess
Hamama, Faten
O’Connor, Frank (I)
Kinship
relations
Hamdi, Imad
Whole Town’s Talking, The
Ard el ahlam
Sullivan, Charles (I)
Nancy Drew... Reporter
Dust Be My Destiny
Projections
Sarhan, Shukry
Port Said
Riad, Hussein
Saum, Cliff
Wells Fargo
Shawqi, Farid
Meet John Doe
Holmes, Stuart
Baad al wedah
Massiada, Al
Asrar el naas
Baba Amin
Beyt al Taa
Haked, El
Osta Hassan, El
Ibn al ajar
Ana bint min?
Murra kulshi, El
Mohtal, El
Zalamuni el habaieb
Ashki limin?
Ana zanbi eh?
Castle on the Hudson
Valley of the Giants
Collaboration
Racket Busters
Kid Galahad
Go Getter, The
Other derived
networks
They Made Me a Criminal
Women in the Wind
Mower, Jack
Man Who Talked Too Much, The
Naughty But Nice
Yankee Doodle Dandy
EU projects
Kid From Kokomo, The
King of the Underworld
They Drive by Night
Secret Service of the Air
Bad Men of Missouri
Adventures of Mark Twain, The
Knockout
Fatawa, El
El Dekn, Tewfik
Smashing the Money Ring
Sittat afarit, alFatat el mina
Hareb min el ayyam
Abu Hadid
Elf laila wa laila
Souk el selah
Nashal, El
Maktub alal guebin
Fatawat el Husseinia
Amir el antikam
Abid el gassad
Ghaltet ab
Abu Dahab
Aguazet seif
Hamida
Batal lil nehaya
Namrud, El
Ebn el-hetta
Nassab, El
Zoj el azeb, El
Abid el mal
Cass el azab
Ghazal al-banat
Rasif rakam khamsa
Laab bil nar, El
Iskanderija... lih?
Imlak, El
Matloub zawja fawran
El-Meliguy, Mahmoud
Abu Ahmad
Pajek
18 / 65
Example: Island for w4
Polizeiruf 110 and Starkes Team
Two-mode
Maranow, Maja
Starkes Team, Ein
V. Batagelj
Starkes Team - Eins zu Eins, Ein
’Affre Semmeling, Die’
Direct
methods
2-mode cores
Starkes Team - Kollege Mrder, Ein
Starkes Team - Sicherheitsstufe 1, Ein
Martens, Florian
Starkes Team - Erbarmungslos, Ein
4-ring weights
Starkes Team - Das Bombenspiel, Ein
Polizeiruf 110 - Ein Bild von einem Mrder
Polizeiruf 110 - Kopf in der Schlinge
Polizeiruf 110 - Zerstrte Trume
Polizeiruf 110 - Angst um Tessa Blow
Polizeiruf 110 - Rosentod
Starkes Team - Blutsbande, Ein
Polizeiruf 110 - Doktorspiele
Starkes Team - Tdliche Rache, Ein
Polizeiruf 110 - Jugendwahn
Starkes Team - Der Mann, den ich hasse, Ein
Polizeiruf 110 - Heikalte Liebe
Multiplication
Kinship
relations
Starkes Team - Kindertrume, Ein
Starkes Team - Mrderisches Wiedersehen, Ein
Lansink, Leonard
Starkes Team - Auge um Auge, Ein
Schwarz, Jaecki
Starkes Team - Lug und Trug, Ein
Starkes Team - Der letzte Kampf, Ein
Polizeiruf 110 - Todsicher
Polizeiruf 110 - Der Spieler
Polizeiruf 110 - Mordsfreunde
Starkes Team - Kleine Fische, groe Fische, Ein
Projections
Starkes Team - Roter Schnee, Ein
Starkes Team - Der Todfeind, Ein
Starkes Team - Mordlust, Ein
Collaboration
Other derived
networks
Winkler, Ein
Wolfgang
Starkes Team - Das groe Schweigen,
Starkes Team - Der schne Tod, Ein
Bademsoy, Tayfun
Starkes Team - Der Verdacht, Ein
Starkes Team - Trume und Lgen, Ein
Polizeiruf 110 - Kurschatten
Polizeiruf 110 - Tote erben nicht
Polizeiruf 110 - Der Pferdemrder
Polizeiruf 110 - Henkersmahlzeit
Starkes Team - Bankraub, Ein
Starkes Team - Verraten und verkauft, Ein
EU projects
Starkes Team - Braunauge, Ein
Starkes Team - Im Visier des Mrders, Ein
Starkes Team - Die Natter, Ein
Lerche, Arnfried
19 / 65
5-rings
Two-mode
V. Batagelj
Direct
methods
In the future we intend to implement in Pajek also weights w5 .
Again there are only 4 types of directed 5-rings.
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
cyclic
transitive
????
????
EU projects
20 / 65
Two mode networks from data tables
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
EU projects
A data table T is a set of records T = {Tk : k ∈ K}, where K is the set of
keys. A record has the form Tk = (k, q1 (k), q2 (k), . . . , qr (k)) where qi (k)
is the value of the property (attribute) qi for the key k.
21 / 65
. . . Two mode networks from data tables
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Suppose that the property q has the range 2Q . For example:
Authors(SNA) = { S. Wasserman, K. Faust },
PubYear(SNA) = { 1994 },
Keywords(SNA) = { network, centrality, matrix, . . . }, . . .
If Q is finite (it can always be transformed into such set by partitioning the
set Q and recoding the values) we can assign to the property q a
two-mode network K × q = (K, Q, E, w ) where (k, v ) ∈ E iff v ∈ q(k), and
w (k, v ) = 1.
...
Projections
Collaboration
Other derived
networks
EU projects
...
GenCores
Islands
ESNA2
IFCS09
SNA
...
Bata
gelj
Faust
1
1
1
1
de
Nooy
Kej
žar
Kore
njak
Mrvar
Wasse
rman
Zaver
šnik
...
1
1
1
1
1
1
1
1
Single-valued properties can be represented by a partition.
We can always transform the partition into corresponding network.
22 / 65
Record from Web of Science
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
EU projects
PT J
AU Dipple, H
Evans, B
TI The Leicestershire Huntington’s disease support group: a social network
analysis
SO HEALTH & SOCIAL CARE IN THE COMMUNITY
LA English
DT Article
C1 Rehabil Serv, Troon Way Business Ctr, Leicester LE4 9HA, Leics, England.
RP Dipple, H, Rehabil Serv, Troon Way Business Ctr, Sandringham
Suite,Humberstone Lane, Leicester LE4 9HA, Leics, England.
CR BORGATTI SP, 1992, UCINET 4 VERSION 1 0
FOLSTEIN S, 1989, HUNTINGTONS DIS DISO
SCOTT J, 1991, SOCIAL NETWORK ANAL
NR 3
TC 3
PU BLACKWELL SCIENCE LTD
PI OXFORD
PA P O BOX 88, OSNEY MEAD, OXFORD OX2 0NE, OXON, ENGLAND
SN 0966-0410
J9 HEALTH SOC CARE COMMUNITY
JI Health Soc. Care Community
PD JUL
PY 1998
VL 6
IS 4
BP 286
EP 289
PG 4
SC Public, Environmental & Occupational Health; Social Work
GA 105UP
UT ISI:000075092200008
ER
WoS2Pajek
23 / 65
Records from BiBTEX
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
EU projects
@Article{int:Mizuno1,
author =
"S. Mizuno",
title =
"An \${O(n^{3}L)}\$ algorithm using a sequence for
linear complementarity problems",
journal =
"Journal of the Operations Research Society of Japan",
volume =
"33",
year =
"1990",
pages =
"66--75",
}
@InCollection{int:Vorst1,
author =
"{J. G. G. van de} Vorst",
title =
"An attempt to use parallel computing in large scale
optimisation",
booktitle =
"Logistics, Where Ends Have to Meet~: Proceedings of
the Shell Conference on Logistics in Apeldoorn, The
Netherlands, November 1988",
editor =
"{C. F. H. van} Rijn",
year =
"1989",
pages =
"112--119",
publisher =
"Pergamon Press",
address =
"Oxford, United Kingdom",
}
Bib2Pajek.py
24 / 65
Two mode networks from data tables
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
EU projects
For data from the Web of Science (Knowledge) we can obtain the
corresponding networks using the program WoS2Pajek:
• citation network Ci: works × works;
• authorship network WA: works × authors, for works without
complete description only the first author is known;
• keywords network WK: works × keywords, only for works with
complete description;
• journals network WJ: works × journals;
• partition of works by the publication year;
• partition of works – complete description (1) / ISI name only
(0);
Similar programs exist also for other bibliographic sources/formats:
Scopus, BibTEX, Zentralblatt Math, Google Scholar, DBLP, IMDB,
etc.
25 / 65
Multiplication of networks
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
EU projects
To a simple (no parallel arcs) two-mode network N = (I, J , A, w );
where I and J are sets of vertices, A is a set of arcs linking I and
J , and w : A → R (or some other semiring) is a weight; we can
assign a network matrix W = [wi,j ] with elements: wi,j = w (i, j) for
(i, j) ∈ A and wi,j = 0 otherwise.
Given a pair of compatible networks NA = (I, K, AA , wA ) and
NB = (K, J , AB , wB ) with corresponding matrices AI×K and BK×J
we call a product of networks NA and NB a network
NC = (I, J , AC , wC ), where AC = {(i, j) : i ∈ I, j ∈ J , ci,j 6= 0}
and wC (i, j) = ci,j for (i, j) ∈ AC . The product matrix
C = [ci,j ]I×J = A ∗ B is defined in the standard way
X
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).
26 / 65
Multiplication of networks
Two-mode
V. Batagelj
Direct
methods
i
2-mode cores
j
ai,k
4-ring weights
bk,j
Multiplication
k
Kinship
relations
Projections
I
A
K
B
J
Collaboration
Other derived
networks
EU projects
ci,j =
X
ai,k · bk,j
k∈NA (i)∩NB− (j)
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.
27 / 65
Multiplication of networks
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
The standard matrix multiplication has the complexity
O(|I| · |K| · |J |) – it is too slow to be used for large networks.
For sparse large networks we can multiply much faster
considering only nonzero elements.
for k in K do
for (i, j) in NA− (k) × NB (k) do
if ∃ci,j then ci,j := ci,j + ai,k · bk,j
else new ci,j := ai,k · bk,j
Collaboration
Other derived
networks
EU projects
Networks/Multiply Networks
In general the multiplication of large sparse networks is a
’dangerous’ operation since the result can ’explode’ – it is not
sparse.
28 / 65
Multiplication of networks
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
EU projects
From the network multiplication algorithm we see that each
intermediate node k ∈ K adds to a product network a complete
two-mode subgraph KN − (k),NB (k) (or, in the case I = J , a
A
complete subgraph KN(k) ). If both degrees degA (k) = |NA− (k)|
and degB (k) = |NB (k)| are large then already the computation
of this complete subgraph has a quadratic (time and space)
complexity – the result ’explodes’.
If at least one of the sparse networks NA and NB has small
maximal degree on K then also the resulting product network
NC is 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.
29 / 65
Kinship relations
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
EU projects
Anthropologists typically use a basic vocabulary of kin types to
represent genealogical relationships. One common version of
the vocabulary for basic relationships:
Kin Type
P
F
M
C
D
S
G
Z
B
E
H
W
English Type
Parent
Father
Mother
Child
Daughter
Son
Sibling
Sister
Brother
Spouse
Husband
Wife
The genealogies are usually described in GEDCOM format.
Examples family, Bouchards. Paper
30 / 65
Calculating kinship relations
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
EU projects
Pajek generates three relations when reading genealogy as Ore
graph:
F: is a father of
M: is a mother of
E: is a spouse of
Additionally we must generate two binary diagonal matrices, to
distinguish between male and female:
L: is a male
/ 1-male, 0-female
J: is a female
/ 1-female, 0-male
F ∩ M = ∅,
L ∪ J ⊆ I,
L∩J=∅
31 / 65
Derived kinship relations
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
EU projects
Other basic relations can be obtained using macros based on
identities:
is a parent of
P = F ∪M
is a child of
C = PT
is a son of
S = L∗C
is a daughter of
D = J ∗C
is a husband of
H = L∗E
is a wife of
W = J ∗E
is a sibling of
G = ((F T ∗ F ) ∩ (M T ∗ M)) \
is a brother of
B = L∗G
is a sister of
Z = J ∗G
is an uncle of
U = B ∗P
is an aunt of
A = Z ∗P
is a semi-sibling of
Ge = (P T ∗ P) \ I
and using them other relations can be determined
is a grand mother of
M2 = M ∗ P
is a niece of
Ni = D ∗ G
32 / 65
Relative sizes of kinship relations in genealogies
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
EU projects
Kin Type
P-Parent
F-Father
M-Mother
C-Child
D-Daughter
S-Son
G-Sibling
Z-Sister
B-Brother
E-Spouse
H-Husband
W-Wife
U-Uncle
A-Aunt
Ge-Semi-sibling
n
mE = Spouse
mA = Parent
Turks Ragusa
1.000 1.000
0.514 0.532
0.486 0.468
1.000 1.000
0.431 0.384
0.569 0.616
1.250 0.943
1.135 0.746
1.366 1.140
0.205 0.215
0.205 0.215
0.205 0.215
1.920 1.789
1.750 1.143
1.473 1.155
1269
407
1987
5999
2002
9315
Loka
1.000
0.504
0.496
1.000
0.480
0.520
1.019
0.983
1.055
0.208
0.208
0.208
1.200
1.190
1.128
Silba
1.000
0.519
0.481
1.000
0.469
0.531
0.811
0.760
0.861
0.230
0.230
0.230
1.181
1.097
0.932
Royal
1.000
0.540
0.460
1.000
0.427
0.573
0.767
0.707
0.828
0.306
0.306
0.306
0.927
0.798
0.905
47956
14154
68052
6427
2217
9627
3010
1138
3724
33 / 65
Two-mode network analysis by conversion to
one-mode network
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
Often we transform a two-mode network N = (U, V, E, w ) into
an ordinary (one-mode) network N1 = (U, E1 , w1 ) or/and
N2 = (V, E2 , w2 ), where E1 and w1 are determined by the
P
(1)
T . Evidently
matrix W(1) = WWT , wuv = z∈V wuz · wzv
(1)
(1)
wuv = wvu . There is an edge (u : v ) ∈ E1 in N1 iff
(1)
N(u) ∩ N(v ) 6= ∅. Its weight is w1 (u, v ) = wuv .
The network N2 is determined in a similar way by the matrix
W(2) = WT W.
The networks N1 and N2 are analyzed using standard methods.
EU projects
Network/2-Mode Network/2-Mode to 1-Mode/Rows
34 / 65
Normalizations
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
EU projects
The normalization approach was developed for quick inspection of
(1-mode) networks obtained from two-mode networks – a kind of
network based data-mining.
In networks obtained from large two-mode networks there are often
huge differences in weights. Therefore it is not possible to compare
the vertices according to the raw data. First we have to normalize
the network to make the weights comparable.
There exist several ways how to do this. Some of them are presented
in the following table. They can be used also on other networks.
In the case of networks without loops we define the diagonal weights
for undirected networks P
as the sum of out-diagonal elements in the
row (or column) wvv = u wvu and for directed networks as some
mean value
P of the row
P and column sum, for example
wvv = 12 ( u wvu + u wuv ). Usually we assume that the network
does not contain any isolated vertex.
35 / 65
. . . Normalizations
Two-mode
V. Batagelj
Direct
methods
Geouv
=
Inputuv
=
Minuv
=
MinDiruv
=
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
wuv
√
wuu wvv
wuv
wvv
wuv
min(wuu , wvv )
(
wuv
wuu ≤ wvv
wuu
0
sicer
GeoDeguv
=
wuv
p
degu degv
Outputuv
=
wuv
wuu
Maxuv
=
MaxDiruv
=
wuv
max(wuu , wvv )
(
wuv
wuu ≤ wvv
wvv
0
sicer
Collaboration
Other derived
networks
After a selected normalization the important parts of network are obtained
by line-cuts or islands approaches.
EU projects
Network/2-Mode Network/2-Mode to 1-Mode/Normalize 1-Mode/
Reuters Terror News: GeoDeg, MaxDir, MinDir.
Slovenian journals and magazins.
36 / 65
MinDir of Slovenian journals 2000
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
EU projects
Over 100000 people were asked in the years 1999 and 2000 about the journals they read.
They mentioned 124 different journals. (source Cati)
37 / 65
GeoDeg normalization of Reuters terror news
network
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
EU projects
38 / 65
Co-authorship networks
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
EU projects
Let WA be the works × authors two mode co-authorship
network; wapi ∈ {0, 1} is describing the authorship of author i
of work p.
X
∀p ∈ W :
wapi = outdegWA (p) = # authors of work p
i∈A
Let N be its normalized version
X
npi ∈ {0, 1}
∀p ∈ W :
i∈A
obtained from WA by npi = wapi / max(1, outdegWA (p)), or by
some other rule determining the author’s contribution.
39 / 65
Some transformations of networks
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Binarization b(N ) is a network obtained from the N in which all
weights are set to 1.
Transposition N T or t(N ) is a network obtained from N in which to
all arcs their direction is reversed. AW = WAT , KW = WKT , . . .
(Out) normalization n(N ) is a network obtained from N in which the
weight of each arc a is divided by the sum of weights of all arcs
having the same initial vertex as the arc a. For binary networks
Projections
Collaboration
n(A) = diag(
Other derived
networks
EU projects
1
)i∈I ∗ A
max(1, outdegWA (i))
N = n(WA), WA = b(N)
40 / 65
First collaboration network
Two-mode
V. Batagelj
Co = AW ∗ WA
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
EU projects
coij =
X
wapi wapj =
X
1
p∈N − (i)∩N − (j)
p∈W
coij = the number of works that authors i and j wrote together
It holds: coij = coji .
Using the weights coij we can determine the Salton’s cosine
similarity or Ochiai coefficient between authors i and j as
cos(i, j) = √
coij
,
coii cojj
for coij > 0
41 / 65
Cores of orders 20–47 in Co(SN5)
Two-mode
Network SN5 (2008): for "social network*" + most frequent references + around 100 social networkers;
|W | = 193376, |C | = 7950, |A| = 75930, |J| = 14651, |K | = 29267
V. Batagelj
WASSERMA_S
DOREIAN_P
KRACKHAR_D
FAUST_K
Direct
methods
KALICHMA_S
SNIJDERS_T
FERLIGOJ_A
MCAULIFF_T
VANDUIJN_M
PETRESCU_M
BATAGELJ_V
KELLY_J
2-mode cores
BUTTS_C
STEVENSO_L
4-ring weights
Multiplication
MAJ_M
ZWEBEN_A
Kinship
relations
MALANGON_C
MAGLIANO_L
STOUT_R
FIORILLO_A
DEROSA_C
LONGABAU_R
WIRTZ_P
Projections
RYCHTARI_R
CONNORS_G
KADDEN_R
Collaboration
LITT_M
Other derived
networks
ATKINSON_J
MCCUTCHA_J
WASSERMA_L
STRAITST_K
EU projects
ZISOOK_S
PATTERSO_T
GRANT_I
NEWMAN_V
SEMPLE_S
42 / 65
Pajek
Papers by number of authors
Two-mode
V. Batagelj
Direct
methods
2-mode cores
Problem: The Co network is composed of complete graphs on
the set of work’s authors. Works with many authors produce
large complete subgraphs and are over-represented, thus
bluring the collaboration structure.
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
EU projects
outdeg
1
2
3
4
5
6
7
8
9
10
11
frequency
2637
2143
1333
713
396
206
114
65
43
24
10
outdeg
12
13
14
15
21
22
23
26
41
42
48
frequency
8
4
3
2
1
1
1
1
1
1
1
paper
Pierce et al. (2007)
Allen et al. (1998)
Kelly et al. (1997)
Semple et al. (1993)
Magliano et al. (2006)
Doll et al. (1992)
Snijders et al. (2007)
43 / 65
Snijders et al. (2007)
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
EU projects
Snijders et al.(2007): Snijders, T.A.B., Robinson, T.,
Atkinson, A.C., Riani, M., Gormley, I.C., Murphy, T.B.,
Sweeting, T., Leslie, D.S., Longford, N.T., Kent, J.T.,
Lawrance, T., Airoldi, E.M., Besag, J., Blei, D., Fienberg, S.E.,
Breiger, R., Butts, C.T., Doreian, P., Batagelj, V., Ferligoj, A.,
Draper, D., van Duijn, M.A.J., Faust, K., Petrescu-Prahova,
M., Forster, J.J., Gelman, A., Goodreau, S. M., Greenwood,
P.E., Gruenberg, K., Francis, B., Hennig, C., Hoff, P.D.,
Hunter, D.R., Husmeier, D., Glasbey, C., Krackhardt, D.,
Kuha, J., Skrondal, A., Lawson, A., Liao, T. F., Mendes, B.,
Reinert, G., Richardson, S., Lewin, A., Titterington, D.M.,
Wasserman, S., Werhli, A.V. and Ghazal, P.. Discussion on the
paper by Handcock, Raftery and Tantrum. Journal of the Royal
Statistical Society: Series A - Statistics in Society, 170 (2007),
pp. 322-354.
44 / 65
pS -core at level 20 of Co(SN5)
Two-mode
KHOURSIN_R
DEROSA_C
AMIRKHAN_Y
STEVENSO_L
V. Batagelj
GRANT_I
KALICHMA_S
MCAULIFF_T
MAGLIANO_L
ZISOOK_S
DIFRANCE_W
MALANGON_C
KABAKCHI_E
Direct
methods
KELLY_J
VASSILEV_S
STRAITST_K
FIORILLO_A
ZWEBEN_A
KADDEN_R
LONGABAU_R
CONNORS_G
WIRTZ_P
LITT_M
RYCHTARI_R
2-mode cores
ATKINSON_J
MAJ_M
EVERETT_M
STOUT_R
MCCUTCHA_J
PATTERSO_T
BORGATTI_S
SEMPLE_S
4-ring weights
Multiplication
KRACKHAR_D
POTTERAT_J
MUTH_S
DOREIAN_P
VINDING_H
NILSSON_L
FERLIGOJ_A
BJARNASO_O
BUTTS_C
BATAGELJ_V
SNIJDERS_T
Kinship
relations
PETRESCU_M
WOODHOUS_D
SANDLUND_M
WASSERMA_S
BENGTSSO_A
FAUST_K
Projections
HANSSON_L
SORGAARD_K
ROTHENBE_R
VANDUIJN_M
MIDDELBO_T
CURTIS_R
MERINDER_L
JOSE_B
MCINTOSH_B
DESJARLA_D
Collaboration
ROMEO_R
JOYCE_T
EMERSON_E
Other derived
networks
SHELLEY_G
BERNARD_H
GOLDSTEI_M
KNAPP_M
ELLIOTT_J
NEAIGUS_A
HATTON_C
ROBERTSO_J
FRIEDMAN_S
LATKIN_C
SWIFT_P
TOWERS_C
EU projects
ILDEFONS_G
SANDERSO_H
ROUTLEDG_M
OAKES_P
KILLWORT_P
JOHNSEN_E
CELENTAN_D
KRINJEN-_E
KNOWLTON_A
MANDELL_W
MCCARTY_C
OZIEMKOW_M
VLAHOV_D
Pajek
45
/ 65
Second collaboration network
Two-mode
Cn = AW ∗ N
V. Batagelj
cnij =
Direct
methods
X
wapi npj =
X
npj
p∈N − (i)∩N − (j)
p∈W
Multiplication
cnij = contribution of author j to works, that (s)he wrote together with the
author i. X X
X
It holds
wapi npj = outdegWA (p) and
cnij = indegWA (i)
Kinship
relations
cnii =
2-mode cores
4-ring weights
Projections
Collaboration
Other derived
networks
EU projects
j∈A
Xj∈A j∈A
npi is the contribution of author i to his/her works.
p∈N(i)
cnii
outdegWA (i)
Collaborativness: Ki = 1 − Si
XX
X
cnij =
indegWA (i) = mWA
Self-sufficiency: Si =
i∈A j∈A
i∈A
To compute the table we prepared a macro in Pajek.
46 / 65
The ”best” authors in Social Networks
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
EU projects
i
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
author
Burt,R
Newman,M
Doreian,P
Bonacich,P
Marsden,P
Wellman,B
Leydesdorf,L
White,H
Friedkin,N
Borgatti,S
Everett,M
Litwin,H
Freeman,L
Barabasi,A
Snijders,T
Valente,T
Breiger,R
Skvoretz,J
Krackhardt,D
Carley,K
Pattison,P
Wasserman,S
Berkman,L
Moody,J
Scott,J
cnii
43.83
36.77
34.44
30.17
29.42
26.87
24.37
23.50
20.00
19.20
16.92
16.00
15.53
14.99
14.99
14.80
14.44
14.43
13.65
12.93
12.10
11.72
11.21
10.83
10.47
total
53
60
47
41
37
41
35
33
23
41
31
21
20
35
30
34
20
27
25
28
27
26
30
15
15
Ki
0.173
0.387
0.267
0.264
0.205
0.345
0.304
0.288
0.130
0.532
0.454
0.238
0.223
0.572
0.500
0.565
0.278
0.466
0.454
0.538
0.552
0.549
0.626
0.278
0.302
i
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
author
Latkin,C
Morris,M
Rothenberg,R
Kadushin,C
Faust,K
Batagelj,V
Mizruchi,M
[Anon]
Johnson,J
Fararo,T
Lazega,E
Knoke,D
Ferligoj,A
Brewer,D
Klovdahl,A
Hammer,M
White,D
Holme,P
Boyd,J
Kilduff,M
Small,H
Iacobucci,D
Pappi,F
Chen,C
Seidman,S
cnii
10.14
9.98
9.82
9.75
9.72
9.69
9.67
9.00
8.89
8.83
8.50
8.33
8.19
8.03
7.96
7.92
7.83
7.42
7.37
7.25
7.00
7.00
6.83
6.78
6.75
total
37
20
28
11
18
20
15
9
21
16
12
11
19
11
17
10
15
14
13
16
7
12
10
12
9
Ki
0.726
0.501
0.649
0.114
0.460
0.516
0.356
0.000
0.577
0.448
0.292
0.242
0.569
0.270
0.532
0.208
0.478
0.470
0.433
0.547
0.000
0.417
0.317
0.435
0.250
47 / 65
Third collaboration network
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Ct = NT ∗ N
ctij = the total contribution of collaboration of authors i and j to
works.
It holds ctij = ctji and
XX
npi npj = 1
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
i∈A j∈A
The total contribution of a complete subgraph corresponding to the
authors
of X
a work p is 1.
X
ctij =
npi = the total contribution of author i to works from
j∈A
p∈W
W.
EU projects
XX
ctij = |W |
i∈A j∈A
48 / 65
Components in Ct(SN5) cut at level 0.5
Two-mode
V. Batagelj
Network SN5 (2008): for "social network*" + most frequent references + around 100 social networkers;
|W | = 193376, |C | = 7950, |A| = 75930, |J| = 14651, |K | = 29267
Jackson_M
Kogovsek_T
Direct
methods
2-mode cores
Park_J
Mrvar_A
Ferligoj_A
Batagelj_V
Rothenbe_R
Leinhard_
Newman_M
Kilduff_M
Zenou_Y
Barabasi_A
Gastner_M
Potterat_J
Holland_P
Watts_D
Balkundi_P
Willer_DHummon_N
4-ring weights
Krackhar_D
Calvo-Ar_A
Moore_C
Woodard_K
Doreian_P
Muth_S
Demeneze_M
Albert_R
Leinhard_S
Girvan_M
Fararo_T
Mccarty_C
Jeong_H
Parker_A
Shelley_G
Multiplication
Galaskie_J
Skvoretz_J
Faust_K
Kinship
relations
Cross_R
Anderson_C
Borgatti_S
Litwin_H
Knowlton_A
Bowling_A
Bernard_H
Latkin_C
Iacobucc_D
Teresi_J
Shiovitz_S
Sokolovs_J
Browne_P
Everett_M
Cohen_C
Projections
Hopkins_N
Collaboration
Steinhau_H
Bonacich_P
Bjorkman_T
Metzke_C
Bienenst_E
Hansson_L
Konno_N
Sundquis_J
Ennett_S
Wellman_B
Johnson_C
Johansso_S
Bauman_K
Hampton_K
Barer_B
Mandell_W
Boyd_J
Holmes_D
Masuda_N
EU projects
Chou_K
Chi_I
Jolly_A
Yang_H
Banks_D
Tang_J
Farmer_T
Rodkin_P
Morris_M
Kretzsch_M
Grabowsk_A
Kosinski_R
Suitor_J
Hawkins_J
Braha_D
Pillemer_K
Fraser_M
Bar-Yam_Y
Boyack_K
Laumann_E
Ostergre_P
Klavans_R
Wylie_J
Carley_K
Grundy_E
Davey-Ro_M
Breiger_R
Other derived
networks
Hua_W
Wasserma_S Robins_G
Pattison_P
Landau_R
Farquhar_M
Killwort_P
Sherman_S
Hanson_B
Marsden_P
Foster_B
Seidman_S
Carter_W
Feld_S
Fingerma_K
Birditt_K
Stauffer_D
Leydesdo_L
Weisbuch_G
Vandenbe_P
Gronlund_A
Vespigna_A
Bell_D
Berkman_L
Degenne_A
Newton_J
Wallace_D Wallace_R
Keeling_M
Neaigus_A
Feiring_C
Krause_N
Shaw_B
Weisner_C
Ohtsuki_H
Lindstro_D
Lin_N Kimura_M Saito_K
Solomon_P Draine_J
49 / 65
Holme_P
Schneide_J Borlund_P
pS -core at level 0.75 in Ct(SN5)
Two-mode
V. Batagelj
JOLLY_A
CERRITO_P
Direct
methods
LATKIN_C
PILLEMER_K
JOHNSEN_E
KILLWORT_P
BONACICH_P
LEVI_I
WYLIE_J
ROTHENBE_R
LAUMANN_E HOPKINS_N
FRIEDKIN_N
4-ring weights
Multiplication
BARNES_G
MCCARTY_C
SHELLEY_G
HAMPTON_K
2-mode cores
SUITOR_J
WELLMAN_B
VLAHOV_D
MUTH_S
STROGATZ_S
GALASKIE_J
IACOBUCC_D
MARSDEN_P
LEWIS_M
CAIRNS_R
BIENENST_E
Kinship
relations
CHOU_K
Projections
CHI_I
CAIRNS_B
NEWMAN_M
ANDERSON_C
ROBINS_G
KNOWLTON_A
WATTS_D
LIND_P
WASSERMA_S
XIE_H
FEIRING_C
PARK_J
PATTISON_P
FAUST_K
GONZALEZ_M
FARMER_T
BREIGER_R
BALKUNDI_P
BATAGELJ_V
CROSS_R
Collaboration
Other derived
networks
MANDELL_W
POTTERAT_J
BERNARD_H
PARKER_A
BOYD_J
BARABASI_A
FERLIGOJ_A WILLER_D
SKVORETZ_J
WOODARD_K
JEONG_H
VANACKER_R
DOREIAN_P
MRVAR_A
KILDUFF_M
PEARL_R
ALBERT_R
HUMMON_N
KRACKHAR_D
MASUDA_N
KONNO_N
BORGATTI_S
STAUFFER_D
CARLEY_K
HOLMES_D
FOSTER_B
METZKE_C
BAUMAN_K
EVERETT_M
EU projects
RODKIN_P
HERRMANN_H
FARARO_T
JOHANSSO_S
ENNETT_S
WEISBUCH_G
SEIDMAN_S
STEINHAU_H
LEINHARD_
TERESI_J
COHEN_C
SUNDQUIS_J
FARQUHAR_M
HOLLAND_P
OSTERGRE_P
SOKOLOVS_J
LEINHARD_S
HANSON_B
FRASER_M
FINGERMA_K
HANSSON_L
KOSINSKI_R
HAWKINS_J
BIRDITT_K
BJORKMAN_T
GRABOWSK_A
GRUNDY_E
BOWLING_A
50 / 65
Some line islands [5,20] in Ct(SN5)
Line islands at size [K5 GO] in Ct HSNKL
Two-mode
V. Batagelj
Direct
methods
BAERVELD_C
CUMMINGS_J
NOWICKI_K
MCPHERSO_J
POPIELAR_P
SNIJDERS_T
Analysis of Bibliographic Networks
on ISocial NetworksI
CROSS_R
KOSKINEN_J
4-ring weights
PARKER_A
SCHWEINB_M
DUQUENNE_V
KOGOVSEK_T
EVERETT_M
SMITHLOV_L
BOYD_J
Multiplication
WOODARD_K
BORGATTI_S
FREEMAN_L
DUCHARME_F
HUMMON_N
Monika Cerinšek5 Vladimir Batagelj
WHITE_D
DOREIAN_P
Projections
FERLIGOJ_A
CARPENTI_N
FARARO_T
Collaboration
WILLER_D
BREIGER_R
Other derived
networks
MUNCH_A
VANDUIJN_M
2-mode cores
Kinship
relations
DROBNIC_S
KIESLER_S
HIGGINS_M
ZIJLSTRA_B
BATAGELJ_V
SKVORETZ_J
PATTISON_P
ROBINS_G
MRVAR_A
KENIS_P
Sunbelt XXXIII5 May G_th GORT5 Hamburg
BRANDES_U
FAUST_K
WAGNER_D
EU projects
ERLEBACH_T
WASSERMA_S
IACOBUCC_D
HOPKINS_N
ANDERSON_C
SCHANK_T
CORNELSE_S
FLEISCHE_D
GALASKIE_J
51 / 65
Authors’ citations network
Two-mode
V. Batagelj
Direct
methods
2-mode cores
i
was,i
4-ring weights
s
Multiplication
cis,t
Kinship
relations
t
Projections
Collaboration
Other derived
networks
EU projects
j
A
WAT
wat,j
A
W
Ci
W
WA
Ca = AW ∗ 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.
52 / 65
Islands in SN5 authors citation network
Two-mode
Network SN5 (2008): for "social network*" + most frequent references + around 100 social networkers;
|W | = 193376, |C | = 7950, |A| = 75930, |J| = 14651, |K | = 29267
V. Batagelj
LIN_N
LAZEGA_E
ROBINS_G
FRIEDKIN_N
VAPNARSK_V
LAI_G
LEVOT_P
STRAUSS_D
MERTON_R
HOLLAND_P
LYNCH_E
FRANTZ_P
DEYRIS_E
ALAKARE_B
COLEY_J
GERGEN_K
VANDUIJN_M
GALASKIE_J
AALTONEN_J
LEMOIGNE_M
SCHWARTZ_N
BURT_R
MAILLARD_J
PATTISON_P
Direct
methods
SHOTTER_J
BARAN_M
GULATI_R
WHITE_H
LEINHARD_S
SNIJDERS_T
ATRAN_S
MUSSAT_M
MARECHAL_M
ANDERSEN_T
EK_E
BOORMAN_S
FAUST_K
SEIKKULA_J
DEPOMPER_M
SELVINIP
MIZRUCHI_M
CORP_E
ROSS_N
MEDIN_D
LEMOY_A
DELALAUR_L
COLEMAN_J
MCGORRY_P
ANDERSON_C
BREIGER_R
GRANOVET_M
ANDERSON_H
TIMURA_C
LEBEAU_E
ALANEN_Y
KILDUFF_M
WASSERMA_S
2-mode cores
BRASS_D
FIENBERG_S
LAUMANN_E
DOREIAN_P
IACOBUCC_D
MATTOSO_J
ARRUDA_M
MARSDEN_P
FARARO_T
HURLBERT_J
4-ring weights
GIRVAN_M
SKVORETZ_J
COHEN_A
DOROGOVT_S
BALKUNDI_P
FREEMAN_L
IBARRA_H
EVERETT_M
BATAGELJ_V
STEDILE_J
COSTA_L
BENJAMIN_C
MORENO_Y
KIM_D
GRABOWSK_A
HUMMON_N
BOCCALET_S
BIONDI_A
BARTHELE_M
FERLIGOJ_A
BOFF_C
LESBAUPI_I
MOORE_C
WHITE_D
MILLER_M
KRACKHAR_D
Multiplication
PARK_J
COOK_K
CARLEY_K
STROGATZ_S
WILLER_D
TRINDADE_H
GRONLUND_A
NEWMAN_M
PINAUD_J
AMARAL_L
MARKOVSK_B
VLAHOV_D
NEAIGUS_A
GONCALVE_R
MOLLOY_M
WATTS_D
JEONG_H
Kinship
relations
BONACICH_P
KLOVDAHL_A
HOLME_P
ALBERT_R
MASUDA_N
VANDIEN_S
BORGATTI_S
DESJARLA_D
LATKIN_C
BIENENST_E
BURGARD_A
BARABASI_A
MANDELL_W
MAHADEVA_R
ROGERS_E
RODKIN_P
POTTERAT_J
CRICK_N
CELENTAN_D
KLINKE_D
ESPELAGE_D
XIE_H
BROADBEL_L
FRIEDMAN_S
FAMILI_I
MUTH_S
LEUNG_M
VALENTE_T
Projections
ROSSI_M
CASSIRAM_A
GIULINI_G
LATUADA_S
BELTRAMI_L
MAGNUSSO_D
CAIRNS_R
GEST_S
CAIRNS_B
MAVROVOU_M
BELGIOJO_A
GUILINI_G
ZOTTI_S
ARRIGONI_P
BIANCONI_C
FARMER_T
D’AMIA_G
MORRIS_M
ANNONI_A
ROMUSSI_C
AMATI_C
FEDORA_P
NIELSEN_R
FRANCHET_G
VERCELLO_V
GOFORTH_J
HOLLOWEL_J
ROTHENBE_R
KELLY_J
VACANI_C
KANNES_G
Other derived
networks
DARROW_W
UNKNOWN
GATTIPER_M
REGGIORI_F
SABORNIE_E
THOMPSON_J
GOODHART_K
HOYME_H
GOZZOLI_M
MAY_P
VILJOEN_D
MERIGGI_M
BUCHANAN_L
PELLEGRI_A
ADLER_P
WEISNER_C
CHIZZOLI_G
SCOTTI_A
MEZZANOT_G
DISHION_T
HYMEL_S
KRETZSCH_M
HIGGINS_C
LUCCHELL_G
PAPAGNA_P
CATTANEO_C
ASPARI_D
GARIEPY_J
SUMATHI_R
RICCI_G
VALLI_F
BECCARIA_G
MONTALTO_R
PATETTA_L
VANACKER_R
CADWALLA_T
COIE_J
PFAENDTN_J
HONEGGER_A
PIZZAGAL_F
KINDERMA_T
CURTIS_R
AMIRKHAN_Y
PEARL_R
ESTELL_DNECKERMA_H
CLEMMER_J
Collaboration
KNOWLTON_A
WOODHOUS_D
SCHILLIN_C
TRUJILLO_P
GOLDOLI_E
MATZGER_H
DELUCCHI_K
DALLAJ_A
SANDRI_M
MEZZANOT_P
KALBERG_W
ABEL_E
WHITE-CO_M
KASKUTAS_L
GOSSAGE_J
DECOTEAU_S
EU projects
LESAGE_A
OZEL_S
WALKER_B
WESTLEY_F
AYDIN_I
BREWIN_C
BROWN_G
MARASCO_C HELD_T
CARPENTE_S
JANSSEN_M
MACCARTH_B
FARRELL_M
HUNT_J
ZILELI_L
EREN_E
BERKES_F
ADGER_W
DEROSA_C
SOLOMON_P
FOLKE_C
BRUGHA_T
WING_J
OZCURUME_G
BASOGLU_M
GAMBOA_G
REEVE_H
HAHN_T
BEBBINGT_P
SCHEFFER_M
DAPPORTO_L
RAU_P
MALANGON_C
LALE_T
MAGLIANO_L
FIORILLO_A
JEANNE_R
OSTROM_E
HOLLING_C
HENDERSO_S
LEWIS_G
GUNDERSO_L
JENKINS_R
MELTZER_H
OLSSON_P
ROSELER_P
GUARNERI_M
FADDEN_G
TURILLAZ_S
PALAGI_E
TASKINTU_N
KILIC_C
MORGAN_Z
MAJ_M
STARKS_P
STRASSMA_J
KURT_G
WESTEBER_M
Pajek
53 / 65
Bibliographic Coupling
Two-mode
V. Batagelj
Direct
methods
In WoS2Pajek the citation relation means pCiq ≡ work p cites work q.
Therefore the bibliographic coupling network biCo can be determined as
biCo = Ci ∗ CiT
2-mode cores
4-ring weights
Multiplication
Kinship
relations
bicopq = # of works cited by both works p and q. bicopq = bicoqp .
Again we have problems with works with many citations, especially with
review papers. To neutralize their impact we can introduce a normalized
measure such as
Projections
Collaboration
Other derived
networks
EU projects
biCon =
1
(n(Ci) ∗ CiT + Ci ∗ n(Ci)T )
2
It is easy to verify that biconpq ∈ [0, 1] and biconpq = biconqp (symmetry).
It also holds: biconpq = 1 iff the works p and q are referencing the same
works.
54 / 65
Co-Citation and others
Two-mode
V. Batagelj
Direct
methods
The co-citation network coCi can be determined as
coCi = CiT ∗ Ci
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
EU projects
cocipq = # of works citing both works p and q.
cocipq = cociqp .
The weight w (a, p) in the author citation network
ACi = AW ∗ Ci
counts the number of times author a cited work p.
The author co-citation network can be obtained as
ACo = b(ACi) ∗ t(b(ACi))
Authors using keywords AK = AW ∗ WK.
55 / 65
The cited co-authorship network
Two-mode
V. Batagelj
Direct
methods
Quattrociocchi W. et al. (2011): Selection in scientific networks.
Soc. Netw. Anal. Min. proposed the cited co-authorship network:
the weight of two collaborating authors equals to the sum of numbers
of citations to co-authored works
2-mode cores
AW ∗ diag(indegCi (p)) ∗ WA
4-ring weights
Multiplication
where indegCi (p) is number of citations to work p. Normalized:
Kinship
relations
Projections
Cc = AW ∗ diag(
Collaboration
Other derived
networks
XX
EU projects
i∈A j∈A
waip
XX
i∈A j∈A
indegCi (p)
) ∗ WA
outdegCi (p)2
indegCi (p)
awpj = indegCi (p)
outdegCi (p)2
ccij =
X
indegCi (p) = |ACi |
p∈W
56 / 65
EU projects on simulation
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
For the meeting The Age of Simulation at Ars Electronica in
Linz, January 2006 a dataset of EU projects on simulation was
collected by FAS research, Vienna and stored in the form of
Excel table (SimPro.csv).
The rows are the projects participants (idents) and colomns
correspond to different their properties. Three two-mode
networks were produced from this table using Jürgen Pfeffer’s
Text2Pajek program:
Collaboration
• project.net – P = [idents × projects]
Other derived
networks
• country.net – C = [idents × countries]
EU projects
• institution.net – U = [idents × institutions]
|idents| = 8869,
|countries| = 60.
|projects| = 933,
|institutions| = 3438,
57 / 65
EU projects – derived networks
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Since all three networks have the common set (idents) we can
derive from them using network multiplication
Nets/Multiply First*Second
several interesting networks:
Multiplication
• ProjInst.net – W = [projects × institutions] = PT ∗ U
Kinship
relations
• Countries.net – S = [countries × countries] = CT ∗ C
Projections
• Institutions.net – Q = [institutions × institutions]
Collaboration
Other derived
networks
= WT ∗ W
• ...
EU projects
Network/2-Mode Network/2-Mode to 1-Mode/Rows
Network/2-Mode Network/2-Mode to 1-Mode/Columns
58 / 65
Analysis of ProjInst.net
Two-mode
V. Batagelj
Direct
methods
2-mode cores
For identifying important parts of ProjInst.net we first computed
the 4-rings weights and in the obtained network we determined the
line islands
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
Network/Create New Network/With Ring Counts .../4-Rings/Undirected
Network/Create Partition/Islands/Line Weights[Simple] [2,200]
We obtain 101 islands. We extracted 18 islands of the size at least 5.
There are two most important islands: aviation companies and car
companies.
In labels we used the option \n.
EU projects
59 / 65
Analysis of ProjInst.net
Two-mode
ARMINES
PSI FUR PRODUKTE UND
SYS.E DER INFORMATIONSTECH.
BICC GENERAL CABLE
V. Batagelj
25525
BAE SYSTEMS
29817
DASSAULT AVIATION
C. R. FIAT S.C.P.A.
NL ORG. FOR APPLIED
SCIENTIFIC RESEARCH - TNO
BARTENBACH
501084
POLYMAGE SARL
ROSENHEIMER GLASTECH.
ENK6-CT-2002-30023
RUDOLF BRAUNS AND CO. KG
SHERPA ENGINEERING SARL
502889
CENTRE DE RECH. METALLURG.
506503
MECALOG SARL
506257
INST. NAT. DE RECHERCHE
SUR LES TRANSPORTS ET LEUR SCURIT
INST. SUPERIOR TECNICO
G4RD-CT-2002-00836
G4MA-CT-2002-00022
STICHTING NATIONAAL LUCHT
OFFICE NAT. DETUDES ET
DE REC. AEROSPATIALES
BRPR987001
G4RD-CT-2000-00178
502896
G4RD-CT-2001-00403
G4RD-CT-2002-00795
MSO CONCEPT INNOVATION + SOFTWARE
7215-PP/031
EA TECH. LTD
EUROCOPTER S.
502842
AIRBUS FRANCE SAS
ALENIA AERONAUTICA SPA
TRUMPF-BLUSEN-KLEIDER
WALTER GIRNER UND CO. KG
7210-PR/163
Multiplication
VOLKSWAGEN AG
SNECMA MOTEURS SA
AIRBUS DEUTSCHLAND
502917
502909
NAT. TEC. UNIV.
OF ATHENS
BARCO NV
4-ring weights
AIRBUS UK LIMITED
IST-2000-29207
TESSITURA LUIGI SANTI SPA
INST. FUER TEXTIL UND
VERFAHRENSTECH. DENKENDORF
KBC MANUFAKTUR, KOECHLIN,
BAUMGARTNER UND CIE. AG
DAIMLER CHRYSLER AG
BUURSKOV
DE ZENTRUM FUER LUFT
UND RAUMFAHRT E.V.
EADS DE
LMS UMWELTSYS.E, DIPL. ING. DR. HERBERT BACK
2-mode cores
ESI SOFTWARE SA
CHALMERS TEKNISKA HOEGSKOLA
MTU AERO ENGINES
FRAUENHOFER INST. FUER
PRODUKTIONSTECH. UND AUTOMATISIERUNG
Direct
methods
TQT SRL
28283
COLOPLAST A/S
G4RD-CT-2000-00395
7210-PR/233
Kinship
relations
INST. DE RECHERCHES
DE LA SIDERURGIE FR
T3.2/99
EVG3-CT-2002-80012
THYSSENKRUPP STAHL A.G.
DISENO DE SISTEMAS EN SILICIO
CENTRE FOR EUROP. ECONOMIC
SMT4982223
ILEVO AB
7210-PR/095
Projections
Collaboration
CATALYSE SARL
VOEST-ALPINE STAHL
FONDAZIONE ENI - ENRICO MATTEI
IST-2001-35358
CSTB
JERNKONTORET
UNIV. DER BUNDESWEHR MUENCHEN
LANDIS & GYR - EUROPE AG
OESTERREICHISCHER BERGRETTUNGSDIENST
IFEN GES. FUER SATELLITENNAVIGATION
JOE3980089
WYKES ENGINEERING COMPANY
IST-2000-30158
ENEL.IT
UNIV. PANTHEON-ASSAS - PARIS II
SSAB TUNNPL¯T
7215-PP/034
LH AGRO EAST S.R.O.
EU projects
T3.5/99
HELP SERVICE REMOTE SENSING
CINAR LTD.
INST. CARTOGRAFIC DE CATALUNYA
LESPROJEKT SLUZBY S.R.O.
BAYER. ROTES KREUZ
RESEARCH INST. OF THE FINNISH ECONOMY
QLK6-CT-2002-02292
TECHNOFARMING S.R.L.
Other derived
networks
HPSE-CT-2002-00108
CHIPIDEA - MICROELECTRONICA, S.A.
BUILDING RESEARCH
THE AARHUS SCHOOL OF BUSINESS
MEFOS, FOUNDATION FOR
METALLURGICAL RESEARCH
HPSE-CT-2002-00143
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.
UNIV. OF ABERDEEN
ENK5-CT-2000-00335
ORAD HI TEC SYS. POLAND
CENTRE
DE
ROBOTIQUE
FRIMEKO INT. AB
CRE GROUP LTD.
MJM GROUP, A.S.
INOX PNEUMATIC AS
BBL
DFA DE FERNSEHNACHRICHTEN AGENTUR
TPS TERMISKA PROCESSER AB
PROLEXIA
KOMMANDITGES. HAMBURG 1
A.S.M. S.A. ZAMISEL D.O.O
IST-1999-56418
FERNSEHEN BETEILIGUNGS & CO
INGENIORHOJSKOLEN HELSINGOR TEKNIKUM
DPME ROBOTICS AB
GATE5 AG
511758
INDUSTRIAS ROYO
LKSOFTWARE
SPORTART
YAHOO! DEOSAUHING EETRIUKSUS
BRST985352
UAB LKSOFT BALTIC
IST-2000-30082
WISDOM TELE VISION
ALBERTSEN & HOLM AS
ASM - DIMATEC INGENIERIA
FFT ESPANA TECH. DE AUTOMOCION,
EDAG ENGINEERING + DESIGN
SVETS & TILLBEHOR AB
SUPERELECTRIC DI
CARLO PAGLIALUNGA & C. SAS
IST-1999-57451
OK GAMES DI ALESSANDRO CARTA
ENERGITEKNIK HEATEX AB
BROD THOMASSON
GUNNESTORPS SMIDE & MEKANISKA AB
UNIV. DE ZARAGOZA
Pajek
60 / 65
Analysis of Countries.net
Two-mode
Kazakhstan
V. Batagelj
Direct
methods
2-mode cores
Tunisia
Jordan
Canada
EU projects
Network/Create New Network/
Transform/Sort lines/
Line values/Ascending
Algeria
United Kingdom
Italia
The Netherlands
Russian F.
Finland
Turkey
Greece
Germany
Portugal
Spain
Switzerland
Turkmenistan
Cyprus
Sweden
Denmark
Thailand
Austria
Slovakia
USA
Belgium
Poland
Croatia
Latvia
Malta
Israel
Estonia
Luxembourg
Other derived
networks
Lebanon
France
China
Multiplication
Collaboration
Ecuador
Iceland
Belarus
Armenia
Moldavia
Projections
Morocco
Liechtenstein
India
Uzbekistan
4-ring weights
Kinship
relations
To obtain picture in which the
stronger lines cover weaker lines
we have to sort them
Afghanistan
Japan
Azerbaijan
Georgia
Norway
Slovenia
Ireland
Bulgaria Czech R.
Lithuania
Ukraine
Serbia-Montenegro
Macedonia
Hungary
Romania
For dense (sub)networks we get
better visualization by using
matrix display. In this case we
also recoded values (2,10,50).
Albania
To determine clusters we used Ward’s clustering procedure with
dissimilarity measure d5 (corrected Euclidean distance).
The permutation determined by hierarchy can often be improved by
changing the positions of clusters. We get a typical center-periphery
structure.
Pajek
61 / 65
Analysis of Countries.net
Pajek - shadow [0.00,4.00]
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
EU projects
Pajek - Ward [0.00,4785.14]
Ecuador
Thailand
Armenia
Turkmenist
Uzbekistan
Moldavia
Japan
Kazakhstan
Azerbaijan
India
Macedonia
Albania
Liechtenst
Serbia-Mon
Iceland
Canada
Estonia
China
Belarus
Georgia
Tunisia
Lebanon
Jordan
Algeria
Malta
Morocco
Afghanista
Luxembourg
Croatia
Latvia
Lithuania
Cyprus
Turkey
Bulgaria
Ukraine
Slovenia
Romania
Slovakia
USA
Portugal
Denmark
Poland
Finland
Switzerlan
Austria
Czech R.
Ireland
Norway
Hungary
Israel
Russian F.
Sweden
Greece
Belgium
Spain
The Nether
France
United Kin
Germany
Italia
Ecuador
Thailand
Armenia
Turkmenist
Uzbekistan
Moldavia
Japan
Kazakhstan
Azerbaijan
India
Macedonia
Albania
Liechtenst
Serbia-Mon
Iceland
Canada
Estonia
China
Belarus
Georgia
Afghanista
Morocco
Malta
Tunisia
Lebanon
Jordan
Algeria
Croatia
Latvia
Lithuania
Luxembourg
Cyprus
Turkey
Bulgaria
Ukraine
Slovenia
Romania
Slovakia
USA
Russian F.
Israel
Hungary
Ireland
Czech R.
Norway
Poland
Finland
Portugal
Denmark
Switzerlan
Austria
Sweden
Greece
Belgium
Spain
The Nether
Italia
France
United Kin
Germany
Ecuador
Thailand
Armenia
Turkmenist
Uzbekistan
Moldavia
Japan
Kazakhstan
Azerbaijan
India
Macedonia
Albania
Liechtenst
Serbia-Mon
Iceland
Canada
Estonia
China
Belarus
Georgia
Afghanista
Morocco
Malta
Tunisia
Lebanon
Jordan
Algeria
Croatia
Latvia
Lithuania
Luxembourg
Cyprus
Turkey
Bulgaria
Ukraine
Slovenia
Romania
Slovakia
USA
Russian F.
Israel
Hungary
Ireland
Czech R.
Norway
Poland
Finland
Portugal
Denmark
Switzerlan
Austria
Sweden
Greece
Belgium
Spain
The Nether
Italia
France
United Kin
Germany
Two-mode
62 / 65
Analysis of Institutions.net
Two-mode
V. Batagelj
Direct
methods
2-mode cores
U.A.S.ZITTAU/GOERLITZ
U.THE AEGEAN
MIT-MANAGEMENT INTELLIGENTER TECH.N
U.PARIS-DAUPHINE
OTTO VON GUERICKE MAGDEBURG U.
COVENTRY U.
FACULTY OF ELECTRICAL ENG.
FED.UNITARY
ENTERPRISE
FL-SOFT V/JENS
DAEDALUS
INFORMATICS LTD
ALL-RUSSIAN SCIENTIFIC
CENTER
OESTERGAARD
U.PARIS
VI PIERRE ETJOERGEN
MARIE CURIE
BELIMO AUTOMATIONU.LA LAGUNA
SOFIISKI U.SVETI KLIMENT OHRIDSKI
THE U.COURT OF THE U.OF ABERDEEN
SENTIENT MACHINE RESEARCH B.V. SIEMENS BUILDING TECH.S AG
AS.CONOCIMIENTO
U.OULU
I.OF INFORMATION TECH.S
STICHTING NEURALE NETWERKEN
DATAMED HEALTHCARE INF.SYS.
NOTTINGHAM TRENT U.
U.E DE COIMBRA
T.U.CLAUSTHAL
MOMATEC
U.CRETE
CITY U.LONDON
U.ULSTER
GOETHE U.FRANKFURT AM MAIN
U.WIEN
ALLOGG AB
RAUTARUUKKI OY
SOFTECO SISMAT
U.WALES, ABERYSTWYTH
DE MONTFORT U.
I.DALLE MOLLE DI STUDI SULLIA
U.JYVASKYLA
BULGARIAN ACAD.
U.ZAGREB
U.CYPRUS
OF SCIENCES
U.OF CHEMICAL TECH.
BOURNEMOUTH U.
ASS.RECH.SCIENTIFIQUE
AND METALLURGY
KINGS COLLEGE LONDONENTE PER LE
ELITE EUROP.LAB
NUOVE TECNOLOGIE
STICHTINGTECH.
U.NYENRODE
FOR INTELLIGENT
I.NAT.POLITEC.DE TOULOUSE
I.FUER NATURSTOFF-FORSCHUNG E.V.
U.AMSTERDAM
U.GIRONA
U.GENT
AUSTRIAN I.AI
START ENGINEERING JSCO
4-ring weights
ENERGY RESEARCH C.NL
U.GRANADA
TEKNILLINEN KORKEAKOULU
T.U.DELFT
I.NAT.DE RECHERCHE SUR
LES TRANSPORTS ET LEUR SECURITE
HELSINKI T.U.
NAT.U.IRELAND,MAYNOOTH
U.TWENTE
TSS-TRANSPORT SIMULATION SYS.S.L.
U.KLINIKUM AACHEN
KATHOLIEKE U.LEUVEN
Multiplication
Kinship
relations
Projections
U.BRISTOL
FRIEDRICH-SCHILLER-U.JENA
CONSEJO SUP.DE
ERASMUS U.ROTTERDAM
DEP.OF ENVIRONMENT,
QINETIQ
INVEST.CIENTIFICAS
AABO AKADEMI U
AND THE REGIONS
GKSS TRANSPORT
- FORSCHUNGSZENTRUM
GEESTHACHT
JOZEF STEFAN I.
U.P.MADRID
MANNESMANN VDO AG
U.MARIBOR
EUROP.SPACE AGENCY
U.PAUL SABATIER DE TOULOUSE III
U.PAISLEY
TECHSOFT ENGINEERING S.R.O.
TECNOLOGIAS CAE AVANZADAS S.L.
U.STRATHCLYDE
U.VALLADOLID
U.P.CATALUNYA
U.LEEDS
U.S.GENOVA
U.NOTTINGHAM
C.SVILUPPO MATERIALI HERMSDORFER I.FUER TECH.
PT.TORINO
PT.BARI
U.MANCHESTER
OXFORD BROOKES U.
DAIMLER CHRYSLER AG
U.DORTMUND
U.S.PADOVA
SAFE TECH.
BAE SYSTEMS
LOUGHBOROUGH T.U.
NOKIA MOBILE PHONES LTD
CZECH T.U.PRAGUE
AVIO S.P.A.
FOKKER SPACE BV
BRITISH TELEC.
NAT.T.U.ATHENS
T.U.V KOSICIACH
ANAKON
I.SUPERIOR TECNICO
NCODE INT.
U.SHEFFIELD
FUNDACION LABEIN
POLISH ACAD.OF SCIENCES
FINITE ELEMENT ANALYSIS LTD.
RISOE NAT.LAB
TUN ABDUL RAZAK RESEARCH C.LTD.
U.GREENWICH
DANMARKS T.U.
PRINCIPIA INGENIEROS CONSULTORES
U.C.LOUVAIN
FUNDACION INASMET
STAVANGER U.COLLEGE
CRANFIELD U.
SULZER MARKETS AND TECH.AG,
IFP SICOMP AB
SULZER INNOTEC
CHALMERS TEKNISKA HOEGSKOLA
DAMT LTD
SKF R&D COMPANY B.V.
CAESAR SYSTEMS LTD
U.S.NAPOLI
A.U.THESSALONIKI
Collaboration
C.INT.LENGINYERIA
NL ORG.FOR APPLIED
SCIENTIFIC RESEARCH-TNO
C.R.FIAT S.C.P.A.
Other derived
networks
C.NAT.DE LA
RECHERCHE SCIENTIFIQUE
EU projects
INTES - INGENIEURGES.
FUER TECH.SOFTWARE
U.DURHAM
U.S.TRIESTE
CAD - FEM
MSC SOFTWARE
QUEENS U.BELFAST
NAFEMS LTD.
ENGIN SOFT TRADING SRL
MARITIME HYDRAULICS AS
INBIS TECH.LTD
FEMSYS LTD
SOFISTK AG
ABS CONSULTING
ALTAIR ENGINEERING
NLSE VERENIGDE SCHEEPSBOUW BUREAUS B.V.
SAMTECH SA
MERITOR HEAVY VEHICLE
LEUVEN MEASUREMENTS AND SYS.INT.NV
BRAKING
CREA CONSULTANTS
LTDSYS.- UK LTD
TRL
PD&E AUTOMOTIVE B.V.
ACCESS E.V.
NEW TECH.ENGINEERING LTD
ROCKFIELD SOFTWARE LTD.
U.NEWCASTLE UPON TYNE
BEHR &CO.
AIRBUS FRANCE SAS
NAT.NUCLEAR CORP.LTD.
U.GLASGOW
FEMCOS INGENIEURBUERO MBH
ST MECANICA APLICADA S.L.
GERMAN AEROSPACE CENTRE
FRAUENHOFER I.FUER
INGENIEURBUERO FUER
BIOMEDICAL ENGINEERING
TRAGWERKSPLANUNG
KATHOLIEKE HOGESCHOOL SINT-LIEVEN
ROYAL I.OF TECH.
DUNLOP STANDARD
AEROSPACE GROUP
U.HANNOVER
GIFFORD AND PARTNERS LTD.
MECAS S.R.O.
VOLVO AERO CORP.AB
ATOS ORIGIN ENG.
LULEAA T.U.
STRUCTURAL INTEGRITY
CORK I.OF TECHNOLOGY
ASSESSMENTS LTD
HAHN-SCHICKARD-GES.
NORUT TEKNOLOGI A.S.
WS ATKINS CONSULTANTS LTD. EASI ENGINEERING
U.E DO MINHO
NUMERICAL ANALYSIS
U.SPLIT
AND DESIGN&CO KG
ADVIESBUREAU N.V.
WILDE AND TECHNISCH
PARTNERS LTD
INTEGRATED DESIGN &
RANDOM LOADINGANALYSIS
DESIGN CONSULTANTS LTD
FEGS
AWE PLC
D C WHITE&PARTNERS LTD
MERKLE UND PARTNER
DR THELLEN
EATEC LTD
To identify the most important
institutions we first computed
pS -cores vector and use it to determine the corresponding vertex islands. We got essentially
one large island. Again the corresponding subnetwork is very
dense. We prepared also a matrix display.
63 / 65
Analysis of Institutions.net
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
Projections
Collaboration
Other derived
networks
EU projects
ALLOGG AB
AS. CONOCI
ASS. RECH.
AUSTRIAN I
BELIMO AUT
COVENTRY U
DAEDALUS I
DATAMED H
FACULTY OF
FED. UNITA
FL-SOFT V/
INST. OF I
GOETHE UNI
MIT-MANAGE
MOMATEC
NAT. UNIV.
NOTTINGHAM
POLITECNIC
SENTIENT M
SIEMENS BU
SOFIISKI U
START ENGI
STICHTING
STICHTING
THE UNIV.
UNIV. DE L
UNIV.SKLIN
UNIV. DE G
UNIV. PARI
UNIV. OF A
UNIV. OF C
UNIV. OF C
UNIV. OF W
UNIV. OF Z
INST. DALL
RAUTARUUKK
UNIV.E DE
UNIV. OF U
SOFTECO SI
UNIV. GENT
TSS - TRAN
UNIV. DE G
UNIV. DE V
UNIVERZA V
UNIV. PAUL
TECH. UNIV
UNIV. WIEN
UNIV. VAN
ENERGY RES
TEKNILLINE
DE MONTFOR
CITY UNIVE
UNIV. OF J
AABO AKADE
RISOE NAT.
KINGS COLL
UNIV. DORT
FRIEDRICHUNIV. OF C
INST. NAT.
BULGARIAN
ENTE PER L
LOUGHBOROU
HELSINKI U
CRANFIELD
UNIV. CATH
OTTO VON G
UNIV. DEGL
UNIV. OF O
UNIV. OF T
ELITE EURO
ERASMUS UN
INST. FUER
UNIV. PARI
BRITISH TE
BOURNEMOUT
UNIV. OF B
UNIV. OF S
DANMARKS T
DAIMLER CH
INST. NAT.
INST. SUPE
POLITECNIC
POLISH ACA
UNIV. POLI
NAT. TEC.
CONSEJO SU
KATHOLIEKE
UNIV. TWEN
TECH. UNIV
UNIV. POLI
CENTRE NAT
TEC. UNIV.
UNIV. OF P
FUNDACION
JOZEF STEF
CZECH TECH
UNIV. OF N
UNIV. OF S
BAE SYSTEM
UNIV. OF M
ABS CONSUL
ALTAIR ENG
ANAKON
ATOS ORIGI
AWE PLC
BEHR & CO
CAESAR SYS
CORK INST.
CREA CONSU
D C WHITE
DAMT LTD
DEP. OF E
DR THELLEN
DUNLOP STA
EASI ENGIN
EATEC LTD
FEMSYS LTD
FOKKER SPA
FORSCHUNGS
GIFFORD AN
HAHN-SCHIC
HERMSDORFE
INBIS TECH
INGENIEURB
INTEGRATED
KATHOLIEKE
MANNESMANN
MARITIME H
MECAS S.R.
MERITOR HE
MERKLE UND
NAFEMS LTD
NCODE INT.
NLSE VEREN
NEW TECH.
NOKIA MOBI
NORUT TEKN
NUMERICAL
OXFORD BRO
PD & E AUT
RANDOM LOA
SAFE TECH.
SKF R & D
SOFISTK AG
ST MECANIC
STAVANGER
STRUCTURAL
SULZER MAR
TECHNISCH
TECHSOFT E
TECNOLOGIA
TUN ABDUL
UNIV.E DO
UNIV. OF S
WILDE AND
FRAUENHOFE
GKSS - FOR
NAT. NUCLE
UNIV. OF D
ENGIN SOFT
FEGS
IFP SICOMP
INTES - IN
UNIV. DEGL
PRINCIPIA
FINITE ELE
ROCKFIELD
WS ATKINS
ROYAL INST
UNIV. HANN
UNIV. DEGL
UNIV. OF G
UNIV. OF N
CAD - FEM
C. SVILUPP
TRL
LEUVEN MEA
A. UNIV. T
GERMAN AER
CENTRE INT
UNIV. DEGL
QINETIQ
UNIV. OF L
FUNDACION
ACCESS E.V
EUROP. SPA
UNIV. OF G
SAMTECH SA
VOLVO AERO
AVIO S.P.A
MSC SOFTWA
LULEAA UNI
QUEENS UNI
AIRBUS FRA
C. R. FIAT
NL ORG. FO
CHALMERS T
Pajek - shadow [0.00,6.00]
ALLOGG AB
AS. CONOCI
ASS. RECH.
AUSTRIAN I
BELIMO AUT
COVENTRY U
DAEDALUS I
DATAMED H
FACULTY OF
FED. UNITA
FL-SOFT V/
INST. OF I
GOETHE UNI
MIT-MANAGE
MOMATEC
NAT. UNIV.
NOTTINGHAM
POLITECNIC
SENTIENT M
SIEMENS BU
SOFIISKI U
START ENGI
STICHTING
STICHTING
THE UNIV.
UNIV. DE L
UNIV.SKLIN
UNIV. DE G
UNIV. PARI
UNIV. OF A
UNIV. OF C
UNIV. OF C
UNIV. OF W
UNIV. OF Z
INST. DALL
RAUTARUUKK
UNIV.E DE
UNIV. OF U
SOFTECO SI
UNIV. GENT
TSS - TRAN
UNIV. DE G
UNIV. DE V
UNIVERZA V
UNIV. PAUL
TECH. UNIV
UNIV. WIEN
UNIV. VAN
ENERGY RES
TEKNILLINE
DE MONTFOR
CITY UNIVE
UNIV. OF J
AABO AKADE
RISOE NAT.
KINGS COLL
UNIV. DORT
FRIEDRICHUNIV. OF C
INST. NAT.
BULGARIAN
ENTE PER L
LOUGHBOROU
HELSINKI U
CRANFIELD
UNIV. CATH
OTTO VON G
UNIV. DEGL
UNIV. OF O
UNIV. OF T
ELITE EURO
ERASMUS UN
INST. FUER
UNIV. PARI
BRITISH TE
BOURNEMOUT
UNIV. OF B
UNIV. OF S
DANMARKS T
DAIMLER CH
INST. NAT.
INST. SUPE
POLITECNIC
POLISH ACA
UNIV. POLI
NAT. TEC.
CONSEJO SU
KATHOLIEKE
UNIV. TWEN
TECH. UNIV
UNIV. POLI
CENTRE NAT
TEC. UNIV.
UNIV. OF P
FUNDACION
JOZEF STEF
CZECH TECH
UNIV. OF N
UNIV. OF S
BAE SYSTEM
UNIV. OF M
C. R. FIAT
NL ORG. FO
CHALMERS T
SAMTECH SA
VOLVO AERO
AVIO S.P.A
MSC SOFTWA
LULEAA UNI
QUEENS UNI
AIRBUS FRA
CAD - FEM
C. SVILUPP
TRL
LEUVEN MEA
A. UNIV. T
GERMAN AER
CENTRE INT
UNIV. DEGL
QINETIQ
UNIV. OF L
FUNDACION
ACCESS E.V
EUROP. SPA
UNIV. OF G
UNIV. DEGL
UNIV. OF G
UNIV. OF N
FINITE ELE
ROCKFIELD
WS ATKINS
ROYAL INST
UNIV. HANN
FRAUENHOFE
GKSS - FOR
NAT. NUCLE
UNIV. OF D
ENGIN SOFT
FEGS
IFP SICOMP
INTES - IN
UNIV. DEGL
PRINCIPIA
ABS CONSUL
ALTAIR ENG
ANAKON
ATOS ORIGI
AWE PLC
BEHR & CO
CAESAR SYS
CORK INST.
CREA CONSU
D C WHITE
DAMT LTD
DEP. OF E
DR THELLEN
DUNLOP STA
EASI ENGIN
EATEC LTD
FEMSYS LTD
FOKKER SPA
FORSCHUNGS
GIFFORD AN
HAHN-SCHIC
HERMSDORFE
INBIS TECH
INGENIEURB
INTEGRATED
KATHOLIEKE
MANNESMANN
MARITIME H
MECAS S.R.
MERITOR HE
MERKLE UND
NAFEMS LTD
NCODE INT.
NLSE VEREN
NEW TECH.
NOKIA MOBI
NORUT TEKN
NUMERICAL
OXFORD BRO
PD & E AUT
RANDOM LOA
SAFE TECH.
SKF R & D
SOFISTK AG
ST MECANIC
STAVANGER
STRUCTURAL
SULZER MAR
TECHNISCH
TECHSOFT E
TECNOLOGIA
TUN ABDUL
UNIV.E DO
UNIV. OF S
WILDE AND
ALLOGG AB
AS. CONOCI
ASS. RECH.
AUSTRIAN I
BELIMO AUT
COVENTRY U
DAEDALUS I
DATAMED H
FACULTY OF
FED. UNITA
FL-SOFT V/
INST. OF I
GOETHE UNI
MIT-MANAGE
MOMATEC
NAT. UNIV.
NOTTINGHAM
POLITECNIC
SENTIENT M
SIEMENS BU
SOFIISKI U
START ENGI
STICHTING
STICHTING
THE UNIV.
UNIV. DE L
UNIV.SKLIN
UNIV. DE G
UNIV. PARI
UNIV. OF A
UNIV. OF C
UNIV. OF C
UNIV. OF W
UNIV. OF Z
INST. DALL
RAUTARUUKK
UNIV.E DE
UNIV. OF U
SOFTECO SI
UNIV. GENT
TSS - TRAN
UNIV. DE G
UNIV. DE V
UNIVERZA V
UNIV. PAUL
TECH. UNIV
UNIV. WIEN
UNIV. VAN
ENERGY RES
TEKNILLINE
DE MONTFOR
CITY UNIVE
UNIV. OF J
AABO AKADE
RISOE NAT.
KINGS COLL
UNIV. DORT
FRIEDRICHUNIV. OF C
INST. NAT.
BULGARIAN
ENTE PER L
LOUGHBOROU
HELSINKI U
CRANFIELD
UNIV. CATH
OTTO VON G
UNIV. DEGL
UNIV. OF O
UNIV. OF T
ELITE EURO
ERASMUS UN
INST. FUER
UNIV. PARI
BRITISH TE
BOURNEMOUT
UNIV. OF B
UNIV. OF S
DANMARKS T
DAIMLER CH
INST. NAT.
INST. SUPE
POLITECNIC
POLISH ACA
UNIV. POLI
NAT. TEC.
CONSEJO SU
KATHOLIEKE
UNIV. TWEN
TECH. UNIV
UNIV. POLI
CENTRE NAT
TEC. UNIV.
UNIV. OF P
FUNDACION
JOZEF STEF
CZECH TECH
UNIV. OF N
UNIV. OF S
BAE SYSTEM
UNIV. OF M
C. R. FIAT
NL ORG. FO
CHALMERS T
SAMTECH SA
VOLVO AERO
AVIO S.P.A
MSC SOFTWA
LULEAA UNI
QUEENS UNI
AIRBUS FRA
CAD - FEM
C. SVILUPP
TRL
LEUVEN MEA
A. UNIV. T
GERMAN AER
CENTRE INT
UNIV. DEGL
QINETIQ
UNIV. OF L
FUNDACION
ACCESS E.V
EUROP. SPA
UNIV. OF G
UNIV. DEGL
UNIV. OF G
UNIV. OF N
FINITE ELE
ROCKFIELD
WS ATKINS
ROYAL INST
UNIV. HANN
FRAUENHOFE
GKSS - FOR
NAT. NUCLE
UNIV. OF D
ENGIN SOFT
FEGS
IFP SICOMP
INTES - IN
UNIV. DEGL
PRINCIPIA
ABS CONSUL
ALTAIR ENG
ANAKON
ATOS ORIGI
AWE PLC
BEHR & CO
CAESAR SYS
CORK INST.
CREA CONSU
D C WHITE
DAMT LTD
DEP. OF E
DR THELLEN
DUNLOP STA
EASI ENGIN
EATEC LTD
FEMSYS LTD
FOKKER SPA
FORSCHUNGS
GIFFORD AN
HAHN-SCHIC
HERMSDORFE
INBIS TECH
INGENIEURB
INTEGRATED
KATHOLIEKE
MANNESMANN
MARITIME H
MECAS S.R.
MERITOR HE
MERKLE UND
NAFEMS LTD
NCODE INT.
NLSE VEREN
NEW TECH.
NOKIA MOBI
NORUT TEKN
NUMERICAL
OXFORD BRO
PD & E AUT
RANDOM LOA
SAFE TECH.
SKF R & D
SOFISTK AG
ST MECANIC
STAVANGER
STRUCTURAL
SULZER MAR
TECHNISCH
TECHSOFT E
TECNOLOGIA
TUN ABDUL
UNIV.E DO
UNIV. OF S
WILDE AND
Pajek - Ward [0.00,1376.93]
Two-mode
64 / 65
Temporal network and Levels of analysis
Two-mode
V. Batagelj
Direct
methods
2-mode cores
4-ring weights
Multiplication
Kinship
relations
We can also transform the citation network (and other WoS networks) into
temporal network using the partition of works by publication year.
Using the time slices also the temporal sequences of corresponding derived
networks can be obtained.
Note that most of the obtained derived networks are one-mode networks.
To analyze them standard SNA methods can be used.
In the analysis of the obtained networks the comparability of units
could/should be considered.
Projections
Collaboration
Other derived
networks
EU projects
Pajek allows analyses on different levels specified by a partition of the
corresponding set of units and obtained using the shrinking of classes. For
example: partition of authors by institutions, or partition of institutions by
countries, partitions of authors by discipline/ field/ subfield, etc.
Using the extraction of selected classes we can reduce the network to the
area of our interest.
65 / 65
```

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### Network Analysis / Two mode networks

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