Visualization of large networks and Pajek - Vladimir Batagelj

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Visualization oflarge networksand Pajek

Vladimir Batagelj

University of Ljubljana

Slovenia

Workshop on Complex objects visualizationNovember 16-19, 2005, Koper, Slovenia

version: November 17, 2005 / 11 : 25

V. Batagelj: Visualization of large networks and Pajek I-2'

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Outline1 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

Workshop on Complex objects visualization, November 16-19, 2005, Koper ▲ ▲ ❙ ▲ ● ▲ ❙ ▲▲ ☛ ✖

V. Batagelj: Visualization of large networks and Pajek 1'

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Networks in social sciences

Moreno

The use of networks was introduced

in sociology by Moreno developing

the sociometry (1934, 1953, 1960).

An overview of visualization of so-

cial networks was prepared byLin

Freeman(1, 2).


http://moreno.ss.uci.edu/lin.html

http://moreno.ss.uci.edu/lin.html

http://moreno.ss.uci.edu/freeman.pdf

http://moreno.ss.uci.edu/free_gph2.pdf


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Moreno: Who shall survive?

K: 1: 2:

3: 4: 5:

6: 7: 8:


http://www.amazon.com/o/dt/assoc/handle-buy-box=9992695722


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Networks

Alexandra Schuler/ Marion Laging-Glaser:

Analyse von Snoopy Comics

A networkis based on two sets – set

of vertices (nodes), that represent

the selectedunits, and set oflines

(links, ties), that representrelations

between units. They determine a

graph. A line can bedirected– an

arc, or undirected– anedge.

Additional data about vertices or

lines can be known – theirprop-

erties (attributes). For example:

name/label, type, value, . . .

Network = Graph + DataThe data can be measured or computed.


http://www.soziologie.uni-freiburg.de/jenki/lectures/2001/snoopy/default.htm


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Networks / Formally

A networkN = (V,L,P,W) consists of:

• a graphG = (V,L), whereV is the set of vertices,A is the set of arcs,

E is the set of edges, andL = 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 networksBesides 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 asp-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).


http://eclectic.ss.uci.edu/~drwhite/pgraph/p-graphs.html


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Deep South

Classical example of two-mode network

are Southern women (Davis 1941).

Davis.paj . Freeman’soverview.


http://vlado.fmf.uni-lj.si/vlado/podstat/AO/net/Davis.paj

http://books.nap.edu/books/0309089522/html/39.html


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Temporal networks

In a temporal networkthe presence/activity of vertex/line can changethrough time. Two types of descriptions of temporal networks are used –based onpresenceand based onevents.

Moody:

Drug users in Colorado Springs, 5 years


http://www.soc.sbs.ohio-state.edu/jwm/


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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 3251 "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"* arcs224: 314 153 1 [4] 890402 YUG KSV 224 (RIOT) RIOT-TORN212: 314 83 1 [4] 890404 YUG ETHALB 212 (ARREST PERSON) ALB ETHNIC JAILED IN YUG224: 3 83 1 [4] 890407 ALB ETHALB 224 (RIOT) RIOTS123: 83 153 1 [4] 890408 ETHALB KSV 123 (INVESTIGATE) PROBING

...42: 105 63 1 [175] 030731 GER CYP 042 (ENDORSE) GAVE SUPPORT212: 295 35 1 [175] 030731 UNWCT BOSSER 212 (ARREST PERSON) SENTENCED TO PRISON43: 306 87 1 [175] 030731 VAT EUR 043 (RALLY) RALLIED13: 295 35 1 [175] 030731 UNWCT BOSSER 013 (RETRACT) CLEARED121: 295 22 1 [175] 030731 UNWCT BAL 121 (CRITICIZE) CHARGES122: 246 295 1 [175] 030731 SER UNWCT 122 (DENIGRATE) TESTIFIED121: 35 295 1 [175] 030731 BOSSER UNWCT 121 (CRITICIZE) ACCUSED

Kansas Event Data SystemKEDS


http://www.ukans.edu/~keds/


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Size of Networks

The size of a network/graph is expressed by two numbers: number ofverticesn = |V| and number of linesm = |L|.

In a simple undirectedgraph (no parallel edges, no loops)m ≤ 12n(n− 1);

and in asimple directedgraph (no parallel arcs)m ≤ n2. The quotientγ = m

mmaxis adensityof graph. In large networks more intuitive density

measure is theaverage degreed = 1n

∑v∈V deg(v) = 2m

n .

Smallnetworks (some tens vertices) – can be represented by a picture andanalyzed by many algorithms (UCINET , NetMiner).

Also middle sizenetworks (some hundreds vertices) can still be representedby a picture (!?), but some analytical procedures can’t be used.

Till 1990 most networks were small – they were collected by researchersusing surveys, observations, archival records, . . . The advances in IT allowedto create networks from the data already available in the computer(s). Largenetworks became reality.


http://www.analytictech.com/

http://www.netminer.com/


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Large NetworksLargenetwork – several thousands or millions of vertices. Can be stored in

computer’s memory – otherwisehugenetwork.

Usually sparsem << n2; typical: m = O(n) or m = O(n log n) .

Examples:

network size n = |V | m = |L| sourceODLIS dictionary 61K 2909 18419 ODLIS onlineCitationsSOM 168K 4470 12731 Garfield’s collectionMolecula 1ATN 74K 5020 5128 Brookhaven PDBComput. geometry 140K 7343 11898 BiBTEX bibliographiesEnglish words 2-8 520K 52652 89038 Knuth’s English wordsInternet traceroutes 1.7M 124651 207214 Internet Mapping ProjectFranklin genealogy 12M 203909 195650 Roperld.com gedcomsWorld-Wide-Web 3.6M 325729 1497135 Notre Dame NetworksActors 3.9M 392400 1342595 Notre Dame NetworksUS patents 82M 3774768 16522438 NberSI internet 38M 5547916 62259968 Najdi Si


http://vlado.fmf.uni-lj.si/pub/networks/data/dic/ODLIS.zip

http://vax.wcsu.edu/library/odlis.html

http://vlado.fmf.uni-lj.si/pub/networks/data/cite/Kohonen.zip

http://www.garfield.library.upenn.edu/histcomp/index.html

http://vlado.fmf.uni-lj.si/pub/networks/data/PDB/1ATN.zip

http://www.rcsb.org/pdb/

http://vlado.fmf.uni-lj.si/pub/networks/data/ref/geom.zip

http://www.math.utah.edu/~beebe/bibliographies.html

http://vlado.fmf.uni-lj.si/pub/networks/data/dic/dic28.zip

ftp://labrea.stanford.edu/pub/dict/

http://vlado.fmf.uni-lj.si/pub/networks/data/large/chesweb.zip

http://research.lumeta.com/ches/map/

http://vlado.fmf.uni-lj.si/pub/networks/data/GED/franklin.zip

http://www.roperld.com/gedcom/

http://vlado.fmf.uni-lj.si/pub/networks/data/Large/WWW.zip

http://www.nd.edu/~networks/database/index.html

http://vlado.fmf.uni-lj.si/pub/networks/data/Large/Actors.zip

http://www.nd.edu/~networks/database/index.html

http://vlado.fmf.uni-lj.si/pub/networks/data/

http://www.nber.org/patents/

http://vlado.fmf.uni-lj.si/pub/networks/data/

http://www.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 oflarge networks

having some ten or houndred of thousands of

vertices.

In Slovenian languagepajekmeans spider.

The latest version ofPajek 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.


http://vlado.fmf.uni-lj.si/pub/networks/pajek/

http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=0521602629

http://www.amazon.com/exec/obidos/tg/detail/-/0521602629

http://vlado.fmf.uni-lj.si/pub/networks/book/


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Main design goalsThe main goals in the design ofPajek are:

• to support abstraction by (recursive)

decompositionof a large network into

several smaller networks that can be

treated further using more sophisti-

cated methods;

• to provide the user with some powerful

visualizationtools;

• to implement a selection of efficient

subquadraticalgorithms for analysis of

large networks.

With Pajek we can:find clusters (components, neighbourhoods of ‘important’ vertices,

cores, etc.) or patterns (motifs) in a network,extractvertices that belong to the same clusters

andshowthem 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

Pajek

AOL

AT&T

MSFT

Sun

IBM

RealNetworks

TerraLycos

Dell

Compaq

HP

Akamai

Cisco

KPMG

Oracle

Inktomi

Intel

Ariba

Motorola

KPNQwest

E.piphany

CIBER

FoundryNetworks

Pajek

AOL

AT&T

MSFTSun

IBM

RealNetworks

TerraLycos

Dell

Compaq

HP

Akamai

Cisco

KPMG

Oracle

Inktomi

Intel

AribaMotorola

KPNQwest

E.piphany

CIBER

FoundryNetworks

Pajek



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Representations of propertiesPropertiesof verticesP and linesW can be measured in different scales:

numerical, ordinal and nominal. They can beinput as data orcomputed

from the network.

In Pajek numerical properties of vertices are represented byvectors,

nominal properties bypartitions or as labels of vertices. Numerical

property can be displayed assizeof vertex (figure), as itscoordinate; and a

nominal property ascolor or shapeof the figure, or as a vertexlabel.

We can assign inPajek numerical values to links. They can be displayed

asvalue, thicknessor grey level. Nominal vales can be assigned aslabel,

color or line pattern(seePajek manual, section4.3).


http://vlado.fmf.uni-lj.si/pub/networks/pajek/doc/pajekman.pdf


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Analysis and VisualizationThe 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, . . . ?

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 layoutswhere the user controls what (s)he wants to see.


http://drjoe.biology.ecu.edu/foodweb/norwegianNcycle.htm


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Sociograph



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James Moody: Display of properties – school


http://www.soc.sbs.ohio-state.edu/jwm/


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Douglas White: relinking marriages among the Aydinli


http://eclectic.ss.uci.edu/~drwhite/


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Lothar Krempel


http://www.mpi-fg-koeln.mpg.de/people/lk/index.asp


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FAS: The scientific field of Austria


http://www.fas.at/business/en/galery/index.htm


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FAS: Austria’s most important Companies



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Katy Borner: Text analysis


http://ella.slis.indiana.edu/~katy/


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Ulrik Brandes: Discourse network


http://www.inf.uni-konstanz.de/~brandes/


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Jeffrey Johnson: St Marks food web


http://personal.ecu.edu/johnsonje/enter.htm

http://drjoe.biology.ecu.edu/stmarks/estuarybiomassNOtable.html


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Large networksThe 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 symmetrizedEdinburgh Associative Thesaurus


http://vlado.fmf.uni-lj.si/pub/networks/data/dic/eat/Eat.htm


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Big picture

10

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14

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19

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1969

20

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a daisy

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abandon

abate

abatement

abbey

abdicate

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abide

ablative

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abrasive

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abrupt

absent

absent-minded

abuse

acceleration

accept

accident

accomplish

accordance

according

accordion

account

accountant

accounts

accumulate

accurate

aces

ache

aches

achieve

achievement

acid

acne

acorn

acquaintance

acquire

acquired

act

action

actions

active

actor

actress

actual

actually

adam

addaddition

address

adequate

adhere

adjacent

admit

ado

adolescence

adult

adults

advance

advice

aeroplane

aesop

afar

affair

affectionaffirm

affluence

afraid

africa

aft

after

afternoon

afterwards

again

against

age

aged

ageing

ageless

agent

ager

aggression

agitate

ago

agony

agree

agriculture

aground

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ahead

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aid

aided

ail ailing

aim

air

aircraft

airport

airy

ajar

al

alarm

alchemy

alcohol

alcoholic

alcoholism

alderman

ale

alertales

algebra

alien

alike

alimentary

alive

alkali

all

all right

alley

allotment

allow allowance

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almighty

almond

almoner

almost

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alphabet

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alternative

althoughaluminium

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amazement

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ambulance

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amuse

amusement

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anatomy

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and

and again

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angel

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animal

animals

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annoyance

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anonymous

answer

answers

ant

anthem

anthill

anthropoid

anti

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ants

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anxiety

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anybody

anything

anywhere

apart

apartment

ape

apes

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apology

apparent

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appear

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appendix

appetite

apple

apple pie

apples

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arcade

archaeology

archaic

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architecture

arduous

are

argue

argument

arid

arithmetic

ark

arm

armchair

armed

armies

armour

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around

arrange

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arrival

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arrow

arrows

arse

arson

art

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article

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articulation

artificial

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as

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ascend

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ash-tray

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ask

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assistant

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assume

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astonish

astonishment

astray

astronaut

astronomy

asylum

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atheist

athlete

atlantic

atlas

atmosphere

atom

atomic

attack

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attempt

attempted

attempts

attic

attractive

au pair

auction

audio

august

auntauntie

australia

author

autumn

avarice

avenue

average

avoid

avon

awake

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awful

axe

axminster

aye

azure

b

baa

babies

baby

bach

bachelor

back

backside

backward

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bacon

bacteria

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bad habit

badminton

bag

baggage

bagpipes

bait

bake

baked

baker

bakery

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bald

bale

ball

ballet

balloon

balmy

bamboo shoots

ban

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bandit

bang

bank

banks

banner

bar

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barking

barn

barns

baron

barracks

barrel

barrels

barrister

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bars

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basement

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basin

basketball

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bean

beans

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beat

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beatitude

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beauty

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beds

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bedtime

bee

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bees

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behold

being

belfry

belief

believing

bell

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belt

ben

bench

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bent

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bias bible

bicycle

bicycles

bid

bidder

big

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bikes

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bill

billion

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binding

bird

birds

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black

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blade blades

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bleat

bleed

bleeding

blend

blew

blight

blimey

blinds

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blithe

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blow

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blows

blue

bluebell

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boat

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book

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both

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brace

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broad

broadcast

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broth

brother

brothers

brought

brown

brown ale

brows

bruises

brum

brush

brussel

brussels

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bucket

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bud

buddy

budgerigar

budgie

buffalo

bugle

bugs

build

building

built

bulb

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bull ring

bullet

bulletin bullocks

bulls

bumble-bee

bumpy

bunch

bungalow

bunny

buns

burden

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burglar

burial

burn

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bus

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but

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buttercups

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button

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buy

buying

buzz

bye

cab

cabbage

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cadbury’s

cafe

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cake

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cakes

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camel

camera

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camping

campus

can

canal

canals

canasta

cancer

cancerous

candle

candles

candlestickmaker

cane

cannot

canoe

canon

cans

canterbury

canvas

cap

capablecapital

capone

captain

captive

car

caramel

carbonate

cardboard

cardiac

cards

care

career

careful

caress

cargo

carnations

carpenter

carpentry

carpet

carriage

carried

carry

carry on

cars

cart

cartilage

carton

cartridge

carver

carving

case

cash

casks

cassock

cast

castaway

caster

casterbridge

castle

castles

casualty

cat

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stripes

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strive

stroganoff

stroke

stroll

strolled

strong

struck

structure

strudel

struggle

stub

stubble

stubborn

stud

studies

study

studying

stuff

stump

stupendous

stupid

subject

subtract

subtraction

suburb

succeed

success

succour

succulent

such

suds

sues

suet

suffer

sufferer

suffering

suffice

sufficient

sugar

sugar lumps

sugars

suggestion

suicide

suit

suite

sum

summer

summit

sums

sun

sun-tan

sunday

sunnysunrisesunset superficial

superior

supply

sure

surely

surface

surgeon

surgery

surmise

surprise

suspend

swallow

swear

sweat

sweater

swede

sweep

sweet

sweetness

sweets

sweety

swift

swiftly

swim

swimming

switch

switzerland

swoop

sword

swotting

symbol

symphony

synthetic syringe

syrup

system

table

tables

tablet

tablets

tack

tackled

tacks

tadpole

tag

tail

tailor

tails

take

take place

taken

taker

tale

tales

talk

talked

talking

tall

talon

talons

tame

tamer

taming

tan

tang

tangerine

tankard

tanker

tanks

tanned

tantrum

tap

tape

taps

tar

target

tarmac

tart

tartan

tarts

tarzan

task

taste

taste-bud

tasty

taught

tax

taxi

taylor

tea

tea-cup

teach

teacher

teacup

teak

tear

tears

tease

technology

ted

teen

teeth

telegram

television

tell

teller

temper

temperature

tempest

tempo

ten

tenderness

tennis

tent

tenth

terminally

terrain

terribleterribly

terrified

terrify terror

test

tested

tests

text

text book

textile

thames

than

thank

thank you thankful

thanks

that

thatch

the

theatre

theatres

thee

theft

their

theirs

them

theme

themselves

then

therapy

there

therefore

thermodynamics

thermometer

these

they

thick

thicker

thicket

thief

thieve

thieves

thigh

thin

thine

thing

things

think

thinking

thinner

third

thirst

thirsty

thirty

this

thistle

thither

thong

thorn

thoroughly

those

thou

thought

thoughts

thousand

thread

three

three-legged

thrift

thrill

throat

throb

throbbing

throne

throw

throwing

thrush

thrust

thumb

thumbs

thump

thunder

thus

thyself

tick ticket

tickle

tide

tidier

tidings

tidy

tie

tie-pin

tied

ties

tiger

tigers

tight

tights

tigress

tile

tiles

till

tim

timber

time

timer

times

timid

timing

tin

tinker

tinned

tins

tinsel

tiny

tip

tired

tiredness

tissue

tit

title

to

to be

to-day

toad

toadstool

toadstools

toast

tobacco

tock

today

toe

toenail

toenails

toes

toffee

toga

together

togs

toil

toilet

token

tomato

tomatoes

tomb

tomorrow

ton

tongs

tongue

tonic

too

tool

toot

tooth

toothache

toothbrush

top

topic

topical

topper

tops

torch

torn

tornado

tortoise

torture

tory

tot

total

totally

totter

touch

towel

tower

towers

town

towns

toy

toys

tractor

trade

trafalgar

traffic

traffic light

train

trains

trams

tranquil

tranquillity

transform

transfusion

transition

transmit

transplant

transplants

transport

trap

tray

treacle

treasure

treble

tree

trees

trek

tremble

trench

trews

triad

trial

triangle

tribulation

trick

trickle

tricky

tricolour

tried

tries

trigger

trim

trinity

trio

trip

triplet

triste

triumph

trivial

trodden

trooper

troops

tropic

trot

trotted

trotter

trotting

troubled

trouser

trousers

trove

truck

true

truly

trumpet

trunk

truth

try

tse tung

tub

tube

tuck

tug

tulip

tumble

tumbler

tummy

tumour tune

tuner

tunnel

turban

turkish

turn

turning

turnip

turtle

twain

twelve

twentieth

twenty

twice

twig

twin

twins

twist

twit

two

twos

type

tyrant

tyre

u

udder

ugliness

ugly

ulcer

um

umbilical

umbrella

umpire

unbound

uncertain

uncle

unclean

uncommon

under

underground

underlay

understand

unearth

unemployed

uneven

unexpected

unfair

unfinished

unforgivable

unhappiness

unhappy

unharmed

unhealthy

unicorn

uniform

unimportant

union jack

unit

uniteunited

unity

universe

university

unjust

unkind

unknown

unladen

unlike

unlikely

unload

unlucky

unmarried

unnatural

unpleasant

unpleasantness

unpreparedunready

unreal

unsafe

unsure

until

untrue

untruth

unusual

unwell

up

uphill

upon a time

upper

upright

upwards

urban

us

useless

usually

utensils

vacant

vacation

vacations

vacuum

vale

valiant

valid

valley

value

van

vanilla

vanish

vanity

variety

various

vase

vast

veal

vegetarian

vehicle

vein

velocity vendor

venetian

venice

ventricle

venus

verb

verdict

verse

very

vessel

vessels

vest

vicar

vicarage

vietnam

view

vigour

village

ville

vine

vinegar

vines

vintage

viola

violin

violins

virgin

virile

visage

visible

vision

vista

visual

vital

vitamin c

vivid

vocation

vodka

void

volcano

volume

vote

wag

wage

wages

waggon

wagon

wail

wait

waiting

wake

waking

wales

walk

walked

walking

wall

wallpaper

wand

wander

wane

want

wanted

wants

war

ward

warden

warder

wardrobe

wards

ware

warehouse

warm

warmer

warmth

warning

warrant

wary

was

wash

washer

washing

washing up

washington

wasp

waste

watch

watchman

water

water wings

wave

waves

waving

wavy

wax

way

ways

we

weak

weakness

wealth

wealthy

weapon

wear

weary

weasel

weather

weave

weaver web

wed

wedding

wee

weeding

weeds

week

weeks

weep

weight

weights

weighty

weird

welcome

weld

welfare

well

well mannered

went

wept

were

west

westminster

wet

whale

what

what’s

wheat

wheel

wheel chair

wheels

when

where

whether

while

whilst

whimper

whine

whip

whisk

whiskey

whisky

whisper

whistle

white

white collar

who

whole

wholesale

wholesome

whom

whore

why

wick

wicked

wide

wider

width

wife

wig

wild

wilderness

will

william willing

willingly

willow

willows

wilson

win

wind

wind-screen

window

window pane

windows

windsor

wine

wing

wingswink

winner

winter

wipe

wiper

wire

wireless

wish

wishers

wit

witch

with

with the wind

within

without

wits

wizard

wog

wogs

wolf

woman

womb

women

wonderful

woo

wood

wooden

woods

wool

woolly

word

words

wordsworth

work

worker

working works

world

worlds

worm

worried

worry

worse

worship

worst

worth

would

wound

wounded

woven

wow

wrap

wrath

wreck

wriggle

wriggling

wrist

write

writer

writing

wrong

wrongs

y

yacht

yachts

yank

yard

yards

yarn

yawn

year

yearn

years

yell

yellow

yes

yesterday

yield

yolk

york

you

young

your

yours

yourself

youth

z

zebra

zero

zip

zoozoology

Pajek



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Michael Blum



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Internet Movie Databasehttp://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.


http://www.imdb.com/

http://www.ul.ie/gd2005/contest.htm


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Bipartite coresThe subset of verticesC ⊆ V is a (p, q)-core in a bipartite (2-mode)networkN = (V1, V2;L), V = V1 ∪ V2 iff

a. in the induced subnetworkK = (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 ofV satisfying conditiona.

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 ofC 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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(247,2)-core and (27,22)-core

Royal Rumble

Survivor Series

Dumas, AmyEllison, LillianGarcía, LiliÆnGuenard, NidiaHulette, ElizabethKai, LeilaniKeibler, StacyLaurer, JoanieMartel, SherriMartin, Judy (II)McMahon, StephanieMcMichael, DebraMero, RenaMoore, Carlene (II)Moore, Jacqueline (VI)Moretti, LisaPsaltis, Dawn MarieRobin, Rockin’Runnels, TerriStratus, TrishVachon, AngelleWilson, TorrieWright, JuanitaYoung, Mae (I)Adams, Brian (VI)Ahrndt, JasonAl-Kassi, AdnanAlbano, LouAnderson, ArnAndrØ the GiantAngle, KurtAnoai, ArthurAnoai, MattAnoai, RodneyAnoai, SamAnoai, SolofatuApollo, PhilAustin, Steve (IV)Backlund, BobBarnes, Roger (II)Bass, Ron (II)Batista, DaveBenoit, Chris (I)Bigelow, Scott ’Bam Bam’Bischoff, EricBlackman, Steve (I)Blair, Brian (I)Blanchard, TullyBlood, RichardBloom, Matt (I)Bloom, WayneBresciano, AdolphBrisco, GeraldBrunzell, JimBuchanan, Barry (II)Bundy, King KongCalaway, MarkCandido, ChrisCanterbury, MarkCena, John (I)Centopani, PaulChavis, ChrisClarke, BryanClemont, PierreCoachman, JonathanCoage, AllenCole, Michael (V)Connor, A.C.Constantino, RicoCopeland, Adam (I)Cornette, James E.Darsow, BarryDavis, Danny (III)DeMott, WilliamDiBiase, TedDouglas, ShaneDuggan, Jim (II)Eadie, BillEaton, Mark (II)Enos, Mike (I)Eudy, SidFarris, RoyFatu, EddieFifita, UliuliFinkel, HowardFlair, RicFoley, MickFrazier Jr., NelsonFujiwara, HarryFunaki, ShoGarea, TonyGasparino, PeterGill, DuaneGoldberg, Bill (I)Gray, George (VI)Guerrero Jr., ChavoGuerrero, EddieGunn, Billy (II)Guttierrez, OscarHall, Scott (I)Hardy, Jeff (I)Hardy, MattHarris, Brian (IX)Harris, Don (VII)Harris, Ron (IV)Hart, BretHart, Jimmy (I)Hart, OwenHart, StuHayes, Lord AlfredHeath, David (I)Hebner, DaveHebner, EarlHeenan, BobbyHegstrand, MichaelHelms, ShaneHennig, CurtHenry, Mark (I)Hernandez, RayHeyman, PaulHickenbottom, MichaelHogan, HulkHollie, DanHorn, BobbyHorowitz, BarryHouston, SamHoward, JamieHoward, Robert WilliamHuffman, BookerHughes, DevonHyson, MattJackson, TigerJacobs, GlenJames, Brian (II)Jannetty, MartyJarrett, Jeff (I)Jericho, ChrisJohnson, Ken (X)Jones, Michael (XVI)Keirn, SteveKelly, Kevin (VIII)Killings, RonKnight, Dennis (II)Knobs, BrianLauer, David (II)Laughlin, Tom (IV)Laurinaitis, JoeLawler, Brian (II)Lawler, JerryLayfield, JohnLeinhardt, RodneyLeslie, EdLesnar, BrockLevesque, Paul MichaelLevy, Scott (III)Lockwood, MichaelLoMonaco, MarkLong, TeddyLothario, JoseManna, MichaelMarella, Joseph A.Marella, RobertMartel, RickMartin, Andrew (II)Matthews, Darren (II)McMahon, ShaneMcMahon, VinceMero, MarcMiller, ButchMoody, William (I)Mooney, Sean (I)Morgan, Matt (III)Morley, SeanMorris, Jim (VII)Muraco, DonNash, Kevin (I)Neidhart, JimNord, JohnNorris, Tony (I)Nowinski, ChrisOkerlund, GeneOrton, RandyOttman, FredPage, DallasPalumbo, Chuck (I)Peruzovic, JosipPettengill, ToddPfohl, LawrencePiper, RoddyPlotcheck, MichaelPoffo, LannyPowers, Jim (IV)Prichard, TomRace, HarleyReed, Bruce (II)Reiher, JimReso, JasonRhodes, Dusty (I)Rivera, Juan (II)Roberts, Jake (II)Rock, TheRoss, Jim (III)Rotunda, MikeRougeau Jr., JacquesRougeau, RaymondRude, RickRunnels, DustinRuth, GlenSags, JerrySaturn, PerrySavage, RandyScaggs, CharlesSenerca, PeteShamrock, KenShinzaki, KensukeSimmons, Ron (I)Slaughter, Sgt.Smith, Davey BoySnow, AlSolis, MercidSteiner, Rick (I)Steiner, ScottStorm, LanceSzopinski, TerryTajiri, YoshihiroTanaka, PatTaylor, Scott (IX)Taylor, Terry (IV)Tenta, JohnTraylor, RaymondTunney, JackVailahi, SioneValentine, GregVan Dam, RobVaziri, Kazrowvon Erich, KerryWalker, P.J.Waltman, SeanWare, David (II)Warrington, ChazWarriorWhite, LeonWickens, BrianWight, PaulWilson, Al (III)Wright, Charles (II)Zhukov, Boris (I)

Fully Loaded

Invasion

King of the Ring

No Way Out

Royal Rumble

Summerslam

Survivor Series

Wrestlemania 2000

Wrestlemania X-8

Wrestlemania X-Seven

WWE Armageddon

WWE Judgment Day

WWE No Mercy

WWE No Way Out

WWE SmackDown! Vs. Raw

WWE Unforgiven

WWE Vengeance

WWE Wrestlemania X-8

WWE Wrestlemania XX

WWF Backlash

WWF Insurrextion

WWF Judgment Day

WWF No Mercy

WWF No Way Out

WWF Rebellion

WWF Unforgiven

WWF Vengeance

’Raw Is War’

’Sunday Night Heat’

’WWE Velocity’

’WWF Smackdown!’

Dumas, Amy

Keibler, StacyMcMahon, Stephanie

Stratus, TrishAngle, KurtAnoai, SolofatuAustin, Steve (IV)Benoit, Chris (I)Bloom, Matt (I)Calaway, MarkCole, Michael (V)Copeland, Adam (I)Guerrero, EddieGunn, Billy (II)Hardy, Jeff (I)Hardy, Matt

Hebner, EarlHeyman, PaulHuffman, BookerHughes, Devon

Jacobs, GlenJericho, ChrisLawler, JerryLayfield, JohnLevesque, Paul Michael

LoMonaco, Mark

Martin, Andrew (II)

Matthews, Darren (II)

McMahon, ShaneMcMahon, VinceReso, JasonRock, TheRoss, Jim (III)Senerca, PeteSimmons, Ron (I)

Taylor, Scott (IX)Van Dam, Rob

Wight, Paul



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(2,516)-Hard core

1-800-934-Boob40 Something4F Dating ServiceA Is for AsiaA-List, TheAbove the KneeAdult 45Adventures of Billy Blues, TheAdventures of Tracy Dick: The Case of the Missing StiffAfro Erotica 15After MidnightAjaAl Terego’s Double Anal AlternativesAlice in HollyweirdAll the Best, BarbaraAmazing Tails 1Amazing Tails 2Amazing Tails 3Amazing Tails 4Amazing Tails 5Amber Lynn: The Totally AwesomeAmerican BeautyAmerican PieAnal Adventures of Suzy Super SlutAnal AnarchyAnal AttitudeAnal Climax 3Anal Crack MasterAnal Deep RiderAnal Delights 3Anal EcstasyAnal Encounters 1Anal Encounters 2Anal Hellraiser 2Anal Hounds and BitchesAnal InfernoAnal Innocence 2Anal JusticeAnal LoverAnal MystiqueAnal PrincessAnal QueenAnal Riders 106Anal SecretsAnal Sluts and SweetheartsAnal SweetheartAnal TabooAnal Thunder 2Anal Trashy AssAnalizer, TheAngel PussAngel RisingAngelicaAngels of MercyAnimal in MeAnother Rear ViewAnything GoesArizona GoldArmy Brat 2ArousedArt of DesireAss BackwardsAss Busters Inc.Ass Lovers SpecialAss Openers 1Ass Openers 10Ass Openers 3Ass Openers 4Ass Openers 6Ass Openers 8Asspiring ActressesAussie Exchange GirlsBabe WatchBaby Face 2Bachelor PartyBack Doors, TheBack to NatureBackdoor Bonanza 13Backdoor Bonanza 9Backdoor BridesBackdoor Brides Part 2Backdoor Summer IIBackdoor to Hollywood 11Backfield in MotionBacking in 3Backroad to ParadiseBadBadgirls 2: Strip SearchBall StreetBarbara Dare’s BadBarbii UnleashedBare EleganceBare MarketBattle of the SuperstarsBattle of the TitansBazooka County 3Beat Goes On, TheBeaver and ButtcheeksBeaverly Hills CopBeefeatersBest of Amber LynnBest of Caught from BehindBest of Caught from Behind 2Best of Christy CanyonBest of Diamond Collection 11Best of Double PenetrationBest of Loose EndsBest of Shane 1Best of Talk Dirty, Vol. 1, TheBest of the Dark Bros., TheBest of the Dark Bros., Vol. 2, TheBest of the Vivid Girls #30Best Rears of Our Lives, TheBetween the CheeksBetween the Cheeks 2Between the Cheeks 3Beyond Reality: Mischief in the MakingBeyond ThunderboneBig Mellons 25Big Melons 26Big Melons 31Big Melons 4Big Pink, TheBigger They ComeBillionaire Girls ClubBlack StockingsBlack ThroatBlack Valley GirlsBlack Valley Girls 2Blame It On GingerBlondageBlondes Who BlowBloopersBloopers 2Blowin’ the WhistleBod Squad, TheBody MusicBody of InnocenceBoiling DesiresBoiling PointBoobs Butts and Bloopers 1Booty Ho 3Booty MistressBottom Dweller 5: In Search of...Bottom Dweller Part Deux, TheBottom Line, TheBottoms Up! Series 8Brat ForceBrazilian Connection, TheBreaking ItBride, TheBringing Up the RearBritish Are Coming, TheBun BustersBun for the MoneyBurgundy BluesBurning DesireBustedButt Sisters, TheButtiesButts of SteelCajun HeatCalifornia NativeCanned HeatCaptain Butt’s BeachCar Wash AngelsCat AlleyCaught From Behind 10Caught From Behind 2: The SequelCaught From Behind 4Caught From Behind 6Caught From Behind 9Caught in the ActCaught In the MiddleCenterfoldsCertifiably AnalChameleon, TheCharmed and DangerousCheckmateCheek to Cheek 2: The Newest Cheeks on the BlockCheeks 2: The Bitter EndCheerleader AcademyCherry CheeksClub DV8 2Club GingerClub HeadCome Hither, Cum GingerComing of AgeComing on StrongCountry GirlCovergirlCrazedCream of Cumback PussyCum for Me CarolCumback Pussy 4 Get SomeCumback Pussy 6Cumback Pussy 8

Cumback Pussy 9: Your Ass Is Mine!Cumming of AssCumshot Revue 2Cumshot Revue 3Cumshot Revue 5Curse of the CatwomanDarker Side of Shayla 2, TheDarker Side of Shayla, TheDear BridgetteDebutante, TheDecadenceDeep Cheeks 3Deep CoverDeep In Angel’s AssDeep Inside ArianaDeep Inside BarbiiDeep Inside Brittany O’ConnellDeep Inside Ginger LynnDeep Inside Kelly O’DellDeep Inside MissyDeep Inside Nina HartleyDeep Inside P.J. SparxxDeep Inside Racquel DarrianDeep Inside Samantha StrongDeep Inside Shanna McCulloughDeep Inside TraciDeep Inside Vanessa del RioDeep Inside Victoria ParisDeep ObsessionDeep Throat GirlsDeeper, Harder, FasterDelinquents On Butt RowDeRenzy TapesDesktop DollsDevil in Miss Jones 3: A New Beginning, TheDevil in Miss Jones 4: The Final OutrageDevil in Miss Jones 5: The Inferno, TheDevil Made Her Do It, TheDial A for AnalDial a NurseDial F for FantasyDiamond Collection 61Diamond Collection 64Diamond Collection 67Diamond Collection 79Diamond Collection Double X 10Diamond Collection Double X 74Diamond in the RoughDickman and ThrobbinDirty DreamsDirty LooksDirty MoviesDirty PicturesDirty PrancingDouble PenetrationDouble Penetration 2Double Penetration 4Double Penetration 5Double Penetrations 2Double Penetrations 6Double Penetrations 7Dragon Lady 4: Tales from the Bed 3, TheDream LustDream Machine, TheDreams in the Forbidden ZoneDreams of Candace HartDØjà VuE. TVEarth Girls Are SleazyEasy Way, TheEcstasyEdge of HeatEdge of Heat 2EnchantressEncoreEntertainment L.A. StyleErotic Explosions 2Erotic Newcummers 4Erotic Starlets 12: Crystal LeeEscort to EcstasyEternal Lust 2EternityEvery Woman Has a Fantasy 3Executive SuitesExhibitionist, TheExtreme Sex 1: The ClubExtreme Sex 2: The DungeonExtreme Sex 4: The ExperimentEyewitness NudesFame Is a Whore On Butt RowFantasy Inc.Farmer’s Daughter 2Fast GirlsFemme Vanessa, LaFemmes Ørotiques, LesFilet-o-BreastFilm BuffFine Art of Cunnilingus, TheFire in the HoleFirefoxesFirm OfferFirst Annual XRCO Adult Film AwardsFlashbackFlesh Shopping NetworkFluffer, TheFor the Money 1For Your Thighs OnlyForbidden BodiesForbidden CravingsFrench DollFresh MeatFriends and Lovers: The SequelFull Moon FeverFull NestFull Throttle Girls 1: Boredom Pulled the TriggerFuture VoyeurGames Couples PlayGang Bang CummersGang Bang Face BathGang Bang Face Bath 2Gang Bang Face Bath 3Gang Bang Face Bath 4Gang Bang Girl 12Gang Bang Girl 13Gang Bang Girl 17Gang Bang Girl 20Gang Bang Girl 22Gang Bang Jizz JammersGang Bang Jizz QueensGang Bang NymphetteGang Bang Wild Style 2Gang BangsGang Bangs IIGettin’ ReadyGhost TownGinger Effect, TheGinger in EcstasyGinger Lynn and Co.Ginger Lynn Non-StopGinger Lynn: The MovieGinger On the RocksGinger SnacksGinger Then and NowGinger’s Greatest Boy/Girl HitsGinger’s Private PartyGirl with the Heart-Shaped Tattoo, TheGirls of Cell Block FGirls of ParadiseGirls of the A Team, TheGirls of the Double D 11Girls of the Double D 13Girls of the Double D 9Girls Who Love to SuckGirls’ Club, TheGive Me Your Soul...Glamour Girl 5Glen or Glenda?Gluteus to the MaximusGoddess of LoveGoin’ Down SlowGoing ProGood Girls DoGorgeousGraduation from F.U.Grand OpeningGreatest American BlondeGuilty by SeductionHappy EndingsHard as a RockHard RiderHard to HandleHarlequin AffairHawaii Vice 2Hawaii Vice 5Hawaii Vice 6Hawaii Vice Part III: Beyond the BadgeHead ClinicHead GamesHeads and TailsHerman’s BedHershe Highway 4Hidden ObsessionsHienie’s HeroesHindlick Maneuver, TheHoliday for AngelsHolly Does HollywoodHollywood Exposed 2Hollywood StarletsHoney BunsHooter HeavenHospitality SweetHot In the CityHot Nights at the Blue Note CafeHot ShotsHot Sweet HoneyHot Tight Asses 20Hot Tight Asses 6

Hot Tight Asses 8Hot Tight Asses 9Hot WiredHotel FantasyHotel ParadiseHotel SodomHothouse Rose Part 1Hottest TicketHouse of Blue DreamsHouse of Sleeping BeautiesHouse of Sleeping Beauties 2House of the Rising SunHouse On Chasey LaneHunger, TheI Dream of ChristyI Like to Be WatchedI Touch MyselfI Want It AllImages of DesireImmaculate ErectionIn Search of the Golden BoneInches for KeishaIndecent ExposuresIndecent ItchInfernoInsatiableInteractiveIt’s My BodyJaded LoveJezebelJuicy LucyJuicy Sex ScandalsJust Another Pretty FaceKascha and FriendsKeyhole Video #114: Christy Canyon SpecialKinkyKinky CouplesKinky Vision 2Kiss My AspKiss, TheKSEX 106.9Lady in Red, TheLaid OffLascivious Ladies of Dr. Lipo, TheLast Temptation, TheLatin LustLaying the GhostLegend of Barbi-Q and Little Fawn, TheLet’s Play DoctorLife and Loves of Nikki CharmLike a VirginLittle RomanceLoads of Fun 4Loose EndsLoose Ends IILoose Ends IIILoose MoralsLove BitesLove GhostLove LessonsLovers, TheLovin’ USALucky BreakLuscious Lucy in LoveLust at the TopLust Bug, TheLust CollegeLust in the Fast LaneMagic Shower, TheMake Me Want ItMake My NightMake My Wife, PleaseMan Who Loves Women, TheManbaitManbait 2Marilyn Whips WallstreetMark of ZaraMasqueMatter of Size, AMegasexMidnight Hour, TheMidnight PinkMidslumber’s Night DreamMind ShadowsMind Shadows 2MirageMirage 2MiscreantsModel WifeMoonstrokedMore Than FriendsMotel SexMuff ’n’ JeffMystery of the Golden LotusMystic PiecesNaked and NastyNaked AmbitionNaked Truth, TheNasty LoversNasty Nymphos 3Naughty 90’sNaughty ThoughtsNever Say NeverNew Wave HookersNew Wave Hookers 2New Wave Hookers 4Night DepositNight TalesNight TemptressNightbreedNo Tell MotelNobody’s LookingNorma Jeane Anal LegendNurse FantasiesNurse NancyObsessionOffice GirlsOn Golden BlondeOn the LooseOne Night StandOnly the Best of the 80’sOnly the Very Best On VideoOpen Up TraciOral MajorityOral Majority 10Oral Majority 3Oral Majority 4Oral Majority 7Oral Majority 8Oral Majority 9OrgiesOut of LoveOutlaw, TheOutrageous Orgies 5Oval Office, TheOvertime: Oral HijinxPaler Shade of Blue, AParadise LostParty DollParty Doll A Go-Go 2Party Doll A Go-Go, Part 1Passages 1Passages 2Passenger 69Passionate AngelsPassionate HeiressPeggy SuePerfect FitPerksPerverted 1Perverted PassionsPhoto FleshPhysical IIPiece of HeavenPink Pussycat, ThePlay It Again... Samantha!Playing with a Full DickPlaythingPlaything 2Pleasure Hunt Part IIPleasure PartyPleasure SeekersPoonies, ThePorn on the 4th of JulyPornomania 1Portrait of DorianPossessionsPouring It OnPrecious PeaksPretty As You FeelPrivate Affairs: Vol 2Private Affairs: Vol 6Private TeacherProject: GingerProm GirlsPsychic, ThePussymanPussyman 2: The PrizePussyman Takes HollywoodPussypoppersQueen of Hearts 3Rachel Ryan RRRadio K-KUMRadio-activeRainbirdRainwoman 4Rainwoman 6Rambone the DestroyerRaptureRaunch 6Raunch VRear BustersRear Ended RoommatesRed Vibe Diaries 2: Dark DesiresReincarnation of Don JuanReturn to Sex 5th AvenueRibald Tales of Canterbury

Rise of the Roman Empress 2Rising, TheRocky Porno Video Show, TheRoll-x GirlsRoyals: Ginger LynnRuthless AffairsSabotageSatin SeductionSatyrSavanah UnleasedScarlet Bride, TheScarlet Woman, TheScreaming RageSecret Fantasies 3Secret Fantasies 4Secret Life of Nina Hartley, TheSecret of Her SuckcessSeducers, TheSeeing RedSensual ExposureSex 3: After SevenSex Academy 2: The Art of Talking DirtySex AppraisalsSex BeatSex BustersSex Fifth AvenueSex ManiacsSex PlaysSex ShootSex Sluts in the SlammerSex StoriesSex ToysSexperteaseSextectivesSexual FantasiesSexy and 18Sexy Secrets N° 1Shane’s WorldShaved PinkShayla’s GangSheila’s Deep DesiresShot From BehindSimply BlueSimply KiaSindy Does Anal AgainSister DearestSkin GamesSky FoxesSlave to LoveSleeping with EverybodySlightly UsedSlip Into Ginger and AmberSlip of the TongueSloppy SecondsSlumber PartySmart Ass Returns, TheSmart Ass, TheSnatchedSodomania 13Sodomania 18Sodomania: Slop Shots 1Sodomania: The Baddest of the BestSophisticated LadySorority Pink 2: The InitiationSpectacular OrgasmsSpellboundSpermbustersSpiesSplash ShotsSplendor in the AssStar 85Star Cuts 37: Buffy DavisStar Cuts 39: Trinity LorenStar Cuts 4: Ginger LynnStar, TheStarrStarting OverStiff CompetitionStiff Competition 2Strange Sex in Strange PlacesStreet WalkersSuburban Swingers 2Sugarpussy JeansSummer BreakSunny After DarkSuper GroupieSuper TrampSuperstars of Sex: Racquel DarrianSurfside SexSwedish Erotica 54Swedish Erotica 56Swedish Erotica 74TailgunnersTailhouse RockTailiensTailiens 2Tails of PerversityTails of Perversity 2Tails of Perversity 3Tailspin 1Take MeTake My Wife, Please!Takin’ It to the LimitTalk Dirty to Me 9Talk Dirty to Me, Part IIITarnished KnightTaste of ArielTaste of Tawnee, ATaste of Victoria ParisTawnee Be GoodTease, TheTeasersTemptation EyesTerminal Case of LoveTerms of EndowmentTexas CrudeThis Is Your Sex LifeThose Lynn GirlsThree by ThreeThree-way LustThrill Street BluesTight Ends in MotionTight SqueezeTip of the TongueTits AhoyTo the RearTomboyToo Good to Be TrueTop 25 Adult Stars of All Time, TheTop It OffTorrid Without a CauseTouch MeTouch of MischiefToys 4 Us 2Tracie LordsTrashy LadyTrue Legends of Adult Cinema: The Erotic 80’sTrue Legends of Adult Cinema: The Modern Video EraTurnaboutUnbelievable OrgiesUnchain My HeartUnforgivableUp ’n ComingUp Your Ass 5Vagina TownVegas: Snake EyesVictoria and CompanyVideo TrampVirgin DreamsVisions of DesireVoodoo Lust: The PossessionVoyeur’s Favorite Blowjobs and Anals 8, TheVoyeur, TheWacky World of X-Rated BloopersWay They Were, TheWe Love to TeaseWest Coast GirlsWet Dreams Reel FantasiesWhat Gets Me Hot!Where the Sun Never ShinesWhispered LiesWhite BunbustersWho Killed Holly Hollywood?Whore HouseWhore of the WorldsWhore, TheWicked As She SeemsWicked OneWicked Ways #2Wicked WhispersWild and Wicked 3Wild Bananas On Butt RowWild BuckWild in the WildernessWild WeekendWild Women 11: Tanya FoxxWild Women 32: Summer RoseWild Women 61: Rachel RyanWilling WomenWings of PassionWire DesireWitching Hour, TheWith Love from GingerWith Love from SusanWithin and Without YouWoman in Pink, TheWPINK-TV 3Wrapped UpX DreamsX-rated BlondesX-rated Bloopers and OuttakesXTV 1XTV 2Year of the Sex Dragon, TheYoung and NaughtyYoung Girls in Tight JeansYoung Nurses In Lust

Byron, Tom

North, Peter (I)

Wallice, Marc



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4-rings and analysis of 2-mode networks

In bipartite (2-mode) network there are no 3-rings. The densest substruc-

tures are complete bipartite subgraphsKp,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-ringsThere are 4 types of directed 4-rings:

cyclic transitive genealogical diamond

In the case of transitive ringsPajek provides a special weight counting on

how many transitive rings the arc is ashortcut.



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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 23 1978 21 18 39 3 61 14 1639 22 15 40 2 64 15 968 23 9 42 2 67 16 666 24 13 43 3 70 17 394 25 12 45 3 73 18 257 26 6 46 4 76 19 209 27 6 47 5 82 1

10 148 28 5 48 1 86 111 118 29 6 49 2 106 112 87 30 3 50 2 122 113 55 31 6 51 1 135 114 62 32 5 52 2 144 115 46 33 3 53 1 163 116 39 34 1 54 2 269 117 27 35 5 55 1 301 118 28 36 4 57 1 332 219 29 37 7 58 1 673 1

--------------------------------------------------------



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Example: Islands for w4 / Charlie Brown and Adult

Be My Valentine, Charlie Brown

Boy Named Charlie Brown

Charlie Brown Celebration

Charlie Brown Christmas

Charlie Brown Thanksgiving

Charlie Brown’s All Stars!

He’s Your Dog, Charlie Brown

Is This Goodbye, Charlie Brown?

It’s a Mystery, Charlie Brown

It’s an Adventure, Charlie Brown

It’s Flashbeagle, Charlie Brown

It’s Magic, Charlie Brown

It’s the Easter Beagle, Charlie Brown

It’s the Great Pumpkin, Charlie Brown

Life Is a Circus, Charlie Brown

Making of ’A Charlie Brown Christmas’

Play It Again, Charlie Brown

Race for Your Life, Charlie Brown

Snoopy Come Home

There’s No Time for Love, Charlie Brown

You Don’t Look 40, Charlie Brown

You’re a Good Sport, Charlie Brown

You’re In Love, Charlie Brown

You’re Not Elected, Charlie Brown

Charlie Brown and Snoopy ShowAltieri, Ann

Dryer, Sally

Mendelson, Karen

Momberger, Hilary

Stratford, Tracy

Brando, Kevin

Hauer, Brent

Kesten, Brad

Melendez, Bill

Ornstein, Geoffrey

Reilly, Earl ’Rocky’

Robbins, Peter (I)

Schoenberg, Jeremy

Shea, Christopher (I)

Shea, Stephen

Pajek

Boy, T.T.

Byron, Tom

Davis, Mark (V)

Dough, Jon

Drake, Steve (I)

Horner, Mike

Jeremy, Ron

Michaels, Sean

Morgan, Jonathan (I)

North, Peter (I)

Sanders, Alex (I)

Savage, Herschel

Silvera, Joey

Thomas, Paul (I)

Voyeur, Vince

Wallice, Marc

West, Randy (I)

Pajek



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Example: Island for w4 / Polizeiruf 110 and Starkes Team

Polizeiruf 110 - Angst um Tessa Bülow

Polizeiruf 110 - Der Pferdemörder

Polizeiruf 110 - Der Spieler

Polizeiruf 110 - Doktorspiele

Polizeiruf 110 - Ein Bild von einem Mörder

Polizeiruf 110 - Heißkalte Liebe

Polizeiruf 110 - Henkersmahlzeit

Polizeiruf 110 - Jugendwahn

Polizeiruf 110 - Kopf in der Schlinge

Polizeiruf 110 - Kurschatten

Polizeiruf 110 - Mordsfreunde

Polizeiruf 110 - Rosentod

Polizeiruf 110 - Todsicher

Polizeiruf 110 - Tote erben nicht

Polizeiruf 110 - Zerstörte Träume

Starkes Team - Auge um Auge, Ein

Starkes Team - Bankraub, Ein

Starkes Team - Blutsbande, Ein

Starkes Team - Braunauge, Ein

Starkes Team - Das Bombenspiel, Ein

Starkes Team - Das große Schweigen, Ein

Starkes Team - Der letzte Kampf, Ein

Starkes Team - Der Mann, den ich hasse, Ein

Starkes Team - Der schöne Tod, Ein

Starkes Team - Der Todfeind, Ein

Starkes Team - Der Verdacht, Ein

Starkes Team - Die Natter, Ein

Starkes Team - Eins zu Eins, Ein

Starkes Team - Erbarmungslos, Ein

Starkes Team - Im Visier des Mörders, Ein

Starkes Team - Kinderträume, Ein

Starkes Team - Kleine Fische, große Fische, Ein

Starkes Team - Kollege Mörder, Ein

Starkes Team - Lug und Trug, Ein

Starkes Team - Mordlust, Ein

Starkes Team - Mörderisches Wiedersehen, Ein

Starkes Team - Roter Schnee, Ein

Starkes Team - Sicherheitsstufe 1, Ein

Starkes Team - Träume und Lügen, Ein

Starkes Team - Tödliche Rache, Ein

Starkes Team - Verraten und verkauft, Ein

Starkes Team, Ein

’Affäre Semmeling, Die’

Maranow, Maja

Bademsoy, Tayfun

Lansink, Leonard

Lerche, Arnfried

Martens, Florian

Schwarz, Jaecki

Winkler, Wolfgang

Pajek



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New drawing algorithms from GD’05

Tim Dwyer, Yehuda Koren, and Kim Marriott:Stress Majorization with

Orthogonal Ordering Constraints.

The1138busgraph (1138 vertices, 1458 arcs).

we compute the 2-D layout that minimizes the stress, while the y-coordinates of thenodes must obey their hierarchical ordering.

It was shown that this method produces drawings with much more uniform edgelengths making connectivity in large graphs more visible than in drawings produced bystandard hierarchical graph drawing techniques.

We reproduce some example graphs drawn in this style and compare performance ofour solve QPOC algorithm with that of the solver previously used. Figure 3 illustratesthe concept with a small directed graph containing a cycle. Note that since all nodes inthe cycle are in the same hierarchical level they are drawn within the same band. Figure4 shows a much larger example from the matrix market collection [2].

Fig. 3. A directed graph arranged using orthogonal ordering constraints in just the vertical di-mension to preserve layering. The color bars on the left side indicate the layer-bands and the fainthorizontal lines indicate the boundaries between these layers.

Fig. 4. The 1138bus graph (1138 nodes, 1458 edges) from the Matrix market collection[2], dis-played as a directed graph.

10Workshop on Complex objects visualization, November 16-19, 2005, Koper ▲ ▲ ❙ ▲ ● ▲ ❙ ▲▲ ☛ ✖

http://www.csse.monash.edu.au/~tdwyer/LayoutWithOrthConstraints.pdf

http://www.csse.monash.edu.au/~tdwyer/LayoutWithOrthConstraints.pdf


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New drawing algorithms from GD’05

(a) Fruchterman-Reingold model (b) Node-repulsion LinLog model

(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.

Andreas Noack:

Energy-Based Clustering of Graphs

with Nonuniform Degrees.

American airports.


http://www-sst.informatik.tu-cottbus.de/~an/Publications/GD2005.pdf

http://www-sst.informatik.tu-cottbus.de/~an/Publications/GD2005.pdf


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Dense networksDense(r) networks with more than 15 vertices usually can’t be clearly

presented. For such networks a more appropriate display is usingma-

trix representation. Properly reordering vertices can revealpatternsin

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 papers1, 2).

There are different approaches how to determine good orderings: weak,

strong components; topological sort in acyclic networks; special heuris-

tics (Reverse Cuthill-McKee); seriation and clumping (Murtagh, 1985);

clustering; blockmodeling.


http://vlado.fmf.uni-lj.si/pub/networks/doc/part/CorePart.pdf

http://infovis.cs.vt.edu/cs5764/papers/abello.pdf

http://www.csit.fsu.edu/~burkardt/f_src/rcm/rcm.html


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Snyder & Kick’s World trade network / n = 118, m = 514

Pajek - shadow 0.00,1.00 Sep- 5-1998World trade - alphabetic order

afg alb alg arg aus aut bel bol bra brm bul bur cam can car cha chd chi col con cos cub cyp cze dah den dom ecu ege egy els eth fin fra gab gha gre gua gui hai hon hun ice ind ins ire irn irq isr ita ivo jam jap jor ken kmr kod kor kuw lao leb lib liy lux maa mat mex mla mli mon mor nau nep net nic nig nir nor nze pak pan par per phi pol por rum rwa saf sau sen sie som spa sri sud swe swi syr tai tha tog tri tun tur uga uki upv uru usa usr ven vnd vnr wge yem yug zai

afg

a

lb

alg

a

rg

aus

a

ut

bel

b

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bra

b

rm

bul

b

ur

cam

c

an

car

c

ha

chd

c

hi

col

c

on

cos

c

ub

cyp

c

ze

dah

d

en

dom

e

cu

ege

e

gy

els

e

th

fin

fra

gab

g

ha

gre

g

ua

gui

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hon

h

un

ice

ind

ins

ire

irn

irq

isr

ita

ivo

jam

ja

p

jo

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k

en

km

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k

od

kor

k

uw

lao

leb

lib

liy

lux

maa

m

at

mex

m

la

mli

mon

m

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nau

n

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net

n

ic

nig

n

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n

or

nze

p

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pan

p

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per

p

hi

pol

p

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rum

r

wa

saf

s

au

sen

s

ie

som

s

pa

sri

sud

s

we

sw

i

s

yr

tai

tha

tog

tri

tun

tur

uga

u

ki

upv

u

ru

usa

u

sr

ven

v

nd

vnr

w

ge

yem

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zai

Pajek - shadow 0.00,1.00 Sep- 5-1998World Trade (Snyder and Kick, 1979) - cores

uki net bel lux fra ita den jap usa can bra arg ire swi spa por wge ege pol aus hun cze yug gre bul rum usr fin swe nor irn tur irq egy leb cha ind pak aut cub mex uru nig ken saf mor sud syr isr sau kuw sri tha mla gua hon els nic cos pan col ven ecu per chi tai kor vnr phi ins nze mli sen nir ivo upv gha cam gab maa alg hai dom jam tri bol par mat alb cyp ice dah nau gui lib sie tog car chd con zai uga bur rwa som eth tun liy jor yem afg mon kod brm nep kmr lao vnd

uki

n

et

bel

lu

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fr

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it

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en

jap

usa

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bra

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ind

pak

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ut

cub

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uru

n

ig

ken

s

af

mor

s

ud

syr

is

r

s

au

kuw

s

ri

th

a

m

la

gua

h

on

els

n

ic

cos

p

an

col

v

en

ecu

p

er

chi

ta

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k

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vnr

p

hi

ins

nze

m

li

s

en

nir

ivo

upv

g

ha

cam

g

ab

maa

a

lg

hai

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om

jam

tr

i

b

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par

m

at

alb

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yp

ice

dah

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au

gui

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tog

car

c

hd

con

z

ai

uga

b

ur

rw

a

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li

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afg

m

on

kod

b

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nep

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lao

vnd

Alphabetic order of countries (left) and rearrangement (right)



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Contracted clusters – international tradePajek - shadow [0.00,1.00]

usacancubhaidomjamtrimexguahonelsniccospancolvenecuperbrabolparchiarguruukiirenetbelluxfraswispaporwgeegepolaushunczeitamatalbyuggrecypbulrumusrfinswenordenicemlisendahnaunirivoguiupvlibsieghatogcamniggabcarchdconzaiugakenburrwasomethsafmaamoralgtunliysudegyirnturirqsyrlebjorisrsauyemkuwafgchamontaikodkorjapindpakbrmsrinepthakmrlaovndvnrmlaphiinsautnze

usa

can

cub

hai

dom

jam

tri

mex

gua

hon

els

nic

cos

pan

col

ven

ecu

per

bra

bol

par

chi

arg

uru

uki

ire net

bel

lux

fra

swi

spa

por

wge

ege

pol

aus

hun

cze

ita mat

alb

yug

gre

cyp

bul

rum

usr

fin swe

nor

den

ice

mli

sen

dah

nau

nir

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gui

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lib sie

gha

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cam

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gab

car

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uga

ken

bur

rwa

som

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liy sud

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vnd

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N. America

L. America

S. America

EuropeAfrica

Asia

Australia

Snyder and Kick’s international trade. Matrix display of dense networks.

w(Ci, Cj) =n(Ci, Cj)

n(Ci) · n(Cj)


http://vlado.fmf.uni-lj.si/pub/networks/data/mix/SKtrade.zip


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Generalized Blockmodeling

A blockmodelconsists of structures obtained by identifying all units fromthe same cluster of the clusteringC. For an exact definition of a blockmodelwe have to be precise also about which blocks produce an arc in thereduced

graphand which do not, and of whattype.

Book: P. Doreian, V. Batagelj, A. Ferligoj:Generalized Blockmodeling, CUP, 2004.Amazon.


http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=0521840856

http://www.amazon.com/exec/obidos/tg/detail/-/0521840856


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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 networksarXiv:cs 0504107

Graphical representation should be simplified into icon omitting details.


http://arXiv.org


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Dynamic/temporal networksThere 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

Pictures in SVG:66 days. (SVG viwer)

Steve Corman with collab-

orators from Arizona State

University transformed, us-

ing his Centering Resonance

Analysis (CRA), daily Reuters

news (66 days) about Sep-

tember 11th into a temporal

network of words coappear-

ance. This network was a

challange network forViszards

2002 session.

Every year (from 2002) we have at theSunbelt conferencea Viszards

session presenting solutions of Viszards group to a visualizations of

selected network or type of networks.


http://vlado.fmf.uni-lj.si/pub/networks/doc/Terror/deg50/deg50001.htm

http://www.adobe.com/svg/viewer/install/

http://locks.asu.edu/terror/

http://www.insna.org/


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They Rule


http://www.theyrule.net/


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MusicPlasma

Musicvine


http://www.musicplasma.com

http://www.mp3.com/musicvine/index.php


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Networks from the Internet

KartOO network

Internet Mapping Project.

Links among WWW pages.

KartOO, TouchGraph.

Derived from archives of E-

mail, blogs, . . . , server’s logs.

Cybergeography, CAIDA.


http://www.kartoo.com/

http://research.lumeta.com/ches/map/index.html

http://www.kartoo.com/

http://www.touchgraph.com/TGGoogleBrowser.html

http://www.cybergeography.org/

http://www.caida.org/


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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 net-

works)



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Lombardi’s networks

Mark Lombardi(1951-2000)

transformed business

relations into art.


http://www.pierogi2000.com/flatfile/lombardi.html


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Context



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Barcelona / Peter Davies – Joseph Beuys: Text painting


Visualization of large networks and Pajek - Vladimir Batagelj

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