Pajek - Vladimir Batagelj

Transcription

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Analiza
velikih
omrežij
Vladimir Batagelj
Univerza v Ljubljani
FMF, matematika
KartOO network
net konferenca 2007
Ljubljana, 31. januar 2007
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version: 22. januar 2007 / 05 : 27
V. Batagelj: Analiza velikih omrežij
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Kazalo
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Omrežja – osnovni pojmi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Pajek
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Pajek in velika omrežja . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Pristopi k analizi velikih omrežij . . . . . . . . . . . . . . . . . . . . . . . . . .
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Vmesnost . . . . . . . . . .
Kazala in vsebine . . . . . .
Otoki . . . . . . . . . . . . .
Sredice in posplošene sredice
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Dvovrstna omrežja . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Omrežje z They Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Omrežja iz podatkovnih tabel . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Primer: Evropski projekti na temo simulacij . . . . . . . . . . . . . . . . . . . .
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Pretvorba dvovrstnih omrežij na enovrstna . . . . . . . . . . . . . . . . . . . . .
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Dvovrstne sredice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Izbrane knjige o analizi omrežij . . . . . . . . . . . . . . . . . . . . . . . . . .
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Omrežja – osnovni pojmi
Alexandra Schuler/ Marion Laging-Glaser:
Analyse von Snoopy Comics
Osnovni sestavini omrežja sta množica
točk, ki predstavljajo izbrane enote,
in množica povezav, ki predstavljajo
odnose (relacije) med enotami. Točke
in povezave določajo graf .
Pri povezavi je lahko smer pomembna –
usmerjena povezava, ali pa ni neusmerjena povezava.
O točkah in povezavah lahko poznamo
dodatne podatke – njihove lastnosti.
Npr. oznaka, vrsta, vrednost, . . .
Omrežje = Graf + Podatki
Ti podatki so lahko izmerjeni ali izračunani.
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Graf
enota – točka, vozlišče
relacija – povezava
usmerjena povezava (a, d)
a je njen začetek
d pa njen konec.
neusmerjena povezava (c: d)
c in d sta njeni krajišči.
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Omrežja
Omrežje N = (V, L, P, W) je določeno z:
• grafom G = (V, L), kjer je V množica točk, A je množica usmerjenih
povezav, in E je množica neusmerjenih povezav. Z L = E ∪ A
označimo množico vseh povezav.
n = |V|, m = |L|
• P lastnosti / točkovne vrednosti: p : V → A
• W uteži / povezavne vrednosti: w : L → B
Velikost omrežja/grafa je določena z dvema številoma: številom točk n = |V| in
številom povezav m = |L|.
Omrežja na nekaj deset točkah so majhna – lahko jih narišemo in za njihovo analizo
uporabimo veliko algoritmov (UCINET, NetMiner). Tudi srednje velika omrežja
(nekaj sto točk) še lahko narišemo (preglednost !?), nekateri postopki že odpovejo.
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Velika omrežja
Veliko omrežje – več tisoč ali celo milijonov točk. V celoti ga lahko
shranimo v pomnilnik računalnika – sicer ogromno omrežje. Velika
omrežja so postala dejstvo sredi devetdesetih let.
Običajno so redka m << n2 ; pogosto: m = O(n) ali m = O(n log n) .
Primeri:
omrežje
slovar ODLIS
Sklicevanja SOM
Molekula 1ATN
Comput. geometry
angleške besede 2-8
Internetske iskalne poti
Rodovnik Franklin
World-Wide-Web
Igralci
Patenti ZDA
SI internet
velikost
61K
168K
74K
140K
520K
1.7M
12M
3.6M
3.9M
82M
38M
n = |V|
2909
4470
5020
7343
52652
124651
203909
325729
392400
3774768
5547916
m = |L|
18419
12731
5128
11898
89038
207214
195650
1497135
1342595
16522438
62259968
vir
ODLIS online
Garfieldova zbirka
Brookhaven PDB
BiBTEX bibliographies
Knuth’s English words
Internet Mapping Project
Roperld.com gedcoms
Notre Dame Networks
Notre Dame Networks
Nber
Najdi Si
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Zahtevnost algoritmov
Poglejmo časovne zahtevnosti nekaj značilnih algoritmov
(1999, Pentium/64M/90MHz):
Shuffle
HeapSort
AB
T(n)
1.000
10.000
100.000
1.000.000
10.000.000
O(n)
0.00 s
0.015 s
0.17 s
2.22 s
22.2 s
O(n log n)
√
O(n n)
0.00 s
0.06 s
0.98 s
14.4 s
2.8 m
0.01 s
0.32 s
10.0 s
5.27 m
2.78 h
Insert sort
O(n2 )
0.07 s
7.50 s
12.5 m
20.8 h
86.8 d
XY
O(n3 )
0.10 s
1.67 m
1.16 d
3.17 L
3.17 kL
Za interaktivno uporabo na velikih podatkih so že kvadratični algoritmi,
O(n2 ), prezahtevni.
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Pri algoritmih eksponentne zahtevnosti, npr. O(2n ), časovne zahteve
naraščajo izjemno hitro. Recimo, da za n = 20 potrebujemo 1 s, tedaj za
n = 30 potrebujemo 210 s = 1024 s = 17 m; za n = 40 dobimo 1048576 s
= 12.14 d; za n = 50 že 1073741824 s = 34.05 L; . . . za n = 80 pa z 36.56
109 L presežemo domnevno starost Zemlje.
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Pajek
Pajek je program za okolje Windows za analizo
in prikaz velikih omrežij. Z Andrejem Mrvarjem
sva ga začela razvijati leta 1996.
Knjiga: W. de Nooy, A. Mrvar, V. Batagelj: Exploratory Social Network Analysis with Pajek,
CUP, 2005. Amazon. stran ESNA.
Zadnja izdaja programa Pajek je prosto dostopna (za netržne uporabe) na:
http://vlado.fmf.uni-lj.si/pub/networks/pajek/
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Pajek in velika omrežja
Glavni cilji v zasnovi programa Pajek so:
• podpora abstrakciji z (rekurzivnim)
razčlenjevanjem velikega omrežja v
več manjših, ki jih lahko v nadaljevanju posamično obdelamo z zahtevnejšimi postopki;
• ponuditi uporabniku izbor orodij za
prikaz omrežij;
• izbrati/razviti nabor učinkovitih podkvadratičnih algoritmov za analizo velikih omrežij.
S Pajekom lahko: določimo zanimive skupine (komponente, soseščine ‘pomembnih’ točk,
sredice, . . . ) v omrežju, izrežemo del omrežja, ki pripada izbranim skupinam in ga ločeno
prikažemo; lahko s ’povzetkom vpetosti’ v celotno omrežje (lokalni pogled), skrčimo točke, ki
pripadajo isti skupini, in prikažemo odnose med skupinami (globalni pogled).
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Prikaz omrežij
Pomembna sestavina analize omrežij so
prikazi (delov) omrežij.
Prikaze lahko ustvarimo programsko
(vzmetne vložitve) ali ročno.
Za posebne vrste omrežij obstajajo posebni
načini prikazov. Npr. aciklična omrežja
lahko prikažemo po ravneh.
Prikažemo lahko tudi izbrane lastnosti točk
in povezav. Primer: šolarji (Moody).
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Pristopi k analizi velikih omrežij
1 e+06
US Patents degree distribution
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1 e+00
1 e+02
freq
1 e+04
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1
5
10
50
deg
100
500
1000
Običajni pristop k analizi velikih podatkovij je statistika. V zadnjih desetih letih deležni velike pozornosti
brezlestvični (scale free) verjetnostni
modeli omrežij.
Druga pot so postopki za določanje
zanimivih delov omrežij in razkrivanje
zgradbe omrežja. V tem sestavku
bomo prikazali pomembnejše izmed
njih.
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Vmesnost
Obstaja cela vrsta mer pomembnosti točk, ki številsko izrazijo vlogo točke
v omrežju. Kot primer take mere si poglejmo vmesnost.
Pomembne so točke, ki lahko nadzirajo pretok podatkov po omrežju. Če
privzamemo, da so za prenos pomembne le najkrajše poti, dobimo kot mero
vmesnosti (Anthonisse 1971, Freeman 1977)
1
b(v) =
(n − 1)(n − 2)
X
u,t∈V:gu,t >0
u6=v,t6=v,u6=t
gu,t (v)
gu,t
kjer je gu,t število najkrajših poti iz u v t; in gu,t (v) število takih med njimi,
ki gredo skozi točko v.
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Krebsova Internetska podjetja – vmesnost
CVS
BestBuy
DeloitteToucheTohmatsu
RadioShack
AskJeeves
MapInfo
BT
Slate
B&N
CapGemini
Verizon
PivotalSoftware
VerticalNet
BankOne
Excite
Verity
Comcast
Unisys
Spyglass BaltimoreTechnologies
JuniperNetworks
Handspring
Cablevision
Disney/ABC
LiquidAudio
WebMD
DoubleClick
XOComm.
NewsCorp
Audible
NortelNetworksNBC
CharlesSchwab
AutoTrader
McAfee
BellSouth
QXL.com
Ford
CheckPoint
NTT
LookSmart
C&W
EDS
WellsFargo
Qualcomm
MSFT
Starbucks
Prodigy
MP3.com
KPMG
AberdeenGroup
Netopia
RSA
CSC
Broadcom
Staples
Dell
eBay
EMC
Yahoo!
Net2Phone
BofA
Drugstore
GlobalCrossing
Amazon
CMGI
Samsung
RIM
Fujitsu
ToysRUs
Borders
LibertyMedia
CheckFreeGateway
Siemens
Buy.com
IDT
CNN
CareerMosaic
Apple
Monster
Tibco
Travelocity
theStreet
GeneralInstrument
Adobe
Livelink
HP
CircuitCity
AmEx
Tellabs
WebTrends
Lucent
C|Net
Kodak
Inktomi
AP
DigitalIsland
Akamai
NetworkAssociates
Vignette
Lumeta
Ericsson
EarthLink
Ariba
Cisco
divine
BellCanada
METAGroup
OfficeMax
MercuryInteractive
E.piphany
Compaq
RealNetworks
MediaOne
VeriSign
Accenture
NetworkSolutions
Peoplesoft
E*Trade
Participate.com
ExodusComm
TerraLycos
Palm
Loudcloud
RedHat
ViacomCBS
InterNap
RoadRunner
AOL
BMCSoftwareHarbinger
Sprint
Netcentives
CareerBuilder
eLance
CBS
CacheFlow
Agency.com
IBM
EMI CDNow
SportsLine
Novell
Sun
Vodafone
CIBER
ComputerAssociates
iPlanet
Oxygen
USATODAY
Netegrity
FoundryNetworks TARGET
PwC
Oracle
Kana
Intel
Universal
SBC
AlcatelForresterResearch
GartnerGroup3COM
Teleglobe
AvantGo
Interliant
SoftBank
KPNQwest
BEASystems
Motorola
InfoSpace
AT&T
Nokia
AAdvantage
AltaVista
KMartMacromedia
NetZero
Siebel
Sony
Interwoven
Bertelsmann
Nextel
Kinko’s
Blockbuster
napster
VISA
moreover.com
AnswerThink
Sears
bowstreet
Genuity
NaviSite
GM
UPS
SAP
WebMethods
CommerceOne
JDEdwards
MapQuest
i2
BroadVision
Fidelity
MicroStrategy
Lawson
MasterCard GE Veritas Citibank
D&B
ALLTEL
ATG
Juno
Intuit
Level3
WalMart
SonusNetworks
Omrežje sestavljajo izbrana
Internetska podjetja v obdobju
1998 do 2001.
n = 219, m = 631.
rdeča – vsebina,
modra – podpora,
zelena – trgovina.
Podjetji sta povezani, če sta
objavili skupni posel ali sodelovanje.
SAS
Spletni naslov: orgnet
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Kazala in vsebine
Točkam povezanega usmerjenega omrežja N = (V, L) priredimo dve
vrednosti: kakovost vsebine xv in kakovost kazala yv (Kleinberg, 1998).
Na dobro vsebino kažejo dobra kazala in dobro kazalo kaže na dobre
vsebine
X
X
xv =
yu
in
yv =
xu
u:(u,v)∈L
u:(v,u)∈L
Naj bo W matrika omrežja N in x ter y vektorja obeh lastnosti. Tedaj
lahko zvezi zapišemo x = WT y oziroma y = Wx.
Začnimo z y = [1, 1, . . . , 1] in nato zaporedoma izračunamo po obeh zvezah nove približke
za x in y. Oba vektorja po vsakem koraku normaliziramo. To ponavljamo dokler se vektorja
ne ustalita. Pokazati je mogoče, da opisani postopek konvergira. Limitni vektor x∗ je glavni
lastni vektor matrike WT W; y∗ pa matrike WWT .
PageRank, PageRank / Google, HITS / AltaVista, SALSA, teorija.
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. . . Kazala in vsebine: nogometaši
IRN
KOR
IRN
KOR
AUT
TUN
FRA
AUT
TUN
FRA
CHE
CHE
DEU
DEU
CMR
CMR
JPN
JPN
ZAF
BGR
BEL
DNK
PRT
MAR
TUR
ZAF
BGR
BEL
NOR
DNK
PRT
MAR
NGA
NGA
TUR
GRE
NOR
GRE
NLD
NLD
ROM
ROM
GBR
HRV
GBR
HRV
PRY
PRY
ESP
YUG
ESP
SCO
ITA
YUG
SCO
ITA
JAM
MEX
JAM
MEX
BRA
ARG
COL
Izvozniki (kazala/hubs)
CHL
USA
BRA
USA
CHL
ARG
COL
Uvozniki (vsebine/authorities)
Na svetovnem nogometnem prvenstvu v Parizu leta 1998 je sodelovalo 22 nogometnih reprezentanc. V
omrežju so vse države, iz katerih so nogometaši igrali v ligah teh 22 držav, in vse države, v katerih ligah
so igrali nogometaši iz teh 22 držav. Relacija je igralec iz države x igra v državi y; utež je število takih
igralcev. Podatke je zbral Lothar Krempel. football.net
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Otoki
Če dano lastnost/utež točk/povezav predstavimo kot njihovo višino, nam
naše omrežje določa nekakšno pokrajino s hribi in dolinami. Če to pokrajino
potopimo v vodo do izbrane višine, dobimo otoke. S spreminjanjem višine
vode dobivamo različne otoke. V uprabah nas običajno zanimajo ne
preveliki in ne premajhni otoki – le otoki velikosti med izbranima k in K.
Postopek ’otoki’ začne s pokrajino popolnoma potopljeno v vodo. Nato
znižujemo višino, dokler se ne pojavi otok prave velikosti . . .
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Otoki so zelo splošen in učinkovit postopek za določanje ’pomembnih’
podomrežij v danem omrežju.
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Otoki – The Edinburgh Associative Thesaurus
n = 23219, m = 325624, transitivity weight
CHAMPIONSHIP
PLAYING
STUDYING
LECTURER
FIVES
TEAM
TEACHER
ENGINEERING
GAME
SOCCER
BADMINTON
TENNIS
LEARNING
SCHOOL
EDUCATION
RUGGER
SPORT
FOOTBALL
TEACHING
GOALIE
HOMEWORK
PLAYER
NETBALL
WORK
GAMES
TRAINING
LECTURES
BALL
RUGBY
SCIENCE
REFEREE
HOCKEY
BALLS
BASKETBALL
LESSONS
MATHS
STUDY
SCIENTIFIC
RESEARCH
SHORTS
ACTIVITY
GYM
BICYCLE
BIKE
SPIRITS
LORRIES
MOTOR CYCLE
DRIVERS
LIQUOR
DRUNK
ROADS
BICYCLES
WHISKY
KEG BITTER
BIKES
BEER
TRUCK
CAR
WHISKEY
BRANDY
MACHINES
COACH
RAILWAYS
GIN
DRINK
VAN
STREET
TRAIN
RAILWAY
LANE
BEER-MUG
SIPPING
MOVING
MOBILE
ROAD
DRY MARTINI
SIP
STOPPING
STOP
PATH
LEMONADE
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Štetje poti – Search path count method
Metoda štetja poti – search path count
method (SPC) temelji na števcih n(u, v),
ki štejejo število različnih poti iz izvora s v
ponor t, ki gredo čez povezavo (u, v).
Hummon in Doreian uteži so takole
določene:
• search path link count (SPLC) method:
utež wl (u, v) je enaka številu “vseh
možnih poti po omrežju, ki imajo
začetek v izvoru” in gredo po povezavi
(u, v) ∈ R.
• search path node pair (SPNP) method:
wp (u, v) “upošteva vse povezanosti
parov točk s potmi, ki gredo po
povezavi (u, v) ∈ R”.
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Lastnosti uteži SPC
Vrednosti števcev n(u, v) določajo tok po omrežju sklicevanj – zanj velja
Kirchoffov točkovni zakon: v vsaki točki u standardnega omrežja sklicevanj
velja vstopni tok = izstopni tok:
X
X
n(v, u) =
n(u, v) = n− (u) · n+ (u)
v:vRu
v:uRv
Utež n(t, s) je enaka celotnemu toku skozi omrežje in ponuja naravni način
normalizacije uteži
w(u, v) =
n(u, v)
n(t, s)
⇒
0 ≤ w(u, v) ≤ 1
in, če je C minimalni povezavni prerez, velja še
P
(u,v)∈C
w(u, v) = 1.
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Glavna pot in glavni otok v US Patents
5855814
4456712
5683624
5555116
5543077
5124824
5171469
5283677
5122295
5016989
5374374
5016988
5308538
4957349
4877547
4820839
4832462
4797228
4752414
4721367
4704227
4657695
5171469
5122295
4770503
4795579
4877547
4709030
4719032
4695131
4710315
4713197
4659502
4621901
4797228
4630896
4710315
4583826
4510069
4558151
4550981
4659502
4526704
4502974
4514044
4480117
4472293
4472592
4455443
4419263
4422951
4550981
4460770
4526704
4472293
4422951
4415470
4400293
4386007
4330426
4357078
4386007
4349452
4368135
4293434
4290905
4340498
4340498
4387039
4387038
4361494
4302352
4302352
4195916
4229315
4149413
4229315
4202791
4261652
4149413
4198130
4082428
4154697
4113647
4013582
4029595
4130502
4032470
4083797
4082428
4118335
4011173
4077260
4017416
3975286
4011173
4000084
3960752
3954653
3872140
2544659
3675987
3947375
3960752
3876286
3881806
3731986
3795436
3891307
3697150
3636168
3767289
3666948
3322485
3773747
3796479
3795436
2682562
3691755
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Glavni otok – Liquid crystal display
Table 1: Patents on the liquid-crystal display
patent
2544659
2682562
3322485
3636168
3666948
3675987
3691755
3697150
3731986
3767289
3773747
3795436
3796479
3872140
3876286
3881806
3891307
3947375
3954653
3960752
3975286
4000084
4011173
4013582
4017416
4029595
4032470
4077260
4082428
date author(s) and title
Mar 13, 1951 Dreyer. Dichroic light-polarizing sheet and the like and the
formation and use thereof
Jun 29, 1954 Wender, et al. Reduction of aromatic carbinols
May 30, 1967 Williams. Electro-optical elements utilazing an organic
nematic compound
Jan 18, 1972 Josephson. Preparation of polynuclear aromatic compounds
May 30, 1972 Mechlowitz, et al. Liquid crystal termal imaging system
having an undisturbed image on a disturbed background
Jul 11, 1972 Rafuse. Liquid crystal compositions and devices
Sep 19, 1972 Girard. Clock with digital display
Oct 10, 1972 Wysochi. Electro-optic systems in which an electrophoreticlike or dipolar material is dispersed throughout a liquid
crystal to reduce the turn-off time
May 8, 1973 Fergason. Display devices utilizing liquid crystal light
modulation
Oct 23, 1973 Aviram, et al. Class of stable trans-stilbene compounds,
some displaying nematic mesophases at or near room
temperature and others in a range up to 100◦ C
Nov 20, 1973 Steinstrasser. Substituted azoxy benzene compounds
Mar 5, 1974 Boller, et al. Nematogenic material which exhibit the Kerr
effect at isotropic temperatures
Mar 12, 1974 Helfrich, et al. Electro-optical light-modulation cell
utilizing a nematogenic material which exhibits the Kerr
effect at isotropic temperatures
Mar 18, 1975 Klanderman, et al. Liquid crystalline compositions and
method
Apr 8, 1975 Deutscher, et al. Use of nematic liquid crystalline substances
May 6, 1975 Suzuki. Electro-optical display device
Jun 24, 1975 Tsukamoto, et al. Phase control of the voltages applied to
opposite electrodes for a cholesteric to nematic phase
transition display
Mar 30, 1976 Gray, et al. Liquid crystal materials and devices
May 4, 1976 Yamazaki. Liquid crystal composition having high dielectric
anisotropy and display device incorporating same
Jun 1, 1976 Klanderman, et al. Liquid crystal compositions
Aug 17, 1976 Oh. Low voltage actuated field effect liquid crystals
compositions and method of synthesis
Dec 28, 1976 Hsieh, et al. Liquid crystal mixtures for electro-optical
display devices
Mar 8, 1977 Steinstrasser. Modified nematic mixtures with
positive dielectric anisotropy
Mar 22, 1977 Gavrilovic. Liquid crystal compounds and electro-optic
devices incorporating them
Apr 12, 1977 Inukai, et al. P-cyanophenyl 4-alkyl-4’-biphenylcarboxylate,
method for preparing same and liquid crystal compositions
using same
Jun 14, 1977 Ross, et al. Novel liquid crystal compounds and electro-optic
devices incorporating them
Jun 28, 1977 Bloom, et al. Electro-optic device
Mar 7, 1978 Gray, et al. Optically active cyano-biphenyl compounds and
liquid crystal materials containing them
Apr 4, 1978 Hsu. Liquid crystal composition and method
patent
4083797
4113647
4118335
4130502
4149413
Apr 11,
Sep 12,
Oct 3,
Dec 19,
Apr 17,
date
1978
1978
1978
1978
1979
4154697 May 15, 1979
4195916
Apr 1, 1980
4198130 Apr 15, 1980
4202791 May 13, 1980
4229315 Oct 21, 1980
4261652 Apr 14, 1981
4290905
4293434
4302352
Sep 22, 1981
Oct 6, 1981
Nov 24, 1981
4330426 May 18, 1982
4340498
4349452
4357078
Jul 20, 1982
Sep 14, 1982
Nov 2, 1982
4361494
4368135
Nov 30, 1982
Jan 11, 1983
4386007 May 31, 1983
4387038
Jun 7, 1983
4387039
Jun 7, 1983
4400293
4415470
Aug 23, 1983
Nov 15, 1983
4419263
Dec 6, 1983
4422951
4455443
4456712
4460770
4472293
Dec
Jun
Jun
Jul
Sep
27,
19,
26,
17,
18,
1983
1984
1984
1984
1984
4472592
4480117
4502974
Sep 18, 1984
Oct 30, 1984
Mar 5, 1985
4510069
Apr 9, 1985
author(s) and title
Oh. Nematic liquid crystal compositions
Coates, et al. Liquid crystalline materials
Krause, et al. Liquid crystalline materials of reduced viscosity
Eidenschink, et al. Liquid crystalline cyclohexane derivatives
Gray, et al. Optically active liquid crystal mixtures and
liquid crystal devices containing them
Eidenschink, et al. Liquid crystalline hexahydroterphenyl
derivatives
Coates, et al. Liquid crystal compounds
Boller, et al. Liquid crystal mixtures
Sato, et al. Nematic liquid crystalline materials
Krause, et al. Liquid crystalline cyclohexane derivatives
Gray, et al. Liquid crystal compounds and materials and
devices containing them
Kanbe. Ester compound
Deutscher, et al. Liquid crystal compounds
Eidenschink, et al. Fluorophenylcyclohexanes, the preparation
thereof and their use as components of liquid crystal dielectrics
Eidenschink, et al. Cyclohexylbiphenyls, their preparation and
use in dielectrics and electrooptical display elements
Sugimori. Halogenated ester derivatives
Osman, et al. Cyclohexylcyclohexanoates
Carr, et al. Liquid crystal compounds containing an alicyclic
ring and exhibiting a low dielectric anisotropy and liquid
crystal materials and devices incorporating such compounds
Osman, et al. Anisotropic cyclohexyl cyclohexylmethyl ethers
Osman. Anisotropic compounds with negative or positive
DC-anisotropy and low optical anisotropy
Krause, et al. Liquid crystalline naphthalene derivatives
Fukui, et al. 4-(Trans-4’-alkylcyclohexyl) benzoic acid
4’”-cyano-4”-biphenylyl esters
Sugimori, et al. Trans-4-(trans-4’-alkylcyclohexyl)-cyclohexane
carboxylic acid 4’”-cyanobiphenyl ester
Romer, et al. Liquid crystalline cyclohexylphenyl derivatives
Eidenschink, et al. Liquid crystalline fluorine-containing
cyclohexylbiphenyls and dielectrics and electro-optical display
elements based thereon
Praefcke, et al. Liquid crystalline cyclohexylcarbonitrile
derivatives
Sugimori, et al. Liquid crystal benzene derivatives
Takatsu, et al. Nematic halogen Compound
Christie, et al. Bismaleimide triazine composition
Petrzilka, et al. Liquid crystal mixture
Sugimori, et al. High temperature liquid crystal substances of
four rings and liquid crystal compositions containing the same
Takatsu, et al. Nematic liquid crystalline compounds
Takatsu, et al. Nematic liquid crystalline compounds
Sugimori, et al. High temperature liquid-crystalline ester
compounds
Eidenschink, et al. Cyclohexane derivatives
patent
4514044
4526704
4550981
4558151
4583826
4621901
4630896
4657695
4659502
4695131
4704227
4709030
4710315
4713197
4719032
4721367
4752414
4770503
4795579
4797228
4820839
4832462
4877547
4957349
5016988
5016989
5122295
5124824
5171469
5283677
5308538
5374374
5543077
5555116
5683624
5855814
date author(s) and title
Apr 30, 1985 Gunjima, et al. 1-(Trans-4-alkylcyclohexyl)-2-(trans-4’-(p-sub
stituted phenyl) cyclohexyl)ethane and liquid crystal mixture
Jul 2, 1985 Petrzilka, et al. Multiring liquid crystal esters
Nov 5, 1985 Petrzilka, et al. Liquid crystalline esters and mixtures
Dec 10, 1985 Takatsu, et al. Nematic liquid crystalline compounds
Apr 22, 1986 Petrzilka, et al. Phenylethanes
Nov 11, 1986 Petrzilka, et al. Novel liquid crystal mixtures
Dec 23, 1986 Petrzilka, et al. Benzonitriles
Apr 14, 1987 Saito, et al. Substituted pyridazines
Apr 21, 1987 Fearon, et al. Ethane derivatives
Sep 22, 1987 Balkwill, et al. Disubstituted ethanes and their use in liquid
crystal materials and devices
Nov 3, 1987 Krause, et al. Liquid crystal compounds
Nov 24, 1987 Petrzilka, et al. Novel liquid crystal mixtures
Dec 1, 1987 Schad, et al. Anisotropic compounds and liquid crystal
mixtures therewith
Dec 15, 1987 Eidenschink, et al. Nitrogen-containing heterocyclic compounds
Jan 12, 1988 Wachtler, et al. Cyclohexane derivatives
Jan 26, 1988 Yoshinaga, et al. Liquid crystal device
Jun 21, 1988 Eidenschink, et al. Nitrogen-containing heterocyclic compounds
Sep 13, 1988 Buchecker, et al. Liquid crystalline compounds
Jan 3, 1989 Vauchier, et al. 2,2’-difluoro-4-alkoxy-4’-hydroxydiphenyls and
their derivatives, their production process and
their use in liquid crystal display devices
Jan 10, 1989 Goto, et al. Cyclohexane derivative and liquid crystal
composition containing same
Apr 11, 1989 Krause, et al. Nitrogen-containing heterocyclic esters
May 23, 1989 Clark, et al. Liquid crystal devices
Oct 31, 1989 Weber, et al. Liquid crystal display element
Sep 18, 1990 Clerc, et al. Active matrix screen for the color display of
television pictures, control system and process for producing
said screen
May 21, 1991 Iimura. Liquid crystal display device with a birefringent
compensator
May 21, 1991 Okada. Liquid crystal element with improved contrast and
brightness
Jun 16, 1992 Weber, et al. Matrix liquid crystal display
Jun 23, 1992 Kozaki, et al. Liquid crystal display device comprising a
retardation compensation layer having a maximum principal
refractive index in the thickness direction
Dec 15, 1992 Hittich, et al. Liquid-crystal matrix display
Feb 1, 1994 Sagawa, et al. Liquid crystal display with ground regions
between terminal groups
May 3, 1994 Weber, et al. Supertwist liquid-crystal display
Dec 20, 1994 Weber, et al. Supertwist liquid-crystal display
Aug 6, 1996 Rieger, et al. Nematic liquid-crystal composition
Sep 10, 1996 Ishikawa, et al. Liquid crystal display having adjacent
electrode terminals set equal in length
Nov 4, 1997 Sekiguchi, et al. Liquid crystal composition
Jan 5, 1999 Matsui, et al. Liquid crystal compositions and liquid crystal
display elements
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Sredice in posplošene sredice
Pojem sredice je vpeljal Seidman leta 1983. Podgraf H =
(W, L(W)) grafa G = (V, L) porojen z množico W je k-sredica ali
sredica reda k ntk. ∀v ∈ W :
degH (v) ≥ k in je H maksimalni
podgraf s to lastnostjo.
Sredici največjega reda v grafu pravimo tudi glavna sredica. Sredičnost
točke v je enaka največjemu redu sredice, ki še vsebuje to točko.
Privzemimo, da imamo na N določeno funkcijo p(v, U), v ∈ V, U ⊆ V
z realnimi vrednostmi – p-funkcijo. Podgraf H = (C, L(C)) porojen z
množico C ⊆ V je p-sredica na ravni t ∈ R ntk. ∀v ∈ C : t ≤ p(v, C) in je
C maksimalna taka množica.
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GeomBib – navadne sredice reda 10
C.Zelle
H.A.El-Gindy
M.E.Houle
J.Czyzowicz
M.L.Demaine
I.Streinu
S.P.Fekete
P.Belleville
V.Sacristan
K.R.Romanik
D.H.Rappaport
F.Hurtado
H.Meijer
D.Bremner
G.Liotta
A.Lubiw
T.C.Shermer
W.J.Lenhart
S.S.Skiena
H.Everett
B.Zhu
D.M.Avis
T.C.Biedl
M.J.vanKreveld
J.Urrutia
S.M.Robbins
D.M.Mount
P.K.Bose
E.M.Arkin
J.S.B.Mitchell G.T.Wilfong
O.Aichholzer
S.H.Whitesides
M.Yvinec
O.Devillers
J-M.Robert
Te.Asano
M.T.deBerg
E.D.Demaine
N.Katoh
S.Lazard
D.L.Souvaine
I.G.Tollis
T.Roos
M.H.Overmars
H.Alt
J-R.Sack
M.Teillaud
G.Rote
H.Imai
J.O’Rourke
M.T.Goodrich
R.Seidel
D.Halperin
J-D.Boissonnat
J.S.Vitter
S.Suri
J.Erickson
N.M.Amato
M.Sharir
R.Pollack
D.Z.Chen
K.Mehlhorn
B.Chazelle
S-W.Cheng
J.S.Snoeyink
R.Wenger
J.E.Hershberger
O.Schwarzkopf
R.Tamassia R.L.S.Drysdale
P.K.Agarwal
Q.Huang
J.Pach
F.P.Preparata
E.Welzl
L.J.Guibas
K.Kedem
S.J.Fortune
J.Matousek
J.C.Clements
H.S.Sawhney
D.G.Kirkpatrick
C-K.Yap
D.Eppstein
B.Aronov
J.Ashley
S.A.Mitchell
E.Trimble
D.White
D.P.Dobkin
H.Edelsbrunner
F.Aurenhammer D.T.Lee
M.W.Bern
D.Steele
W.J.Bohnhoff
A.Aggarwal
L.P.Chew
R.R.Lober
S.R.Kosaraju
G.D.Sjaardema
T.K.Dey N.Amenta
P.Yanker
D.Petkovic
T.J.Wilson
L.Lopez-Buriek
J.R.Hipp
W.R.Oakes
S.Parker
P.Plassmann
T.J.Tautges
J.Harer
J.Hass
G.T.Toussaint
G.Lerman
E.Sedgwick
D.Letscher
A.Hicks
D.Zorin
T.L.Edwards
C.K.Johnson
M.Flickner
M.Gorkani
C.Grimm
W.Niblack J.Hafner
J.Weeks
S.E.Benzley
T.D.Blacker M.Whitely
B.Dom
Iz B. Jones-ove bibliografija računalniške geometrije Computational geometry database (2002), FTP, Geom.net. smo sestavili omrežje sodelovanj.
Avtorja določata povezavo, če sta napisala skupno delo. Utež povezave je enaka številu skupnih del.
n = 9072, m = 13567/22577 → n0 = 7343, m0 = 11898.
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pS -sredica omrežja GeomBib na ravni 46
E.Arkin
J.Mitchell
I.Tollis
M.Bern
A.Garg
D.Eppstein
L.Vismara
G.diBattista
R.Tamassia
M.Goodrich
G.Liotta
D.Dobkin
S.Suri
J.O’Rourke
J.Vitter
J.Hershberger
B.Chazelle
R.Seidel B.Aronov L.Guibas
H.Edelsbrunner
M.Sharir
F.Preparata
J.Snoeyink
P.Agarwal
R.Pollack
D.Halperin
J.Pach
P.Gupta
M.Smid
E.Welzl
M.Overmars
P.Bose
M.vanKreveld
J.Boissonnat
O.Devillers
J.Matousek
C.Yap
J.Majhi
M.Yvinec
M.deBerg
O.Schwarzkopf
R.Janardan
J.Schwerdt
G.Toussaint
M.Teillaud
J.Urrutia
J.Czyzowicz
C.Icking
R.Klein
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Dvovrstna omrežja
Dvovrstno omrežje je omrežje N = (U, V, A, w), v katerem je množica
točk sestavljena iz dveh ločenih podmnožic U in V ter imajo povezave iz
množice A svoj začetek v množici U in svoj konec v množici V. w : A → R
je utež povezav. Če utež ni podana, postavimo w(u, v) = 1 za vse povezave
(u, v) ∈ A. Množica povezav A določa relacijo A ⊆ U × V.
Dvovrstno omrežje lahko predstavimo tudi s pravokotno matriko A =
[auv ]U ×V .
w(u, v)
(u, v) ∈ A
auv =
0
sicer
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Omrežje z They Rule
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Omrežja iz podatkovnih tabel
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Podatkovna tabela T je sestavljena iz množice zapisov T = {Tk :
k ∈ K}, kjer je K množica ključev. Posamezni zapis ima obliko Tk =
(k, q1 (k), q2 (k), . . . , qr (k)) kjer je qi (k) vrednost lastnosti qi za ključ k.
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. . . Omrežja iz podatkovnih tabel
Naj ima lastnost q zalogo vrednosti Q. Če je ta končna (to lahko vselej
dosežemo z razbitjem na razrede), lahko lastnosti q priredimo dvovrstno
omrežje K × q = (K, Q, E, w) določeno z usmerjenimi povezavami
(k, v) ∈ E ntk. q(k) = v, z utežmi w(k, v) = 1. txt2pajek (Jürgen Pfeffer)
Dvovrstno omrežje qi × qj = (Qi , Qj , E, w) lahko definiramo tudi za
lastnosti qi in qj , kjer je (u, v) ∈ E natanko takrat, ko ∃k ∈ K : (qi (k) =
u ∧ qj (k) = v), in je w(u, v) = card {k ∈ K : (qi (k) = u ∧ qj (k) = v)}.
Naj bo še [qi × qj ]T = qj × qi .
Potem velja qi × qj = [K × qi ]T ∗ [K × qj ] = [qi × K] ∗ [K × qj ].
Par lastnosti qi in qj lahko združimo tudi glede na neko tretjo lastnost qs :
dobimo dvovrstno omrežje [qi × qj ]/qs = [qi × qs ] ∗ [qs × qj ].
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Primer: Evropski projekti na temo simulacij
Za srečanje The Age of Simulation januarja 2006 na Ars Electronica v
Linzu smo skupaj s sodelavci podjetja FAS z Dunaja analizirali podatke o
evropskih projektih na temo simulacij. Podatke so zbrali sodelavci FASa s
spletišča projektov in jih uredili v obliki velike tabele v Excelu. Posamezni
zapis sestavljajo različni podatki o posamezni sodelujoči ustanovi na
posameznem projektu. Tabelo smo najprej shranili v obliki CSV in nato s
programom Text2Pajek iz nje ustvarili tri dvovrstna omrežja:
• project.net – idents × projects = P
• country.net – idents × countries = C
• institution.net – idents × institutions = U
l y
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s
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%
s
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s
Velikosti posameznih množic so naslednje:
|idents| = 8869, |projects| = 933, |institutions| = 3438,
|countries| = 60.
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Evropski projekti – množenje omrežij
Ker imajo vsa tri omrežja skupno množico K =idents, lahko na prej opisani
način iz njih z množenjem pridobimo različna omrežja:
• ProjInst.net – projects × institutions W = PT ? U
• Countries.net – countries × countries S = CT ? C
• Institutions.net – institutions × institutions Q = WT ? W
Za določitev pomembnih delov omrežja ProjInst.net smo najprej
določili omrežje 4-obročnih uteži in na tem omrežju določili povezavne
otoke:
Dobili smo 101 otok, 18 med njimi ima velikost vsaj 5 (točk). Najpomembnejša otoka sestavljajo letalske ustanove in avtomobilske ustanove.
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Analiza omrežja ProjInst.net
ARMINES
PSI FUR PRODUKTE UND
SYS.E DER INFORMATIONSTECH.
BICC GENERAL CABLE
TQT SRL
ESI SOFTWARE SA
CHALMERS TEKNISKA HOEGSKOLA
28283
COLOPLAST A/S
MTU AERO ENGINES
25525
FRAUENHOFER INST. FUER
PRODUKTIONSTECH. UND AUTOMATISIERUNG
EADS DE
LMS UMWELTSYS.E, DIPL. ING. DR. HERBERT BACK
BAE SYSTEMS
29817
DASSAULT AVIATION
C. R. FIAT S.C.P.A.
NL ORG. FOR APPLIED
SCIENTIFIC RESEARCH - TNO
BARTENBACH
501084
POLYMAGE SARL
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
7210-PR/163
ROSENHEIMER GLASTECH.
ENK6-CT-2002-30023
RUDOLF BRAUNS AND CO. KG
SHERPA ENGINEERING SARL
502889
CENTRE DE RECH. METALLURG.
506503
MECALOG SARL
506257
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PRINCIPIA
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BEHR & CO
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GIFFORD AN
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MARITIME H
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MERITOR HE
MERKLE UND
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WILDE AND
ALLOGG AB
AS. CONOCI
ASS. RECH.
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BELIMO AUT
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DAEDALUS I
DATAMED H
FACULTY OF
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FL-SOFT V/
INST. OF I
GOETHE UNI
MIT-MANAGE
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SIEMENS BU
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START ENGI
STICHTING
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PRINCIPIA
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D C WHITE
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FORSCHUNGS
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INTEGRATED
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MARITIME H
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MERKLE UND
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WILDE AND
Pajek - Ward [0.00,1376.93]
* 6
34
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$
Pretvorba dvovrstnih omrežij na enovrstna
Z uporabo množenja omrežij lahko dvovrstno omrežje N = (I, J , E, w)
pretvorimo v dve enovrstni omrežji N1 = N ∗N T in/ali N2 = N T ∗N . Naj
bo A matrika omrežja N in B matrika omrežja N1 . Tedaj velja B = AAT ,
P
P
T
buv = z∈J auz · azv = z∈J auz · avz . Očitno velja buv = bvu –
matrika B je simetrična.
Tudi omrežju N2 pripadajoča matrika C = AT A je simetrična.
Enovrstni omrežji N1 in N2 lahko analiziramo z običajnimi postopki
analize enovrstnih omrežij. Osnovna težava je, da sta lahko eno ali celo obe
preveliki.
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V enovrstnih omrežjih dobljenih iz velikih dvovrstnih omrežij so pogosto
razlike v utežeh zelo velike. Zato ni mogoče primerjati točk glede na
te vrednosti. Pred primerjavo jih moramo normalizirati – poskrbeti za
primerljivost uteži.
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35
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$
. . . Normalizacije
Obstaja več načinov normalizacije. Uporabimo jih lahko tudi na drugih
enovrstnih uteženih omrežjih.
Geouv
=
wuv
√
wuu wvv
Inputuv
=
wuv
wvv
Minuv
=
MinDiruv
=
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
Normalizirano omrežje analiziramo z uporabo povezavnih prerezov ali
otokov.
Reuters Terror News: GeoDeg, MaxDir, MinDir.
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36
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$
MinDir na omrežju Slovenski časopisi 2000
Čez 100000 oseb je bilo v letih 1999 in 2000 vprašanih, katere časopise berejo. Navedli so 124 različnih časopisov. (vir Cati) SVG
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* 6
37
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$
Internet Movie Database http://www.imdb.com/
Omrežje IMDB je bilo pripravljeno za 12th Annual Graph Drawing Contest, 2005. Je
dvovrstno in ima 1324748 = 428440 + 896308 točk ter 3792390 povezav.
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38
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$
Dvovrstne sredice
Podmnožica točk C ⊆ V je (p, q)-sredica dvovrstnega omrežja N =
(V1 , V2 ; L), V = V1 ∪ V2 natanko takrat, ko
a. v s C porojenem podomrežju K = (C1 , C2 ; L(C)), C1 = C ∩ V1 ,
C2 = C ∩V2 velja ∀v ∈ C1 : degK (v) ≥ p in ∀v ∈ C2 : degK (v) ≥ q;
b. C je maksimalna podmnožica V, ki zadošča pogoju a.
Za določitev (p, q)-sredice lahko uporabimo postopek podoben postopku za
določanje običajnih sredic.
Težava je v tem, da je lahko veliko dvovrstnih sredic. Kako izbrati
zanimive? Pomagamo si lahko s tabelo značilnosti sredic.
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39
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$
(247,2)-sredica in (27,22)-sredica
Survivor Series
Royal Rumble
Zhukov, Boris (I)
Wright, Charles (II)
Wilson, Al (III)
Wight, Paul
Wickens, Brian
White, Leon
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)
Taylor, Scott (IX)
Tanaka, Pat
Tajiri, Yoshihiro
Szopinski, Terry
Storm, Lance
Steiner, Scott
Steiner, Rick (I)
Solis, Mercid
Snow, Al
Smith, Davey Boy
Slaughter, Sgt.
Simmons, Ron (I)
Shinzaki, Kensuke
Shamrock, Ken
Senerca, Pete
Scaggs, Charles
Savage, Randy
Saturn, Perry
Sags, Jerry
Ruth, Glen
Runnels, Dustin
Rude, Rick
Rougeau, Raymond
Rougeau Jr., Jacques
Rotunda, Mike
Ross, Jim (III)
Rock, The
Roberts, Jake (II)
Rivera, Juan (II)
Rhodes, Dusty (I)
Reso, Jason
Reiher, Jim
Reed, Bruce (II)
Race, Harley
Prichard, Tom
Powers, Jim (IV)
Poffo, Lanny
Plotcheck, Michael
Piper, Roddy
Pfohl, Lawrence
Pettengill, Todd
Peruzovic, Josip
Palumbo, Chuck (I)
Page, Dallas
Ottman, Fred
Orton, Randy
Okerlund, Gene
Nowinski, Chris
Norris, Tony (I)
Nord, John
Neidhart, Jim
Nash, Kevin (I)
Muraco, Don
Morris, Jim (VII)
Morley, Sean
Morgan, Matt (III)
Mooney, Sean (I)
Moody, William (I)
Miller, Butch
Mero, Marc
McMahon, Vince
McMahon, Shane
Matthews, Darren (II)
Martin, Andrew (II)
Martel, Rick
Marella, Robert
Marella, Joseph A.
Manna, Michael
Lothario, Jose
Long, Teddy
LoMonaco, Mark
Lockwood, Michael
Levy, Scott (III)
Levesque, Paul Michael
Lesnar, Brock
Leslie, Ed
Leinhardt, Rodney
Layfield, John
Lawler, Jerry
Lawler, Brian (II)
Laurinaitis, Joe
Laughlin, Tom (IV)
Lauer, David (II)
Knobs, Brian
Knight, Dennis (II)
Killings, Ron
Kelly, Kevin (VIII)
Keirn, Steve
Jones, Michael (XVI)
Johnson, Ken (X)
Jericho, Chris
Jarrett, Jeff (I)
Jannetty, Marty
James, Brian (II)
Jacobs, Glen
Jackson, Tiger
Hyson, Matt
Hughes, Devon
Huffman, Booker
Howard, Robert William
Howard, Jamie
Houston, Sam
Horowitz, Barry
Horn, Bobby
Hollie, Dan
Hogan, Hulk
Hickenbottom, Michael
Heyman, Paul
Hernandez, Ray
Henry, Mark (I)
Hennig, Curt
Helms, Shane
Hegstrand, Michael
Heenan, Bobby
Hebner, Earl
Hebner, Dave
Heath, David (I)
Hayes, Lord Alfred
Hart, Stu
Hart, Owen
Hart, Jimmy (I)
Hart, Bret
Harris, Ron (IV)
Harris, Don (VII)
Harris, Brian (IX)
Hardy, Matt
Hardy, Jeff (I)
Hall, Scott (I)
Guttierrez, Oscar
Gunn, Billy (II)
Guerrero, Eddie
Guerrero Jr., Chavo
Gray, George (VI)
Goldberg, Bill (I)
Gill, Duane
Gasparino, Peter
Garea, Tony
Funaki, Sho
Fujiwara, Harry
Frazier Jr., Nelson
Foley, Mick
Flair, Ric
Finkel, Howard
Fifita, Uliuli
Fatu, Eddie
Farris, Roy
Eudy, Sid
Enos, Mike (I)
Eaton, Mark (II)
Eadie, Bill
Duggan, Jim (II)
Douglas, Shane
DiBiase, Ted
DeMott, William
Davis, Danny (III)
Darsow, Barry
Cornette, James E.
Copeland, Adam (I)
Constantino, Rico
Connor, A.C.
Cole, Michael (V)
Coage, Allen
Coachman, Jonathan
Clemont, Pierre
Clarke, Bryan
Chavis, Chris
Centopani, Paul
Cena, John (I)
Canterbury, Mark
Candido, Chris
Calaway, Mark
Bundy, King Kong
Buchanan, Barry (II)
Brunzell, Jim
Brisco, Gerald
Bresciano, Adolph
Bloom, Wayne
Bloom, Matt (I)
Blood, Richard
Blanchard, Tully
Blair, Brian (I)
Blackman, Steve (I)
Bischoff, Eric
Bigelow, Scott ’Bam Bam’
Benoit, Chris (I)
Batista, Dave
Bass, Ron (II)
Barnes, Roger (II)
Backlund, Bob
Austin, Steve (IV)
Apollo, Phil
Anoai, Solofatu
Anoai, Sam
Anoai, Rodney
Anoai, Matt
Anoai, Arthur
Angle, Kurt
AndrØ the Giant
Anderson, Arn
Albano, Lou
Al-Kassi, Adnan
Ahrndt, Jason
Adams, Brian (VI)
Young, Mae (I)
Wright, Juanita
Wilson, Torrie
Vachon, Angelle
Stratus, Trish
Runnels, Terri
Robin, Rockin’
Psaltis, Dawn Marie
Moretti, Lisa
Moore, Jacqueline (VI)
Moore, Carlene (II)
Mero, Rena
McMichael, Debra
McMahon, Stephanie
Martin, Judy (II)
Martel, Sherri
Laurer, Joanie
Keibler, Stacy
Kai, Leilani
Hulette, Elizabeth
Guenard, Nidia
Garca, LiliÆn
Ellison, Lillian
Dumas, Amy
Taylor, Scott (IX)
Van Dam, Rob
Matthews, Darren (II)
LoMonaco, Mark
Hughes, Devon
Huffman, Booker
Heyman, Paul
Hebner, Earl
McMahon, Stephanie
Keibler, Stacy
Wight, Paul
Simmons, Ron (I)
Senerca, Pete
Ross, Jim (III)
Rock, The
Reso, Jason
McMahon, Vince
McMahon, Shane
Martin, Andrew (II)
Levesque, Paul Michael
Layfield, John
Lawler, Jerry
Jericho, Chris
Jacobs, Glen
Hardy, Matt
Hardy, Jeff (I)
Gunn, Billy (II)
Guerrero, Eddie
Copeland, Adam (I)
Cole, Michael (V)
Calaway, Mark
Bloom, Matt (I)
Benoit, Chris (I)
Austin, Steve (IV)
Anoai, Solofatu
Angle, Kurt
Stratus, Trish
Dumas, Amy
’WWF Smackdown!’
’WWE Velocity’
’Sunday Night Heat’
’Raw Is War’
WWF Vengeance
WWF Unforgiven
WWF Rebellion
WWF No Way Out
WWF No Mercy
WWF Judgment Day
WWF Insurrextion
WWF Backlash
WWE Wrestlemania XX
WWE Wrestlemania X-8
WWE Vengeance
WWE Unforgiven
WWE SmackDown! Vs. Raw
WWE No Way Out
WWE No Mercy
WWE Judgment Day
WWE Armageddon
Wrestlemania X-Seven
Wrestlemania X-8
Wrestlemania 2000
Survivor Series
Summerslam
Royal Rumble
No Way Out
King of the Ring
Invasion
Fully Loaded
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40
'
$
(2,516)-Hard core
Hot Tight Asses 6
Hot Tight Asses 20
Hot Sweet Honey
Hot Shots
Hot Nights at the Blue Note Cafe
Hot In the City
Hospitality Sweet
Hooter Heaven
Honey Buns
Hollywood Starlets
Hollywood Exposed 2
Holly Does Hollywood
Holiday for Angels
Hindlick Maneuver, The
Hienie’s Heroes
Hidden Obsessions
Hershe Highway 4
Herman’s Bed
Heads and Tails
Head Games
Head Clinic
Hawaii Vice Part III: Beyond the Badge
Hawaii Vice 6
Hawaii Vice 5
Hawaii Vice 2
Harlequin Affair
Hard to Handle
Hard Rider
Hard as a Rock
Happy Endings
Guilty by Seduction
Greatest American Blonde
Grand Opening
Graduation from F.U.
Gorgeous
Good Girls Do
Going Pro
Goin’ Down Slow
Goddess of Love
Gluteus to the Maximus
Glen or Glenda?
Glamour Girl 5
Give Me Your Soul...
Girls’ Club, The
Girls Who Love to Suck
Girls of the Double D 9
Girls of the A Team, The
Girls of Paradise
Girls of Cell Block F
Girl with the Heart-Shaped Tattoo, The
Ginger’s Private Party
Ginger’s Greatest Boy/Girl Hits
Ginger Then and Now
Ginger Snacks
Ginger On the Rocks
Ginger Lynn: The Movie
Ginger Lynn Non-Stop
Ginger Lynn and Co.
Ginger in Ecstasy
Ginger Effect, The
Ghost Town
Gettin’ Ready
Gang Bangs II
Gang Bangs
Gang Bang Wild Style 2
Gang Bang Nymphette
Gang Bang Jizz Queens
Gang Bang Jizz Jammers
Gang Bang Girl 22
Gang Bang Girl 20
Gang Bang Girl 17
Gang Bang Girl 13
Gang Bang Girl 12
Gang Bang Face Bath 4
Gang Bang Face Bath
Gang Bang Cummers
Games Couples Play
Future Voyeur
Full Throttle Girls 1: Boredom Pulled the Trigger
Full Nest
Full Moon Fever
Friends and Lovers: The Sequel
Fresh Meat
French Doll
Forbidden Cravings
Forbidden Bodies
For Your Thighs Only
For the Money 1
Fluffer, The
Flesh Shopping Network
Flashback
First Annual XRCO Adult Film Awards
Firm Offer
Firefoxes
Fire in the Hole
Fine Art of Cunnilingus, The
Film Buff
Filet-o-Breast
Femmes Ørotiques, Les
Femme Vanessa, La
Fast Girls
Farmer’s Daughter 2
Fantasy Inc.
Fame Is a Whore On Butt Row
Eyewitness Nudes
Extreme Sex 4: The Experiment
Extreme Sex 2: The Dungeon
Extreme Sex 1: The Club
Exhibitionist, The
Executive Suites
Every Woman Has a Fantasy 3
Eternity
Eternal Lust 2
Escort to Ecstasy
Erotic Starlets 12: Crystal Lee
Erotic Newcummers 4
Erotic Explosions 2
Entertainment L.A. Style
Encore
Enchantress
Edge of Heat 2
Edge of Heat
Ecstasy
Easy Way, The
Earth Girls Are Sleazy
E. TV
DØj Vu
Dreams of Candace Hart
Dreams in the Forbidden Zone
Dream Machine, The
Dream Lust
Dragon Lady 4: Tales from the Bed 3, The
Double Penetrations 7
Double Penetration 5
Double Penetration
Dirty Prancing
Dirty Pictures
Dirty Movies
Dirty Looks
Dirty Dreams
Dickman and Throbbin
Diamond in the Rough
Diamond Collection Double X 74
Diamond Collection Double X 10
Diamond Collection 79
Dial F for Fantasy
Dial a Nurse
Dial A for Anal
Devil Made Her Do It, The
Devil in Miss Jones 5: The Inferno, The
Devil in Miss Jones 4: The Final Outrage
Devil in Miss Jones 3: A New Beginning, The
Desktop Dolls
DeRenzy Tapes
Delinquents On Butt Row
Deeper, Harder, Faster
Deep Throat Girls
Deep Obsession
Deep Inside Victoria Paris
Deep Inside Vanessa del Rio
Deep Inside Traci
Deep Inside Shanna McCullough
Deep Inside Samantha Strong
Deep Inside Racquel Darrian
Deep Inside P.J. Sparxx
Deep Inside Nina Hartley
Deep Inside Missy
Deep Inside Kelly O’Dell
Deep Inside Ginger Lynn
Deep Inside Brittany O’Connell
Deep Inside Barbii
Deep Inside Ariana
Deep In Angel’s Ass
Deep Cover
Deep Cheeks 3
Decadence
Debutante, The
Dear Bridgette
Darker Side of Shayla, The
Darker Side of Shayla 2, The
Curse of the Catwoman
Cumshot Revue 5
Cumshot Revue 3
Cumshot Revue 2
Cumming of Ass
Cumback Pussy 9: Your Ass Is Mine!
Cumback Pussy 8
Cumback Pussy 6
Cumback Pussy 4 Get Some
Cum for Me Carol
Cream of Cumback Pussy
Crazed
Covergirl
Country Girl
Coming on Strong
Coming of Age
Come Hither, Cum Ginger
Club Head
Club Ginger
Club DV8 2
Cherry Cheeks
Cheerleader Academy
Cheeks 2: The Bitter End
Cheek to Cheek 2: The Newest Cheeks on the Block
Checkmate
Charmed and Dangerous
Chameleon, The
Certifiably Anal
Centerfolds
Caught In the Middle
Caught in the Act
Caught From Behind 9
Caught From Behind 2: The Sequel
Cat Alley
Car Wash Angels
Captain Butt’s Beach
Canned Heat
California Native
Cajun Heat
Butts of Steel
Butties
Butt Sisters, The
Busted
Burning Desire
Burgundy Blues
Bun for the Money
Bun Busters
British Are Coming, The
Bringing Up the Rear
Bride, The
Breaking It
Brazilian Connection, The
Brat Force
Bottoms Up! Series 8
Bottom Line, The
Bottom Dweller Part Deux, The
Bottom Dweller 5: In Search of...
Booty Mistress
Booty Ho 3
Boobs Butts and Bloopers 1
Boiling Point
Boiling Desires
Body of Innocence
Body Music
Bod Squad, The
Blowin’ the Whistle
Bloopers 2
Bloopers
Blondes Who Blow
Blondage
Blame It On Ginger
Black Valley Girls 2
Black Valley Girls
Black Throat
Black Stockings
Billionaire Girls Club
Bigger They Come
Big Pink, The
Big Melons 4
Big Melons 31
Big Melons 26
Big Mellons 25
Beyond Thunderbone
Beyond Reality: Mischief in the Making
Between the Cheeks 3
Between the Cheeks 2
Between the Cheeks
Best Rears of Our Lives, The
Best of the Vivid Girls #30
Best of the Dark Bros., Vol. 2, The
Best of the Dark Bros., The
Best of Talk Dirty, Vol. 1, The
Best of Shane 1
Best of Loose Ends
Best of Double Penetration
Best of Diamond Collection 11
Best of Christy Canyon
Best of Caught from Behind 2
Best of Caught from Behind
Best of Amber Lynn
Beefeaters
Beaverly Hills Cop
Beaver and Buttcheeks
Beat Goes On, The
Bazooka County 3
Battle of the Titans
Battle of the Superstars
Bare Market
Bare Elegance
Barbii Unleashed
Barbara Dare’s Bad
Ball Street
Badgirls 2: Strip Search
Bad
Backroad to Paradise
Backing in 3
Backfield in Motion
Backdoor to Hollywood 11
Backdoor Summer II
Backdoor Brides Part 2
Backdoor Brides
Backdoor Bonanza 9
Backdoor Bonanza 13
Back to Nature
Back Doors, The
Bachelor Party
Baby Face 2
Babe Watch
Aussie Exchange Girls
Asspiring Actresses
Ass Openers 8
Ass Openers 6
Ass Openers 4
Ass Openers 3
Ass Openers 10
Ass Openers 1
Ass Lovers Special
Ass Busters Inc.
Ass Backwards
Art of Desire
Aroused
Army Brat 2
Arizona Gold
Anything Goes
Another Rear View
Animal in Me
Angels of Mercy
Angelica
Angel Rising
Angel Puss
Analizer, The
Anal Trashy Ass
Anal Thunder 2
Anal Taboo
Anal Sweetheart
Anal Sluts and Sweethearts
Anal Secrets
Anal Riders 106
Anal Queen
Anal Princess
Anal Mystique
Anal Lover
Anal Justice
Anal Innocence 2
Anal Inferno
Anal Hounds and Bitches
Anal Hellraiser 2
Anal Encounters 2
Anal Encounters 1
Anal Ecstasy
Anal Delights 3
Anal Deep Rider
Anal Crack Master
Anal Climax 3
Anal Attitude
Anal Anarchy
Anal Adventures of Suzy Super Slut
American Pie
American Beauty
Amber Lynn: The Totally Awesome
Amazing Tails 5
Amazing Tails 4
Amazing Tails 3
Amazing Tails 2
Amazing Tails 1
All the Best, Barbara
Alice in Hollyweird
Al Terego’s Double Anal Alternatives
Aja
After Midnight
Afro Erotica 15
Adventures of Tracy Dick: The Case of the Missing Stiff
Adventures of Billy Blues, The
Adult 45
Above the Knee
A-List, The
A Is for Asia
4F Dating Service
40 Something
1-800-934-Boob
North, Peter (I)
Wallice, Marc
Byron, Tom
Ribald Tales of Canterbury
Return to Sex 5th Avenue
Reincarnation of Don Juan
Red Vibe Diaries 2: Dark Desires
Rear Ended Roommates
Rear Busters
Raunch V
Raunch 6
Rapture
Rambone the Destroyer
Rainwoman 6
Rainwoman 4
Rainbird
Radio-active
Radio K-KUM
Rachel Ryan RR
Queen of Hearts 3
Pussypoppers
Pussyman Takes Hollywood
Pussyman 2: The Prize
Pussyman
Psychic, The
Prom Girls
Project: Ginger
Private Teacher
Private Affairs: Vol 6
Private Affairs: Vol 2
Pretty As You Feel
Precious Peaks
Pouring It On
Possessions
Portrait of Dorian
Pornomania 1
Porn on the 4th of July
Poonies, The
Pleasure Seekers
Pleasure Party
Pleasure Hunt Part II
Plaything 2
Plaything
Playing with a Full Dick
Play It Again... Samantha!
Pink Pussycat, The
Piece of Heaven
Physical II
Photo Flesh
Perverted Passions
Perverted 1
Perks
Perfect Fit
Peggy Sue
Passionate Heiress
Passionate Angels
Passenger 69
Passages 2
Passages 1
Party Doll A Go-Go, Part 1
Party Doll A Go-Go 2
Party Doll
Paradise Lost
Paler Shade of Blue, A
Overtime: Oral Hijinx
Oval Office, The
Outrageous Orgies 5
Outlaw, The
Out of Love
Orgies
Oral Majority 9
Oral Majority 8
Oral Majority 7
Oral Majority 4
Oral Majority 3
Oral Majority 10
Oral Majority
Open Up Traci
Only the Very Best On Video
Only the Best of the 80’s
One Night Stand
On the Loose
On Golden Blonde
Office Girls
Obsession
Nurse Nancy
Nurse Fantasies
Norma Jeane Anal Legend
Nobody’s Looking
No Tell Motel
Nightbreed
Night Temptress
Night Tales
Night Deposit
New Wave Hookers 4
New Wave Hookers 2
New Wave Hookers
Never Say Never
Naughty Thoughts
Naughty 90’s
Nasty Nymphos 3
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
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41
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Primer: 4-obroči – otoka za w4 / Charlie Brown in Adult
Morgan, Jonathan (I)
Kesten, Brad
Brando, Kevin
Robbins, Peter (I)
Shea, Christopher (I)
Altieri, Ann
Schoenberg, Jeremy
Boy, T.T.
Hauer, Brent
Voyeur, Vince
Charlie Brown and Snoopy Show
Reilly, Earl ’Rocky’
Charlie Brown Celebration
Ornstein, Geoffrey
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
Charlie Brown Christmas
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
Stratford, Tracy
Davis, Mark (V)
Melendez, Bill
You’re a Good Sport, Charlie Brown
Drake, Steve (I)
It’s a Mystery, Charlie Brown
Boy Named Charlie Brown
It’s an Adventure, Charlie Brown
Byron, Tom
Silvera, Joey
It’s Flashbeagle, Charlie Brown
Play It Again, Charlie Brown
Momberger, Hilary
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
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42
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Izbrane knjige o analizi omrežij
• J. P Scott: Social Network Analysis: A Handbook. SAGE Publications, 2000. Amazon.
• A. Degenne, M. Forsé: Introducing Social Networks. SAGE Publications, 1999.
Amazon.
• S. Wasserman, K. Faust: Social Network Analysis: Methods and Applications. CUP,
1994. Amazon.
• W. de Nooy, A. Mrvar, V. Batagelj: Exploratory Social Network Analysis with Pajek,
CUP, 2005. Amazon. ESNA page.
• P. Doreian, V. Batagelj, A. Ferligoj: Generalized Blockmodeling, CUP, 2004. Amazon.
• E. Lazega: The Collegial Phenomenon: The Social Mechanisms of Cooperation among
Peers in a Corporate Law Partnership. OUP, 2001. Amazon.
• P.J. Carrington, J. Scott, S. Wasserman (Eds.): Models and Methods in Social Network
Analysis. CUP, 2005. Amazon.
• U. Brandes, T. Erlebach (Eds.): Network Analysis: Methodological Foundations. LNCS,
Springer, Berlin 2005. Amazon.
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Pajek - Vladimir Batagelj

Transcription

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