Visualization of large networks and Pajek

Transcription

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Visualization of
large networks
and Pajek
Vladimir Batagelj
University of Ljubljana
Slovenia
Workshop on Complex objects visualization
November 16-19, 2005, Koper, Slovenia
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V. Batagelj: Visualization of large networks and Pajek
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Outline
1
Networks in social sciences . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
3
Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
5
Types of networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
10
Large Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
11
Pajek . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
14
Representations of properties . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
15
Analysis and Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
26
Large networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
31
Bipartite cores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
35
Directed 4-rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
41
Dense networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
45
New graphical elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
47
Dynamic/temporal networks . . . . . . . . . . . . . . . . . . . . . . . . . . . .
47
52
Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
52
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Workshop on Complex objects visualization, November 16-19, 2005, Koper
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Networks in social sciences
The use of networks was introduced
in sociology by Moreno developing
the sociometry (1934, 1953, 1960).
An overview of visualization of social networks was prepared by Lin
Freeman (1, 2).
Moreno
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Moreno: Who shall survive?
K:
1:
2:
3:
4:
5:
6:
7:
8:
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Networks
Alexandra Schuler/ Marion Laging-Glaser:
Analyse von Snoopy Comics
A network is based on two sets – set
of vertices (nodes), that represent
the selected units, and set of lines
(links, ties), that represent relations
between units. They determine a
graph. A line can be directed – an
arc, or undirected – an edge.
Additional data about vertices or
lines can be known – their properties (attributes). For example:
name/label, type, value, . . .
Network = Graph + Data
The data can be measured or computed.
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Networks / Formally
A network N = (V, L, P, W) consists of:
• a graph G = (V, L), where V is the set of vertices, A is the set of arcs,
E is the set of edges, and L = E ∪ A is the set of lines. n = card(V),
m = card(L)
• P vertex value functions / properties: p : V → A
• W line value functions / weights: w : L → B
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Types of networks
Besides ordinary (directed, undirected, mixed) networks some extended
types of networks are also used:
• 2-mode networks, bipartite (valued) graphs – networks between two
disjoint sets of vertices.
• multi-relational networks.
• temporal networks, dynamic graphs – networks changing over time.
• specialized networks: representation of genealogies as p-graphs;
Petri’s nets, . . .
The network (input) file formats should provide means to express all these
types of networks. All interesting data should be recorded (respecting
privacy).
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Deep South
Classical example of two-mode network
are Southern women (Davis 1941).
Davis.paj. Freeman’s overview.
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Temporal networks
In a temporal network the presence/activity of vertex/line can change
through time. Two types of descriptions of temporal networks are used –
based on presence and based on events.
Moody:
Drug users in Colorado Springs, 5 years
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Multi-relational temporal network – KEDS/WEIS
% Recoded by WEISmonths, Sun Nov 28 21:57:00 2004
% from http://www.ku.edu/˜keds/data.dir/balk.html
*vertices 325
1 "AFG" [1-*]
2 "AFR" [1-*]
3 "ALB" [1-*]
4 "ALBMED" [1-*]
5 "ALG" [1-*]
...
318 "YUGGOV" [1-*]
319 "YUGMAC" [1-*]
320 "YUGMED" [1-*]
321 "YUGMTN" [1-*]
322 "YUGSER" [1-*]
323 "ZAI" [1-*]
324 "ZAM" [1-*]
325 "ZIM" [1-*]
*arcs :0 "*** ABANDONED"
*arcs :10 "YIELD"
*arcs :11 "SURRENDER"
*arcs :12 "RETREAT"
...
*arcs :223 "MIL ENGAGEMENT"
*arcs :224 "RIOT"
*arcs :225 "ASSASSINATE TORTURE"
*arcs
224: 314 153 1 [4]
890402 YUG
212: 314 83 1 [4]
890404 YUG
224: 3 83 1 [4]
890407 ALB
123: 83 153 1 [4]
890408 ETHALB
...
42: 105 63 1 [175]
030731 GER
212: 295 35 1 [175]
030731 UNWCT
43: 306 87 1 [175]
030731 VAT
13: 295 35 1 [175]
030731 UNWCT
121: 295 22 1 [175]
030731 UNWCT
122: 246 295 1 [175]
030731 SER
121: 35 295 1 [175]
030731 BOSSER
KSV
ETHALB
ETHALB
KSV
224
212
224
123
(RIOT) RIOT-TORN
(ARREST PERSON) ALB ETHNIC JAILED IN YUG
(RIOT) RIOTS
(INVESTIGATE)
PROBING
CYP
BOSSER
EUR
BOSSER
BAL
UNWCT
UNWCT
042
212
043
013
121
122
121
(ENDORSE)
(ARREST PERSON)
(RALLY) RALLIED
(RETRACT)
(CRITICIZE)
(DENIGRATE)
(CRITICIZE)
GAVE SUPPORT
SENTENCED TO PRISON
CLEARED
CHARGES
TESTIFIED
ACCUSED
Kansas Event Data System KEDS
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Size of Networks
The size of a network/graph is expressed by two numbers: number of
vertices n = |V| and number of lines m = |L|.
In a simple undirected graph (no parallel edges, no loops) m ≤ 12 n(n − 1);
and in a simple directed graph (no parallel arcs) m ≤ n2 . The quotient
m
γ = mmax
is a density of graph. In large networks more intuitive density
P
1
¯
measure is the average degree d = n v∈V deg(v) = 2m
n .
Small networks (some tens vertices) – can be represented by a picture and
analyzed by many algorithms (UCINET, NetMiner).
Also middle size networks (some hundreds vertices) can still be represented
by a picture (!?), but some analytical procedures can’t be used.
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Till 1990 most networks were small – they were collected by researchers
using surveys, observations, archival records, . . . The advances in IT allowed
to create networks from the data already available in the computer(s). Large
networks became reality.
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Large Networks
Large network – several thousands or millions of vertices. Can be stored in
computer’s memory – otherwise huge network.
Usually sparse m << n2 ; typical: m = O(n) or m = O(n log n) .
Examples:
network
ODLIS dictionary
Citations SOM
Molecula 1ATN
Comput. geometry
English words 2-8
Internet traceroutes
Franklin genealogy
World-Wide-Web
Actors
US patents
SI internet
size
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
source
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
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Pajek
Large networks are too big to be displayed in details; special algorithms are
needed for their analysis.
Pajek is a program, for Windows, for
analysis and visualization of large networks
having some ten or houndred of thousands of
vertices.
In Slovenian language pajek means spider.
The latest version of Pajek is freely available, for noncommercial use, at
its home page:
http://vlado.fmf.uni-lj.si/pub/networks/pajek/
Book: W. de Nooy, A. Mrvar, V. Batagelj: Exploratory Social Network Analysis with Pajek,
CUP, 2005.
Amazon. ESNA page.
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Main design goals
The main goals in the design of Pajek are:
• to support abstraction by (recursive)
decomposition of a large network into
several smaller networks that can be
treated further using more sophisticated methods;
• to provide the user with some powerful
visualization tools;
• to implement a selection of efficient
subquadratic algorithms for analysis of
large networks.
With Pajek we can: find clusters (components, neighbourhoods of ‘important’ vertices,
cores, etc.) or patterns (motifs) in a network, extract vertices that belong to the same clusters
and show them separately, possibly with the parts of the context (detailed local view), shrink
vertices in clusters and show relations among clusters (global view).
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Line-cut: Krebs Internet Industries, 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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Pajek
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Representations of properties
Properties of vertices P and lines W can be measured in different scales:
numerical, ordinal and nominal. They can be input as data or computed
from the network.
In Pajek numerical properties of vertices are represented by vectors,
nominal properties by partitions or as labels of vertices. Numerical
property can be displayed as size of vertex (figure), as its coordinate; and a
nominal property as color or shape of the figure, or as a vertex label.
We can assign in Pajek numerical values to links. They can be displayed
as value, thickness or grey level. Nominal vales can be assigned as label,
color or line pattern (see Pajek manual, section 4.3).
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Analysis and Visualization
The network visualization is an iterative process that combines analysis and
creation of layouts.
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Some comments
While the technical graph drawing problems could ask for a single ’the
best’ picture, the social network analysis is a part of data analysis. Its goal
is to get insight into the structure and characteristics of a given network, but
also how it influences related social processes.
What is the goal: exploration of network data (layout editor), presentation
of the obtained results (layout viewer), . . . ?
What is a GD result: picture or layout ?
What is the medium of the result: static picture on ’paper’, interactive
layout, . . . ?
What kind of user will use the result: simple, advanced, . . . ?
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Most methods are ’paper’ oriented. In larger/denser networks there is
often too much information to be presented at once. A possible answer are
interactive layouts where the user controls what (s)he wants to see.
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Sociograph
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James Moody: Display of properties – school
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Douglas White: relinking marriages among the Aydinli
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Lothar Krempel
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FAS: The scientific field of Austria
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FAS: Austria’s most important Companies
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Katy Börner: Text analysis
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Ulrik Brandes: Discourse network
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Jeffrey Johnson: St Marks food web
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Large networks
The simplest solution would be to take very large ’paper’.
The standard solution is abstraction – clustering. We could also introduce
different new graphical objects representing typical parts of network, LOD.
The other possibility is dynamic navigation through network: visualization
of the neighborhood with indications of position in the global network
(darker/brighter background – distribution of neighbors) complemented
with a global map.
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Big picture, V. Batagelj, AE’04
subnetwork (n = 5952, m = 18008) of the symmetrized Edinburgh Associative Thesaurus
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Big picture
thrust
moorland
slowest
ted
heath
possessing
jumping
latter
staying
phoney
haemorrhoids
strike
rear
afar
nigh
far
nightmare
detector
reverie
bye
cheat
fantasy
scooters
deceive
mantis
preying
previous
proceed
praying
lover
hater
sought
pictures
market
road works
leaving
next
mexico
limit
jagged
gulf
hammock
nap
nightmares
fantasies
untrue
sleeping
cigarettes
smoke
swift
rest
hose
asleep
ash-tray
horizon
sheets
bedroom
beds
letter
pillows
ahead
in front
doubtful
behind
postman
divan
misdeed
who
predicate
nippy
bash
quickly
sluggish
solitary
east
recognise
mourning
speedy
stud
mare
very
spine
tries
attempts
hobby
hurry
information
bike
ladder
if
struck
rungs
hit
miss
gelding
argue
gonzales
ridden
filly
stable
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jockey
cavalry
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ire
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deliver
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promenade
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will
shall
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add
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searching
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wilson
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sadism
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confirm
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assume
presume
listened wireless
radio
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scaffoldingwere
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legal
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gin
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break
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books
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than
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mortality
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instead
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destroy
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rush
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odds
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year
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yearn
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height
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opposite
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rather
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therapy
anaemic
donor
anatomy
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body
haemoglobin
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object
wary
polythene
wriggle
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twain
mark
loss
outboard
profit
stack
fragrance
manhole
heart
brakes
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crash
oil
better
keep
commons
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company
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country
jest
spare
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mortgage
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chill
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capital
total
stifling
mansion
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sum
city
sums
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america
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newyork
london
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stone
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column
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gramme
cherish
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gram
free
lanky
scales
pray
kneel
opener
date
minimum
bruises
dejected
delight
queer
unbound
nisi
suburb
decree
gained
maze
discovered
figures
numbers
angry
gents
miles
gentlemen
pyramid
ladies
egypt
indication
skeleton
compound
labyrinth chemical
forgotten
homosexual
1969
mend
repair
gratify
unusual please
goodness
gracious
neuter
grieving
hoar
crucifix
surely
charge
christ
jesus
cross
peace
tranquillity
trap
candles
hand
bunch
crucified
bastard
illegitimacy
stoat
satisfy
kinky
expect
liberal
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thankful
anticipate
grateful
corrosion
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lust
received
masturbate
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contrary
department
fetched
tiger
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sight
command
glad
disobey
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social
mournful
unhappy
pleased
miserable sad
fornicate
happy
reproduce maniac
fray
weasel
annihilate
healer
jonathan
faire
goliath
eternal
march
carried
brows
pessimism
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private satiate
warehouse
rifles
make
carbonate
create
unload
masturbating
manufacture amends
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rabbit
spaghetti
ager
fierce
iniquity
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title
eye
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shiner
wink
buttercup
burrow
ancient
daisy
armed
defence
napkin
duodenal
camp
crimson
fete
tot
balloon
melody
ascend
try
bell
theme
rang
menstrual
alarm
transition clock
dictionary
shop
words
o’clock
roars
shovel
pupil
teacher
adult
ferocious
hope
faith
socks
sneak
honest
district
urban
sin
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omit
abate
row
states
colon
warm
skip
puppet
needle
lace
pin
prick
ounce
string
refill
sew
semi
sweat
vintage
lovers
empire
reeling composition
endure
haystack
knit
switzerland
detached
godmother
flint
snug
d.c.
exception
beg
abrasive
not quite
cox
perspire
dental
pencil
crayon
active
dentistry
fangs
dentist
gums
how
mistake
blunder
passive
sunset
search
population
disc
rant
sure
straw
spooky
apparition
sat
forthwith
porcelain
litre
liquor
ouch
lungs
made
lay
injured
ghoul
shudder
alien
harm
hurt
hurting
loser
legion
foreign
injure
harmed
injury
painful
winner
explosion
hoarse
rave
at once
handkerchief select
ink
pen
sharpener
terrain
whisky
dentists
teeth
fillings
silky
washington
rough
sharpen bitten
scotch
brace
monger
several
edition
uneven
tropic
reading
pile
now
injection
blob
pants
immediately
definite
safe
reflection
then
ground
comprehend
understand
magician
option
choice
flying
knitting
instantly
quest
secure
reflect
fairies
vest
already
twist
selection risk
produced
masculine
slabs
wound
topic
feminine
soaring
kit
mixer
worker
wooden
creepy
until
reflections
error
offend
sank
find out
unharmed
mirror
sword
ark
optics
conjurer hazard
when
revolve
white collar
noah
trick
itch
crawly
factory
at
cancer
scratch
cup
look for
image
desire
growl
lung
ferrite
iron
detective
weeding
regulation rule
abandon
first
event
measures
fist
various
graves
coarse
happening
forward
weights
leave
initially
steel
fables
farther
incredible alert
complete
depart
whether
cuddly
wounded
document
snarl
heap
corrugated
need
quarto
ferry
sail
foundry
pocket
herald
grapes
teacup
exclude
require
necessity
want
toothbrush
ore
george
foil
occurence
connect
alphabet
distance
doctor
physician consultant
winter
greatest
and again
club
thump
rung
gallop
hasten
dolittle
rider
lodge
necklace injustice
lone
stains
extremely
cycle
shorts
livery
epsom
prescription medic
metal
finals
paper
gazette
canoe
crane
filings
boxer
accomplish aesop
numerous
few
office
moment
scrap
token
start
producer
many
borrow
skipping
backward
snatch
cord
galore
chain
van
tractor
stall
incorrect
hired
babies
farm
die
gossip
pedal
smack kingdom
hooves horses
west
alone
quarrel
beads
moped
confinement
intermediate
promise
wrong
umbilical
link
expire
live
hearsay
events
forgetting
stallion
lente
law-court
khaki
irritation
springs
rapidly judicial
trot
matchbox
hasty
bias
fast
remembering happenings
incidents
proof
quick
evidence
owner
nappies
pills
dwell
judge
correct
letters
elf
toy
rope
grab
smash
stethoscope
eighteen occur
nineteen
exist
right
persevere
dozy
dawdle
swiftly
gradual slow
slowly
jury
tablets
cuff
plaything
bureau
lend
correspondence
doctor’s
parcel
pyjamas
happen
handed
take place
rapid
left
lead
cha
hypothalamus
hesitation
jeffreys
tribulation
lag
strive
pillow
remainder
pack
snail
remaining
nook
slept
trial
brisk
dubious
cranny
however
lagging
trotted
hanging
et
but
ending
finish
begin
terminally
conclusion
else
envelope
conclude
beginning end
fleet
boat
exams
tissue
spotted
starched
tea-cup
include
triumph
saucer
knickers
extinct
emery
clip
matelot
oar
weapon
girders
rigging
decks
matches antimony
final
gallows
and
pillowslip
posted
package
nevertheless
actual
sheet
post
mattress
bed
ornament
consciousness
name
bedtime
came
went
ink-pot
contain
bulletin
oars
crew
august
journal
pulp
stationery
sailor
dingy
scribble
newspaper
news
silk
material
harpoon
cloth
folder
hornpipe
spacious
donated
presented
wreck
cargo
given
newsagent
legend
myth
sailing
chez
ruin
volume
vines
fabric
literature
nous
indians
uncertain
rack
since
cowboys
naval
unsure
studies
spoil
satin
occupied
meths
file
launching
july
gave
patient
plastic
june
provide
fail
cruise
ship
berth
port
whiskey
beware
spanner
woven
printing
papers
lately
steward
prow
funnel
director
grasp
artificial
finality
or
deck
vessel
pole vault
pass
liner
elevate
driving
take
anchor
signal
whale
obvious
recently press
receive
donate
seaman
tail
dock
lift
hopes
give
mast
captain
enter
fate
elevator
finally
either
former
stated
nom
awake
cosine
sine
real
coma
wake
fags
repose
pipe
into
dreaming
said
kittens
doze
genuine
results
audio
unite
fume
fag
mentioned
armour
snooze
sleep
snore
wag
14
muslin
apparent
pull
stiff
fears
overtake
heave
aground
shipment
destiny
locks
done
suspend
writing
tar
rigid
push
13
yield
guardian
memoir
grip
shove
topical
strips
journalism
sort
unlucky
abel
paddle
strap
times
ed
hold
battery
baron
waking
dreams
slumbers
visual
knock
ajar
begun
finished ever ready
at last
slumber
de plume
ashtray
open
hang
waste
keys
accept
offer
soon
dwellings
handle
doors
started
docks
errant
knight
knob
closed
began
commenced
boats
chivalry
snoring
shut
nearby
ended
ships
aluminium
playing
pillow-case
lighter
cigarette
bride
groom
ports
harbours
homes
hinge
close
proffer
houses
slug
funnels
knocker door
slams
marvellous
yachts
cigars
cigar
sky-line
napping
lying
tobacco
label
astray
morbid
coming
before
stub
images
mail
bad habit
tight
masts
going
tag
lung cancer
smoking
sailors
industry
gone
after
hinges
operation
jib
merchant
key-hole
fred
lock
key
navigation
rasp
cain
works
working
studying
showing
print
exact
accurate
swotting
succeed
weave
precise
rocket
remove
loom
taken
bind
render
yacht
schooner
stamp
editor
hoyle
sweater
padlock
slack
great
liners
polo
mint
false
gospel
dream
slide
oath
swear
earlier
higher
or not
jumper
loose
fabulous
afterwards
true
honesty
falsehood
deceit
perjury
britain
with the wind
lower
penultimate
lies
truth
lie
fib
upper
although
distant
lethal
pouch
slip
latest
later
from home
away
pullover
magazine
direct
nova
kangaroo
pea
pod
sooner
paws
near
methylated spirits
fantastic
nit
hindered
rover
indirect
bored
tie-pin
tie
source
roofs
flats
syringe
rayon
puncher knot
shy
maisonettes
to be
or not to be
collar
cravat
filter
demand
profession
ask
tug
supply
orthopaedic
thicker
thinner
surgeon
timid
woolly
yarn
enquire
greek
stopped
private eye
sent
flux
wit
sarcasm
sender
closeness
odontology
piles
untruth
recline
speaking
invalid
neurology
proper
solder
boost
weld
tops
sorts
request
text book mythology
necessities
venice
sitting
jamb
nylon
emigrate
fifteen
tack
kinds
writer
vessels
pops
scrape
wonderful
type
textile
telegram
especiallyweaver
australia
sixteen
possessed
owned
stress
postcard
onward
raise
valid
talking
unreal
adjacent wheel chair
tiredness
stupendous
wits
vein
cripple
perfect
practice
leaping
all right
jugular
tails
faster
consulate
unsafe
aunt
uncle
origin
o.k.
next to
dangerous
dad
deadly
strain
slower
precarious
mum
treasure
auntie
capone
al
signature
fastest
having
trove
heads
scotia
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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29
'
$
Michael Blum
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30
'
$
Internet Movie Database http://www.imdb.com/
12th Annual Graph Drawing Contest, 2005. The IMDB network is bipartite (2-mode) and has
1324748 = 428440 + 896308 vertices and 3792390 arcs.
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31
'
$
Bipartite cores
The subset of vertices C ⊆ V is a (p, q)-core in a bipartite (2-mode)
network N = (V1 , V2 ; L), V = V1 ∪ V2 iff
a. in the induced subnetwork K = (C1 , C2 ; L(C)), C1 = C ∩ V1 , C2 =
C ∩ V2 it holds ∀v ∈ C1 : degK (v) ≥ p and ∀v ∈ C2 : degK (v) ≥ q ;
b. C is the maximal subset of V satisfying condition a.
Properties of bipartite cores:
• C(0, 0) = V
• K(p, q) is not always connected
• (p1 ≤ p2 ) ∧ (q1 ≤ q2 ) ⇒ C(p1 , q1 ) ⊆ C(p2 , q2 )
• C = {C(p, q) : p, q ∈ IN}. If all nonempty elements of C are different it is a
lattice.
• To determine a (p, q)-core the procedure similar to the ordinary core procedure
can be used.
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32
'
$
(247,2)-core and (27,22)-core
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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33
'
$
(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-rings and analysis of 2-mode networks
In bipartite (2-mode) network there are no 3-rings. The densest substructures are complete bipartite subgraphs Kp,q . They contain many 4-rings.
w4 (Kp,q ) = (p − 1)(q − 1)
The 4-rings weights were implemented in
Pajek only recently, in August 2005.
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Directed 4-rings
There are 4 types of directed 4-rings:
cyclic
transitive
genealogical
diamond
In the case of transitive rings Pajek provides a special weight counting on
how many transitive rings the arc is a shortcut.
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Simple line islands in IMDB for w4
We obtained 12465 simple line islands on 56086 vertices. Here is their size
distribution.
Size Freq
Size Freq
Size Freq
Size Freq
-------------------------------------------------------2 5512
20
19
38
4
59
2
3 1978
21
18
39
3
61
1
4 1639
22
15
40
2
64
1
5
968
23
9
42
2
67
1
6
666
24
13
43
3
70
1
7
394
25
12
45
3
73
1
8
257
26
6
46
4
76
1
9
209
27
6
47
5
82
1
10
148
28
5
48
1
86
1
11
118
29
6
49
2
106
1
12
87
30
3
50
2
122
1
13
55
31
6
51
1
135
1
14
62
32
5
52
2
144
1
15
46
33
3
53
1
163
1
16
39
34
1
54
2
269
1
17
27
35
5
55
1
301
1
18
28
36
4
57
1
332
2
19
29
37
7
58
1
673
1
--------------------------------------------------------
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Example: Islands for w4 / Charlie Brown and 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
Stratford, Tracy
Davis, Mark (V)
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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Example: Island for w4 / Polizeiruf 110 and 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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New drawing algorithms from GD’05
Fig. 3. A directed graph arranged using orthogonal ordering constraints in just the vertical dimension to
preserve layering.
The color
on theMarriott:
left side indicate
the layer-bands
and the faint
Dwyer,
Yehuda
Koren,
andbars
Kim
Stress
Majorization
horizontal lines indicate the boundaries between these layers.
Tim
Orthogonal Ordering Constraints.
with
The 1138bus graph (1138 vertices, 1458 arcs).
Fig. 4. The 1138bus graph (1138 nodes, 1458 edges) from the Matrix market collection[2], displayed as a directed graph.
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New drawing algorithms from GD’05
(a) Fruchterman-Reingold model
(b) Node-repulsion LinLog model
Andreas Noack:
Energy-Based Clustering of Graphs
with Nonuniform Degrees.
American airports.
(c) Edge-repulsion LinLog model
Fig. 4. Direct flights between US airports (332 nodes, 2126 edges). The airports in
Alaska and the South Sea (e.g. Guam) are omitted to improve readability.
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Dense networks
Dense(r) networks with more than 15 vertices usually can’t be clearly
presented. For such networks a more appropriate display is using matrix representation. Properly reordering vertices can reveal patterns in
corresponding matrix display.
Matrix representation can be supplemented with display of properties of
vertices. It is also compatible with shrinking/ expanding with respect to a
given hierarchy (see papers 1, 2).
There are different approaches how to determine good orderings: weak,
strong components; topological sort in acyclic networks; special heuristics (Reverse Cuthill-McKee); seriation and clumping (Murtagh, 1985);
clustering; blockmodeling.
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Snyder & Kick’s World trade network / n = 118, m = 514
Pajek - shadow 0.00,1.00
World trade - alphabetic order
Sep- 5-1998
Sep- 5-1998
uki
net
bel
lux
fra
ita
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jap
usa
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pol
por
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sie
som
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usr
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aus
aut
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bol
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por
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tog
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uki
upv
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usa
usr
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Pajek - shadow 0.00,1.00
World Trade (Snyder and Kick, 1979) - cores
Alphabetic order of countries (left) and rearrangement (right)
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Contracted clusters – international trade
Pajek - shadow [0.00,1.00]
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S. America
Europe
Africa
Asia
N. America
L. America
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Australia
Snyder and Kick’s international trade. Matrix display of dense networks.
w(Ci , Cj ) =
n(Ci , Cj )
n(Ci ) · n(Cj )
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Generalized Blockmodeling
A blockmodel consists of structures obtained by identifying all units from
the same cluster of the clustering C. For an exact definition of a blockmodel
we have to be precise also about which blocks produce an arc in the reduced
graph and which do not, and of what type.
Book: P. Doreian, V. Batagelj, A. Ferligoj: Generalized Blockmodeling, CUP, 2004. Amazon.
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New graphical elements
To improve the pictures new graphical elements could be introduced:
• Almost clique or bipartite complete graph could be replaced by the
circle/quadrangle with the inverse drawing of missing edges.
• ’multiedges’
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Core based layout
I. Alvarez-Hamelin, L. DallAsta, A. Barrat, and A. Vespignani: k-core decomposition: a tool
for the visualization of large scale networks arXiv:cs 0504107
Graphical representation should be simplified into icon omitting details.
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Dynamic/temporal networks
There are different types of temporal networks:
• networks with implicit time dimension: genealogies
• (recorded) sequence of time slices: Sampson’s monks
• (recorded) sequence of events changing the network: KEDS
• online networks: They rule
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Temporal networks / September 11
Steve Corman with collaborators from Arizona State
University transformed, using his Centering Resonance
Analysis (CRA), daily Reuters
news (66 days) about September 11th into a temporal
network of words coappearance.
This network was a
challange network for Viszards
2002 session.
Pictures in SVG: 66 days. (SVG viwer)
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Every year (from 2002) we have at the Sunbelt conference a Viszards
session presenting solutions of Viszards group to a visualizations of
selected network or type of networks.
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They Rule
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MusicPlasma
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Musicvine
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Networks from the Internet
Internet Mapping Project.
Links among WWW pages.
KartOO, TouchGraph.
Derived from archives of Email, blogs, . . . , server’s logs.
Cybergeography, CAIDA.
KartOO network
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Challenges
• Visualization of properties
• Drawing/display styles
• Interactive layouts, common format(s) ?
• Matrix layout, generalized blockmodeling of large networks
• Additional graphical elements to improve layouts
• Visualization (and analysis) of multi-relational networks
• Visualization (and analysis) of dynamic/temporal networks
• Visualization of dense acyclic networks (genealogies, citation networks)
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Lombardi’s networks
Mark Lombardi
(1951-2000)
transformed business
relations into art.
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Context
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Barcelona / Peter Davies – Joseph Beuys: Text painting
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Visualization of large networks and Pajek

Transcription

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