prosojnice - Vladimir Batagelj

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Pajčevine
Vladimir Batagelj
FMF, matematika
Univerza v Ljubljani
Foto: V. Batagelj, Pajčevina
57. občni zbor, DMFAS
Cerkno, 25/26. november 2005
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različica: 26. november 2005 / 18 : 22
V. Batagelj: Pajčevine
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Kazalo
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Analiza omrežij . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Omrežja . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Velika omrežja . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Slučajni grafi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Porazdelitve stopenj . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Pajek . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Razčlenitve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Uteži v omrežjih sklicevanj . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Sredice in posplošene sredice
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k-obroči . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Otoki . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Dvodelne sredice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Usmerjeni 4-obroči . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Iskanje vzorcev . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Pa še to . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Viri . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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57. občni zbor DMFAS, Cerkno 25/26. november 2005
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Analiza omrežij
Korenine analize omrežij so precej razvejane – Euler, Hamilton, Kirchoff, Kekule, Jarnik, Moreno, Ford in Fulkerson, Dijkstra, Erdős, . . .
V preteklem stoletju se je analiza omrežij razvijala predvem v elektrotehniki, operacijskih raziskavah, matematiki,
računalništvu, kemiji in družboslovju.
Teorijo grafov zanimajo predvsem grafi, ki imajo ’pravilno’
zgradbo – v analizi omrežij pa zgradbo omrežja določa stanje stvari.
Do prve polovice 90. let prejšnjega stoletja so bila omrežja
povečini razmeroma majhna – nekaj 10 ali 100 točk. Razvoj IT, pretvorba podatkovij v ustrezna omrežja in zbiranje
podatkov s spleta so omogočili ustvarjanje velikih omrežij
s tisoči ali celo milijoni točk in povezav. Kaj lahko povemo
o takih omrežjih?
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Moreno: Who shall survive? / Kdo bo preživel?
K:
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Omrežja
Alexandra Schuler/ Marion Laging-Glaser:
Analyse von Snoopy Comics
Osnova omrežja je graf , ki ga
določata množica točk V , ki predstavljajo izbrane enote, in množica
povezav L, ki predstavljajo odnose
med enotami. Posamezna povezava
je lahko usmerjena ali neusmerjena.
O točkah in povezavah pogosto poznamo še dodatne podatke – lastnosti točk (oznaka, zvrst, pomembnost, . . . )
in/ali uteži povezav
(oznaka, pogostost, . . . )
Omrežje = Graf + Podatki
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Podatki so lahko izmerjeni ali izračunani.
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Prikaz lastnosti – šolarji (Moody)
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FAS: Znanost v Avstriji
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Velika omrežja
Omrežje je veliko, če ima vsaj nekaj tisoč (lahko pa tudi milijone) točk in
ga je mogoče shraniti v delovni pomnilnik računalnika. Obstajajo tudi večja
– ogromna omrežja. Velika omrežja so ponavadi redka m << n2 .
omrežje
ODLIS dictionary
Citations SOM
Molecula 1ATN
Comput. geometry
English words 2-8
Internet traceroutes
Franklin genealogy
World-Wide-Web
Actors
US patents
SI internet
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
Garfield’s collection
Brookhaven PDB
BiBTEX bibliographies
Knuth’s English words
Internet Mapping Project
Roperld.com gedcoms
Notre Dame Networks
Notre Dame Networks
Nber
Najdi Si
Na voljo sta dva pristopa k velikim omrežjem: statistika in razčlenitve.
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Slučajni grafi
Erdős in Rényi sta definirala slučajni
graf takole: vsako mogočo povezavo
vključimo v slučajni graf z dano verjetnostjo p.
V programu Pajek (Net / Random
Network / Erdos-Renyi) uporabljamo namesto verjetnosti p povprečno
stopnjo
1 X
deg =
deg(v)
n
v∈V
Na sliki je prikazan slučajni graf na 100 točkah s povprečno stopnjo 3.
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Porazdelitve stopenj
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US Patents degree distribution
1 e+06
Random graph degree distribution, n=100000, degav=30
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Dejanska omrežja so vse prej kot slučajna. Analiza porazdelitev je dala
nov pogled na zgradbo dejanskih omrežij – Watts (Small worlds), Barabási
(nd/networks, Linked) – brezlestvična omrežja.
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Pajek
Novembra 1996 sva z Andrejem Mrvarjem
začela razvijati program Pajek za analizo in
prikaz velikih omrežij. Napisan je v Delphiju
in teče pod Windowsi. Nekaj postopkov je
sprogramiral tudi Matjaž Zaveršnik.
Pajek je prosto dostopen (za netržne uporabe) na:
http://vlado.fmf.uni-lj.si/pub/networks/pajek/
de Nooy, W., Mrvar, A., Batagelj V.:
Exploratory Social Network Analysis with Pajek,
CUP, 2005.
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Razčlenitve
Glavni cilji v zasnovi programa Pajek so:
• omogočiti abstrakcijo s podporo
(rekurzivnega) razčlenjevanja velikih
omrežij v obvladljive dele, nad
katerimi lahko uporabimo zahtevnejše
postopke;
• ponuditi uporabniku orodja za prikaze
omrežij;
• vgraditi, in po potrebi razviti, izbor
podkvadratnih postopkov za analizo
velikih omrežij.
S programom Pajek lahko: v omrežju poiščemo skupine (komponente, soseščine ‘pomembnih’ točk, sredice, itd.) ; iz omrežja izrežemo podomrežje določeno s skupino in ga prikažemo
ločeno, morda vpetega v kontekst; v omrežju skrčimo točke posameznih skupin in prikažemo
odnose med skupinami.
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Prerezi
Pogosto nas v omrežju, glede na neko lastnost točk, zanimajo skupine
povezanih točk, katerih vrednosti so večje od vrednosti točk v okolici. Za
lažjo predstavo bomo vrednosti v dani točki rekli kar višina točke. Tako nam
omrežje s točkami na danih višinah določa nekakšno pokrajino. Neprazna
skupina točk C ⊆ V je pravi točkovni otok, če njene točke določajo povezan
podgraf in so višine sosednih točk manjše ali enake višinam točk iz skupine.
Preprost postopek, kako določiti nekatere otoke, je z uporabo točkovnih
prerezov. Točkovni prerez danega omrežja na ravni t dobimo tako, da iz
omrežja odstranimo vse točke (in pripadajoče povezave), katerih vrednost je
manjša od t. Hitro se lahko prepričamo, da je vsaka komponenta točkovnega
prereza pravi točkovni otok.
Na podoben način vpeljemo povezavne prereze / otoke.
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Točkovni izrez: Krebs-ova Internetska podjetja, core=6
Lucent
CommerceOne
UPS
SAP
CIBER
Motorola
Ariba
Yahoo!
EMC
FoundryNetworks
HP
Peoplesoft
Oracle
EDS
Sun
IBM
Siebel
WebMethods
divine
E.piphany
BMCSoftware
Cisco
Novell Intel
ExodusComm
KPNQwest
AT&T
Vignette
CacheFlow
Loudcloud
Compaq
RealNetworks
RedHat
Dell
Akamai
MSFT
Inktomi
AOL
Pajek
Vsaka točka predstavlja Internetsko podjetje, 1998 do 2001. n = 219, m = 631. rdeča – vsebina, modra – podpora,
zelena – trgovina. Podjetji sta povezani, če sta oznanili skupni projekt, zvezo ali kako drugo obliko sodelovanja.
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Povezavni izrez: Krebs-ova Internetska podjetja, w3 ≥ 5
CIBER
Motorola
Ariba
FoundryNetworks
Oracle
Sun
IBM
E.piphany
HP
Cisco
Intel
AT&T
KPNQwest
KPMG
Compaq
RealNetworks
Dell
Akamai
MSFT
Inktomi
AOL
TerraLycos
FoundryNetworks
RealNetworks
KPMG
TerraLycos
AT&T
AOL
Pajek
Compaq
Inktomi
Sun
MSFT
HP
Dell
Akamai
IBM
Cisco
Intel
KPNQwest
Ariba
Oracle
Motorola
CIBER
E.piphany
Pajek
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Uteži v omrežjih sklicevanj
POGGIO-T-1975-V19-P201
KOHONEN-T-1976-V21-P85
ANDERSON-JA-1977-V84-P413
PFAFFELHUBER-E-1975-V18-P217
COOPER-LN-1979-V33-P9
WOOD-CC-1978-V85-P582
AMARI-SI-1977-V26-P175
PALM-G-1980-V36-P19
BIENENSTOCK-EL-1982-V2-P32
SUTTON-RS-1981-V88-P135
HOPFIELD-JJ-1982-V79-P2554
ANDERSON-JA-1983-V13-P799
KNAPP-AG-1984-V10-P616
MCCLELLAND-JL-1985-V114-P159
CARPENTER-GA-1987-V37-P54
GROSSBERG-S-1987-V11-P23
GROSSBERG-S-1988-V1-P17
SEJNOWSKI-TJ-1988-V241-P1299
BROWN-TH-1988-V242-P724
BROWN-TH-1990-V13-P475
TREVES-A-1991-V2-P371
HASSELMO-ME-1994-V7-P13
BARKAI-E-1994-V72-P659
AMARI-S-1980-V42-P339
HECHTNIELSEN-R-1987-V26-P1892
Analizo omrežij sklicevanj je začel
s svojim člankom leta 1964 Garfield s sodelavci. Leta 1989 sta
Hummon in Doreian predlagala 3
vrste uteži na povezavah, ki so sorazmerne številu različnih vrst poti
skozi povezavo. Leta 1991 sem
razvil hiter postopek za izračun teh
uteži.
Na sliki je prikazan povezavni prerez glede na te uteži na ravni
0.007 omrežja sklicevanj za področje SOM (selforganizing maps)
(4470 točk, 12731 povezav).
Glej članek.
GLUCK-MA-1997-V48-P481
ASHBY-FG-1999-V6-P363
Pajek
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Sredice in posplošene sredice
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.Schwerdt
G.Toussaint
M.Teillaud
J.Urrutia
C.Icking
R.Klein
J.Majhi
M.Yvinec
M.deBerg
O.Schwarzkopf
R.Janardan
J.Czyzowicz
Pojem sredice je vpeljal Seidman leta 1983. Točke, ki
pripadajo k-sredici imajo vsaj
k sosedov v njej. Sredica
je največja podmnožica, ki
zadošča temu pogoju. Obstaja zelo učinkovit postopek
za določanje sredic.
Pojem sredice je mogoče posplošiti s stopenj na druge lastnosti točk in za več izmed
njih je mogoče uporabiti podoben učinkovit postopek za njih
določanje.
Slika prikazuje pS -sredico na ravni 46 v omrežju sodelovanj (7343 točk, 11898 povezav, uteži
štejejo skupna dela) na področje računalniške geometrije.
Glej članek.
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k-obroči
k-obroč je enostavna sklenjena veriga dolžine k. k-obroči nam omogočajo
vpeljati naslednjo utež
wk (e) = število k-obročev, ki vsebujejo povezavo e ∈ L
Ker za polni graf Kr , r ≥ k ≥ 3 velja wk (Kr ) =
(r − 2)!/(r − k)!, imajo povezave, ki pripadajo klikam
v omrežju, velike uteži. Torej lahko te uteži uporabimo
za odkrivanje ’gostih’ delov omrežja. Na primer: vse
r-klike pripadajo povezavnemu prerezu na ravni r − 2
za utež w3 .
Danemu grafu lahko priredimo trikotniško omrežje, v katerem ima vsaka povezava za utež število trikotnikov, ki
jim pripada.
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Trikotniška povezanost
Tesno povezana s trikotniškim omrežjem je trikotniška povezanost
ki jo lahko uporabimo za operacionalizacijo pojma krepkih povezav.
Te pojme lahko posplošimo na povezanost s kratkimi cikli (glej članek).
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Povezavni prerez na ravni 16 trikotniškega omrežja nad
Erdős-ovim grafom sodelovanj
WORMALD, NICHOLAS C.
LASKAR, RENU C.
SHELAH, SAHARON
MCKAY, BRENDAN D.
HEDETNIEMI, STEPHEN T.
MAGIDOR, MENACHEM
KLEITMAN, DANIEL J.
CHUNG, FAN RONG K.
GRAHAM, RONALD L.
SAKS, MICHAEL E.
LINIAL, NATHAN
ARONOV, BORIS
PACH, JANOS
POLLACK, RICHARD M.
HENNING, MICHAEL A.
SPENCER, JOEL H.
ALON, NOGA
OELLERMANN, ORTRUD R.
LOVASZ, LASZLO
KOMLOS, JANOS
GODDARD, WAYNE D.
FRANKL, PETER
FUREDI, ZOLTAN
ALAVI, YOUSEF
CHARTRAND, GARY
HARARY, FRANK
KUBICKI, GRZEGORZ
SCHWENK, ALLEN JOHN
TUZA, ZSOLT
BABAI, LASZLO
SZEMEREDI, ENDRE
BOLLOBAS, BELA
AJTAI, MIKLOS
RODL, VOJTECH
NESETRIL, JAROSLAV
brez Erdős-a,
n = 6926,
m = 11343
ROSA, ALEXANDER
GYARFAS, ANDRAS
SCHELP, RICHARD H.
LEHEL, JENO
STINSON, DOUGLAS ROBERT
CHEN, GUANTAO
MULLIN, RONALD C.
FAUDREE, RALPH J.
COLBOURN, CHARLES J.
JACOBSON, MICHAEL S.
PHELPS, KEVIN T.
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Usmerjeni 3-obroči
V usmerjenih omrežjih obstajata dve vrsti 3-obročev:
ciklični
tranzitivni
Uteži nad 3-obroči su bile vključene v program Pajek maja 2002.
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Povezavni prerez na ravni 11 glede na tranzitivne 3-obroče
v omrežju slovarja ODLIS
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Pajek
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Otoki
Pri prerezu je od izbire nivoja t odvisno, na koliko povezanih komponent
razpade omrežje in kako velike so te komponente. Dobimo lahko komponente najrazličnejših velikosti - od izoliranih točk do neobvladljivo velikih
komponent. To pa ni ravno tisto, kar si želimo. Rajši bi imeli otoke,
katerih velikosti bi lahko vnaprej določili. Da pa bi to dosegli, moramo
v omrežju narediti več rezov na različnih nivojih in pri vsakem prerezu
določiti povezane komponente. To je lahko precej zamudno, pa še isti otok
lahko dobimo večkrat.
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. . . Otoki
Boljši postopek je seveda takšen, da nam vsak otok vrne natanko enkrat.
Delovanje tega postopka bomo najlažje razumeli, če si predstavljamo,
da celotno omrežje potopimo v vodo, nato pa gladino vode postopoma
znižujemo in opazujemo, kakšni otoki se pojavljajo. Pri tem nam gladine
vode ni treba zniževati zvezno, pač pa samo po višinah točk od najvišje do
najnižje. Razvili smo učinkovit postopek, ki določi vse take otoke izbranih
velikosti med k in K.
Glej podrobnosti.
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Otoki – Reuter-ove novice po 11. septembru
united_airlines
plant
flight
train
arabic-language
power
pilot
bin_laden
saudi-born
uniform
inhale
scare
firefighter
dissident
jet
leader
airport
afghanistan
police
knife-wielding
anthrax
skin
phone
airliner
officer
support
country
hijack
trace
jonn
help
special
terrorism
war
united_states
embassy
business
wednesday
deadly
plane
mighty
force
thursday
pakistan
official
hijacker
arab
cell
agent
world
commercial
case
necessary
taliban
fbi
call
man
congressional
newspaper
chemical
member
rental
suspect
saudi
service
passenger
car
boston
organization
weapon
manual
contain
herald
pakistani
twin
week
strike
space
plea
specialist
110-story
world_trade_ctr
edmund
pentagon
air
north
cheyenne
tower
wyoming
offutt
news
late
new_york
city
florida
action
africa
anti-american
terror
group
responsibility
mayor
air_force
pfc
nebraska
barksdale
mayor_giuliani
landmark
team
exchange
american
conference
debris
miss
effort
thousand
rescue
market
center
aid
edward
fire
smoke
people
stock
dept
buildng
financial
toll
worker
plaugher
large
postal
emergency
chief
district
state
&
death
Pajek
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east
headquarters
morning
tuesday
south
military
terrorist
apparent
the_worst
washington
louisiana
base
act
attack
S. Corman in K. Dooley sta razvila postopek
CRA, s katerim so ustvarili
časovno omrežje Reuterovih novic po 11. septembru, ki povzema sopojavljanje besed v Reuterovih novicah izdanih v prvih 66 dneh po terorističnem napadu 11. septembra in se nanašajo na
ta dogodek. Uteži povezav štejejo pogostost sopojavljanja. Omrežje ima
n = 13332 točk in m =
243447 povezav.
Prikaz rezin po dnevih.
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attendant
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Otoki – Ameriški patenti
NBER-ovo omrežje US Patents ima 3774768 točk in 16522438 usmerjenih
povezav (1 zanka). Je v bistvu veliko omrežje sklicevanj – vsak patent se
sklicuje na uporabljene predhodne patente. Na njem smo določili uteži kot
pri omrežju SOM in nato vse povezavne (2,90)-otoke. Podomrežje otokov
ima 470137 točk, 307472 povezav in za posamezne k: C2 =187610,
C5 =8859,C30 =101, C50 =30 otokov. Rolex
[1]
0 139793
[11] 190
125
[21] 17
16
[31] 12
3
[41]
1
3
[51]
2
3
[61]
0
0
[71]
0
0
[81]
2
0
29670 9288 3966 1827 997 578 362 250
104
71
47
37 36 33 21 23
8
7
13
10 10
5
5
5
7
3
3
3
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6
6
2
4
1
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2
1
1
1
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0
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0
2
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1
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0
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0
7
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Themevelikosti
size distribution
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Glavna pot in glavni otok v Patentih
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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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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Otoki – The Edinburgh Associative Thesaurus
n = 23219, m = 325624, tranzitivnostne trikotniške uteži
HAPPEN
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AGAIN
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ALREADY
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MATHS
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LOVELY
SHAPELY
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Velika slika, V. Batagelj, Ars Electronica’04
simetrizirano podomrežje (n = 5952, m = 18008) iz Edinburgh Associative Thesaurus
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Velika slika
thrust
moorland
slowest
ted
heath
possessing
having
auntie
capone
jumping
o.k.
next to
latter
nigh
piles
untruth
recline
lie
fib
detector
falsehood
deceit
bye
cheat
fantasy
reverie
mantis
preying
proceed
praying
lover
sought
pictures
market
road works
leaving
next
mexico
napping
hose
ash-tray
horizon
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asleep
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stains
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customs
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professor seeing
nobody
statesman politician
hoop
presume
scaffoldingwere
believing
broadcast
everywhere
radio
anywhere follow
such
november
arrival
departure
natural
regulations
assume
listened wireless
erected
justice
multiply
divide
halifax
december
hearer
know
perceived
abrupt
pledge
endlessness
sprinted
theirs
magistrate
listener
magistrates themselves
smelling ourselves
gin
sunday
dagger
tablet
karl
mushroom
toadstool
regard
conditioned member
conception
grave
has not
will
be
here
addition
in addition
rummy
fairy
airy
fracture
on
off
scrawl
nude
something also
anything
all
eve
circumstance pomp
portion
argument
communicate
everybody
manchester
dung
meet
bricks
suffering
danger
cloak
patience
handler
encounter
mortar
high
busy
ease
flock
flocks
sport
placed
hut
shearing
baa
wool
reel
put
guides
stairs
glow
infliction
cotton
flesh
lino
scouts
ceiling
discomfort
bounty
employment
absent
daughters
floor
broader
mobile
morrow
lens
goats
industrious
pious
shears
mosaic
reactor
shepherd
wider
totter
sod
pattern
nuclear
fuel
groin
paw
pet
cruiser
ledger
centimetre caution
nearly
too
everything
nought
corpse
saw
yawn
weary
fatigued
at all
ahoy
there
looked
shirt
debate
throbbing
according
belonging
promenade
fatigue
low
mutiny
jersey
discovery
devalue
heather
pup
puppy
dog
hound
brick
lofty
alive
tired
sleepiness
speak
chat
shelf
where
nil
nothing
spear
athlete
discuss
slippy
lace
pin
prick
exam
essay
sufferer
suffer
pain
distress
spasm
sons
ghost
lambs
shepherds
drip
facility
fold
article
agony
worm
torture
damsel
stories
robe
wriggling
groove
passed
poodle
leash
barking
record
failed
tales
gallon
severe
toothache
created
dry martini
spooky
apparition
sat
forthwith
porcelain
litre
liquor
straw
lungs
made
lay
injured
ouch
certainty
letter-box
locket
zero
hop
leather
scent
desist
everyone
chatter
residing
living
arrive
pause
halt
get ready
hoist
desk
blouse
exhausted
sleepy
ire
rats
occasionally
measure
shooting
exhaustion
care
slow down
stop
go
simultaneous discussion talk
feel
prevent
bring
get set
semi
sweat
united
thread
needle
setter
player
fell
pick
join
quid
shaggy
disk
falling
devalued pound
wall
thong
carry
switzerland
detached
states
warm
skip
fetch
choke
abate
medicine
come
have to
d.c.
row
smooth
dose
minute
discontinue
bicycle
section
haste
wrath
anger
dispute
walk
stroll
bridle
saddle
harness
trotting
riding
necklace injustice
rage
perambulate to
flee
breed
seller
touch
freeway
rodents
belong
runner
foal
rider
lodge
livery
perfume
ever
sometime
cough
speed
guard
stubble
agree
pony
horse
acceleration
beard
always
vendor
hay fever
surgery
concur
disagree
ride
sneeze
velocity
beg
hour
sometimes
never
washington
perspire
godmother
flint
colon
ounce
grape
cartridge
haystack
sew
certain
egg-shaped
wine
vine
string
refill
knit
crayon
cox
fangs
dental
pencil
blunder
passive
active
dentistry
dentist
gums
how
snug
exception
second
last
foremost
safety
flagstones
pavement
dressing-gown
not at all
personally
links
argue
sprint
omit
back
continue
measures
sidewalk
quack
front
event
forward
abrasive
first
several
rough
teeth
fillings
silky
not quite
sharpener
terrain
whisky
dentists
vintage
puppet
ink
pen
disc
choose
fibre
reeling composition
endure
blob
pants
mistake
scotch
reading
pile
monger
detective
edition
uneven
ferrite
brace
weeding
regulation rule
abandon
initially
fables
farther
incredible alert
complete
leave
whether
happening
connect
weights
duck
graves
occurence
fist
various
cross-country
carriage
hoof
doctor
office
ore
george
depart
few
borrow
alphabet
distance
physician consultant
winter
greatest
and again
club
struck
rungs
gelding
gallop
hasten
thump
rung
cycle
shorts
hurry
dolittle
toy
lend
skipping
backward
snatch
cord
galore
chain
stall
incorrect
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babies
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elf
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rope
grab
smash
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link
die
gossip
hired
cuff
expire
live
hearsay
pedal
smack kingdom
hooves horses
promise
judge
correct
events
moped
forgetting
intermediate
happen
nineteen
metal
corrugated
foundry
definite
search
secure
reflection
error
sharpen bitten
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injection
lovers
empire
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quest
safe
reflect
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sword
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creepy
until
reflections
mirror
at
cancer
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find out
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sank
revolve
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legion
foreign
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harmed
injury
painful
winner
explosion
rant
rave
at once
ground
hoarse
comprehend
understand
magician
option
choice
flying
knitting
instantly
immediately
now
when
crawly
factory
already
twist
selection risk
produced
masculine
slabs
wound
topic
feminine
soaring
kit
mixer
worker
wooden
then
itch
cup
look for
image
desire
growl
lung
heap
iron
necessity
want
snarl
toothbrush
accomplish aesop
numerous
many
bureau
correspondence
doctor’s
parcel
pyjamas
handed
pills
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stallion
lente
law-court
solitary
khaki
fast
springs
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bias
remembering happenings
incidents
proof
who
quick
evidence
tablets
exist
right
persevere
dozy
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swiftly
gradual slow
slowly
jury
take place
rapid
left
lead
cha
hypothalamus
hesitation
jeffreys
remainder
lag
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snail
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nook
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trial
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trotted
ahead
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et
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token
start
producer
foil
plaything
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need
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ferry
sail
crane
filings
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cuddly
scrap
require
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canoe
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boat
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weapon
clip
pocket
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teacup
exclude
offend
conjurer hazard
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herald
grapes
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tea-cup
include
tissue
saucer
knickers
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emery
ark
optics
trick
triumph
material
white collar
noah
volume
harpoon
cloth
folder
hornpipe
pulp
stationery
bulletin
sailor
crew
moment
decks
matches antimony
ending
begin
terminally
conclusion
and
envelope
finish
gallows
else
pillowslip
sheet
package
nevertheless
actual
final
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girders
rigging
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ink-pot
contain
conclude
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finality
or
came
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chez
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vines
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literature
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indians
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rack
since
cowboys
meths
unsure
studies
spoil
satin
occupied
naval
file
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newspaper
news
wreck
launching
spacious
donated
presented
liner
scribble
given
newsagent
legend
myth
cargo
ship
berth
june
july
sailing
cruise
plastic
provide
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patient
port
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beware
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printing
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lately
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vessel
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yield
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armour
doors
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times
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chivalry
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nightmares
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boats
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gulf
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after
label
yachts
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abel
strap
shove
rigid
topical
strips
journalism
sort
unlucky
cain
paddle
soon
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houses
homes
offer
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merchant
slug
funnels
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nearby
ended
ships
jagged
playing
pillow-case
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marvellous
ports
harbours
mint
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hater
images
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scooters
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gospel
dream
perjury
deceive
hinges
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masts
industry
afterwards
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lock
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proffer
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succeed
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sailors
liners
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with the wind
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or not
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loose
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slide
oath
swear
higher
true
honesty
britain
pouch
earlier
going
lower
penultimate
lies
truth
lethal
nova
slip
gone
upper
although
distant
methylated spirits
nightmare
away
hindered
pullover
magazine
direct
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source
roofs
maisonettes
to be
or not to be
syringe
rayon
puncher knot
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latest
ask
greek
rover
indirect
demand
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cravat
filter
supply
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thinner
surgeon
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timid
woolly
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request
stopped
private eye
fantastic
later
from home
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sent
flux
pea
pod
sooner
paws
near
sorts
kinds
necessities
venice
sitting
jamb
nylon
emigrate
fifteen
tack
text book mythology
weld
tops
wit
sarcasm
sender
closeness
odontology
afar
rear
speaking
invalid
neurology
strike
proper
talking
staying
phoney
haemorrhoids
solder
vessels
pops
scrape
wonderful
possessed
textile
telegram
especiallyweaver
australia
sixteen
type
owned
writer
postcard
onward
raise
valid
wits
unreal
cripple
adjacent wheel chair
tiredness
stupendous
vein
jugular
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practice
leaping
all right
tails
stress
faster
consulate
unsafe
aunt
uncle
origin
al
signature
dangerous
dad
deadly
strain
slower
precarious
mum
treasure
trove
heads
scotia
fastest
slick
tests
needs
theatres
beginner
synthetic
particularly
rangers celtic
appendix wants
plays
learner
grandma
dogfish
completely
grandpa
catfish
consist
comprise
follower disciple
import
satellite
whip
lash
Pajek
imprisonment
gleams
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%
☛ ✖
31
'
$
Internet Movie Database http://www.imdb.com/
12th Annual Graph Drawing Contest, 2005. Omrežje IMDB je dvodelno in ima 1324748 =
428440 + 896308 točk in 3792390 povezav.
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☛ ✖
32
'
$
Dvodelne sredice
Podmnožica točk C = C1 ∪ C2 ⊆ V določa (p, q)-sredico v dvodelnem
omrežju N = (V1 , V2 ; L), V = V1 ∪ V2 , če imajo vse točke iz C1 stopnjo
v C vsaj p in vse točke iz C2 stopnjo v C vsaj q ter je C maksimalna taka
množica.
Veliko možnih parov (p, q). Zanimivi predvsem ’robni’ pari.
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33
'
$
Tabela (p, q : n1 , n2 ) for Internet Movie Database
1 1590: 1590
1 | 22 24: 1854 1153 | 43 14: 29 83
2 516: 788
3 | 23 23:
47
56 | 44 14: 29 83
3 212: 1705
18 | 24 23:
34
39 | 45 13: 30 95
4 151: 4330 154 | 25 22:
42
53 | 46 13: 29 94
5 131: 4282 209 | 26 22:
31
38 | 47 12: 29 101
6 115: 3635 223 | 27 22:
31
38 | 48 12: 28 100
7 101: 3224 244 | 28 20:
36
53 | 49 12: 26 95
8
88: 2860 263 | 29 20:
35
52 | 50 11: 27 111
9
77: 3467 393 | 30 19:
35
59 | 51 11: 26 110
10
69: 3150 428 | 31 19:
35
59 | 52 11: 16 79
11
63: 2442 382 | 32 19:
34
57 | 53 10: 35 162
12
56: 2479 454 | 33 18:
34
62 | 54 10: 35 162
13
50: 3330 716 | 34 18:
34
62 | 55 10: 34 162
14
46: 2460 596 | 35 18:
33
61 | 56 10: 34 162
15
42: 2663 739 | 36 17:
33
65 | 57 9: 35 187
16
39: 2173 678 | 37 16:
33
75 | 58 9: 33 180
17
35: 2791 995 | 38 16:
30
73 | 59 9: 33 180
18
32: 2684 1080 | 39 16:
29
70 | 60 9: 32 178
19
30: 2395 1063 | 40 15:
29
77 | 61 9: 31 177
20
28: 2216 1087 | 41 15:
28
76 | 62 9: 31 177
21
26: 1988 1087 | 42 15:
28
76 | 63 8: 31 202
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34
'
$
(247,2)-sredica and (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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(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
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
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
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4-obroči in analiza dvodelnih omrežij
V dvodelnem omrežju ni nobenega 3-obroča. Najgostejša podomrežja so
polni dvodelni grafi Kp,q . Ti vsebujejo veliko 4-obročev.
w4 (Kp,q ) = (p − 1)(q − 1)
4-obročne uteži so bile vključene v program
Pajek šele avgusta 2005.
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Usmerjeni 4-obroči
Obstajajo 4 vrste usmerjenih 4-obročev:
ciklični
tranzitivni
rodovniški
karo
Pri tranzitivnih obročih omogoča Pajek tudi štetje, kolikokrat nastopa
povezava v tranzitivnem obroču kot bližnjica.
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Enostavni povezavni otoki v IMDB za w4
Dobili smo 12465 enostavnih povezavnih otokov na 56086 točkah. Tu je
porazdelitev njihovih velikosti.
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1
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148
28
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Primer: Otoka za w4 / Charlie Brown in Adult
Morgan, Jonathan (I)
Kesten, Brad
Brando, Kevin
Robbins, Peter (I)
Shea, Christopher (I)
Altieri, Ann
Ornstein, Geoffrey
Schoenberg, Jeremy
Davis, Mark (V)
Voyeur, Vince
Charlie Brown and Snoopy Show
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
Dough, Jon
Sanders, Alex (I)
North, Peter (I)
Michaels, Sean
Charlie Brown Christmas
Race for Your Life, Charlie Brown
Be My Valentine, Charlie Brown
Mendelson, Karen
Stratford, Tracy
Boy, T.T.
Hauer, Brent
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
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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40
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Primer: Otok za w4 / Polizeiruf 110 & Starkes Team
Maranow, Maja
Starkes Team, Ein
Starkes Team - Eins zu Eins, Ein
’Affre Semmeling, Die’
Starkes Team - Kollege Mrder, Ein
Starkes Team - Sicherheitsstufe 1, Ein
Martens, Florian
Starkes Team - Erbarmungslos, Ein
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
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
Starkes Team - Roter Schnee, Ein
Bademsoy, Tayfun
Starkes Team - Der Verdacht, Ein
Starkes Team - Der Todfeind, Ein
Polizeiruf 110 - Kurschatten
Starkes Team - Mordlust, Ein
Winkler, Ein
Wolfgang
Starkes Team - Das groe Schweigen,
Polizeiruf 110 - Tote erben nicht
Starkes Team - Der schne Tod, Ein
Polizeiruf 110 - Der Pferdemrder
Starkes Team - Trume und Lgen, Ein
Polizeiruf 110 - Henkersmahlzeit
Starkes Team - Bankraub, Ein
Starkes Team - Verraten und verkauft, Ein
Starkes Team - Braunauge, Ein
Starkes Team - Im Visier des Mrders, Ein
Starkes Team - Die Natter, Ein
Lerche, Arnfried
Pajek
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Iskanje vzorcev
Če se izbrani vzorec določen z (majhnim) omrežjem ne pojavlja zelo
pogosto v danem omrežju, lahko uporabimo v programu Pajek postopek
iskanja vzorcev, ki določi vse pojavitve vzorca v omrežju.
Iskanje vzorcev pride prav pri pregledovanju velikih organskih molekul
(ogljikovi obroči) in pri analizi rodovnikov – poroke med sorodniki.
Michael/Zrieva/
Francischa/Georgio/
Damianus/Georgio/
Legnussa/Babalio/
Nicolinus/Gondola/
Franussa/Bona/
Marin/Gondola/
Magdalena/Grede/
Junius/Georgio/
Anucla/Zrieva/
Nicola/Ragnina/
Nicoleta/Zrieva/
Junius/Zrieva/
Margarita/Bona/
Sarachin/Bona/
Nicoletta/Gondola/
Marinus/Bona/
Phylippa/Mence/
Marinus/Zrieva/
Maria/Ragnina/
Lorenzo/Ragnina/
Slavussa/Mence/
Tri povezane poroke med sorodniki v parnem rodovniku dubrovniškega plemstva.
Polna povezava ustreza relaciji je sin od
črtkana pa relaciji je hči od . V
vseh treh primerkih sta brat in sestra iz ene
družine našla svoja partnerja v (isti) drugi
družini.
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Vzorci porok med sorodniki v parnih rodovnikih
A2
Vsi vzorci porok med sorodniki v parnih rodovnikih na 2 do 6 točkah. Vzorci
so označeni tako:
A3
A4.1
B4
A4.2
• prvi znak – število začetkov: A –
en, B – dva, C – tri.
A5.2
A5.1
• drugi znak: število točk v vzorcu
(2, 3, 4, 5, ali 6).
B5
A6.3
A6.2
A6.1
C6
B6.4
B6.1
B6.2
B6.3
• zadnji znak: razločnik (če sta prva
znaka enaka).
Vzorci označeni z A ustrezajo krvnim
porokam med sorodniki. V vsakem
vzorcu je število začetkov enako številu
koncev.
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Pogostosti normalizirane s števili parov v parnem
rodovniku × 1000.
vzorec
A2
A3
A4.1
B4
A4.2
A5.1
A5.2
B5
A6.1
A6.2
A6.3
C6
B6.1
B6.2
B6.3
B6.4
Skupaj
Loka
0.07
0.07
0.85
3.82
0.00
0.64
0.00
1.34
1.98
0.00
0.00
0.71
0.00
1.91
3.32
0.00
14.70
Silba
0.00
0.00
2.26
11.28
0.00
3.16
0.00
4.96
12.63
0.90
0.00
5.41
0.45
17.59
13.53
0.00
72.17
Ragusa
0.00
0.00
1.50
10.49
0.00
2.00
0.00
23.48
1.00
0.00
0.00
9.49
1.00
31.47
40.96
2.50
123.88
Turcs
0.00
0.00
159.71
98.28
0.00
36.86
0.00
46.68
169.53
0.00
0.00
36.86
0.00
130.22
113.02
7.37
798.53
Royal
0.00
2.64
18.45
6.15
0.00
11.42
0.00
7.03
11.42
0.88
0.00
4.39
0.00
10.54
11.42
0.00
84.36
Večina porok med sorodniki je v rodovniku turških nomadov; sledi dubrovniško plemstvo;
drugje so veliko redkejše.
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Pa še to
V zadnjem letu smo vgradili v program Pajek tudi podporo za večrelacijska
omrežja, ki je združena s časovnimi omrežji omogočila analize novih vrst
omrežij – kot so na primer omrežja KEDS (Kansas Event Data System ali
Tabari).
Druga nova možnost je produkt omrežij. Ta nam omogoča v rodovnikih
določiti omrežja drugih sorodstvenih relacij, kot so na primer: sestra, stric,
nečakinja, . . .
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Viri
1. Batagelj, V. and Mrvar, A.(1996-): Pajek– program for analysis and visualization of
large network, home page, data sets.
2. Batagelj, V. and Zaveršnik, M.(2002): Generalized Cores, arxiv cs.DS/0202039
3. Batagelj, V. and Zaveršnik, M.(2003): Short cycle connectivity. arxiv cs.DS/0308011
4. Mrvar, A. and Batagelj, V. (2004): Relinking Marriages in Genealogies. Metodološki
zvezki - Advances in Methodology and Statistics, 1, Ljubljana: FDV, 407-418.
5. de Nooy, W., Mrvar, A. and Batagelj V. (2005): Exploratory Social Network Analysis
with Pajek, CUP. Amazon. ESNA page.
6. J. P Scott: Social Network Analysis: A Handbook. SAGE Publications, 2000. Amazon.
7. S. Wasserman, K. Faust: Social Network Analysis: Methods and Applications. CUP,
1994. Amazon.
8. White, D.R., Batagelj, V., and Mrvar, A. (1999): Analyzing Large Kinship and Marriage
Networks with Pgraph and Pajek. Social Science Computer Review – SSCORE, 17,
245-274.
9. Zaveršnik, M. and Batagelj, V. (2004): Islands. Slides from Sunbelt XXIV, Portorož,
Slovenia, 12.-16. May 2004, PDF
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prosojnice - Vladimir Batagelj

Transcription

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