Analysis of Large Networks with Pajek

Transcription

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Analysis of
Large Networks
with Pajek
Vladimir Batagelj
University of Ljubljana
Photo: V. Batagelj
Workshop
Sunbelt XXVIII, St. Pete Beach, Florida, USA, 22-27 January, 2008
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version: January 21, 2008 / 02 : 39
V. Batagelj: Workshop: Analysis of Large Networks with Pajek
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Outline
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Networks . . . . . . . . . . . . . .
Large Networks . . . . . . . . . .
Approaches to large networks . . .
Decompositions . . . . . . . . . .
Connectivity . . . . . . . . . . . .
Cuts . . . . . . . . . . . . . . . .
Citation weights . . . . . . . . . .
Cores and generalized cores . . . .
k-rings . . . . . . . . . . . . . . .
Islands . . . . . . . . . . . . . . .
Bipartite cores . . . . . . . . . . .
Directed 4-rings . . . . . . . . . .
Pattern searching . . . . . . . . . .
Multiplication of networks . . . . .
Networks from data tables . . . . .
EU projects on simulation . . . . .
Clustering with relational constraints
What else? . . . . . . . . . . . . .
References . . . . . . . . . . . . .
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Networks
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 links. n = card(V),
m = card(L)
• P vertex value functions / properties: p : V → A
• W line value functions / weights: w : L → B
In November 1996 we started the development of Pajek – a program, for
analysis and visualization of large networks. The latest version of Pajek
is freely available, for noncommercial use, at its home page:
http://vlado.fmf.uni-lj.si/pub/networks/pajek/
de Nooy, W., Mrvar, A. and Batagelj V.: Exploratory Social Network
Analysis with Pajek, CUP,2005.
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Large Networks
Networks are used in social sciences from thirties (Moreno). Most networks
collected till 1990 are small (some tens of vertices). Development of IT
in nineties enabled collection of large networks – several thousands or
millions of vertices. Large networks are usually sparse m << n2 .
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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Approaches to large networks
In analysis of a large network (several thousands or millions of vertices,
the network can be stored in computer memory) we can’t display it in its
totality; also there are only few algorithms available.
To analyze a large network we can use statistical approach or we can
identify smaller (sub) networks that can be analyzed further using more
sophisticated methods.
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Degrees
degree of vertex v, deg(v) = number
of lines with v as end-vertex;
indegree of vertex v, indeg(v) =
number of lines with v as terminal
vertex (end-vertex is both initial and
terminal);
outdegree of vertex v, outdeg(v) =
number of lines with v as initial vertex.
n = 12, m = 23, indeg(e) = 3, outdeg(e) = 5, deg(e) = 6
X
X
X
indeg(v) =
outdeg(v) = |A| + 2|E|,
deg(v) = 2|L| − |E0 |
v∈V
v∈V
v∈V
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Pajek and R
Pajek 0.89 (and later) supports the use of external programs (menu
Tools). It provides a special support for statistical program R.
In Pajek we determine the degrees of vertices and submit them to R
info/network/general
Net/Partitions/Degree/All
Partition/Make Vector
Tools/Program R/Send to R/Current Vector
In R we determine their distribution and plot it
summary(v2)
t <- tabulate(v2)
c <- t[t>0]
i <- (1:length(t))[t>0]
plot(i,c,log=’xy’,main=’degree distribution’,
xlab=’deg’,ylab=’freq’)
Attention! The vertices of degree 0 are not considered by tabulate. Use
t <- tabulate(v2+1)
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Erdős and Rényi’s random graphs
Erdős and Rényi defined a random graph
as follows: every possible line is included
in a graph with a given probabilty p.
In Pajek’s
Net/Random Network/Erdos-Renyi
instead of probability p a more intuitive
average degree is used
1X
deg =
deg(v)
n
v∈V
It holds p =
m
mmax
and, for simple graphs, also deg =
2m
n .
Random graph in picture has 100 vertices and average degree 3.
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Degree distribution
●●
US Patents degree distribution
1 e+06
Random graph degree distribution, n=100000, degav=30
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Real-life networks are usually not random in the Erdős/Rényi sense. The
analysis of their distributions gave a new view about their structure – Watts
(Small worlds), Barabási (nd/networks, Linked).
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Decompositions
global
The main goals in the design of Pajek are:
hierarchy
local
reduction
inter-links
cut-out
context
• 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.) 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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Connectivity
Vertex u is reachable from vertex v iff
there exists a walk with initial vertex v
and terminal vertex u.
Vertex v is weakly connected with vertex u iff there exists a semiwalk with v
and u as its end-vertices.
Vertex v is strongly connected with vertex u iff they are mutually reachable.
Weak and strong connectivity are equivalence relations.
Equivalence classes induce weak/strong components.
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Weak components
Reordering the vertices of network
such that the vertices from the same
class of weak partition are put together we get a matrix representation consisting of diagonal blocks –
weak components.
Most problems can be solved separately on each component and afterward these solutions combined into
final solution.
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Reduction (condensation)
If we shrink every strong component of a given graph into a vertex, delete
all loops and identify parallel arcs the obtained reduced graph is acyclic.
For every acyclic graph an ordering / level function i : V → N exists s.t.
(u, v) ∈ A ⇒ i(u) < i(v).
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Reduction – Example
Net / Components / Strong [1]
Operations / Shrink Network / Partition [1][0]
Net / Transform / Remove / Loops [yes]
Net / Partitions / Depth / Acyclic
Partition / Make Permutation
Permutation / Inverse
select partition [Strong Components]
Operations / Functional Composition / Partition*Permutation
Partition / Make Permutation
select [original network]
File / Network / Export Matrix to EPS / Using Permutation
Pajek - shadow [0.00,1.00]
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Cuts
The standard approach to find interesting groups inside a network was based
on properties/weights – they can be measured or computed from network
structure (for example Kleinberg’s hubs and authorities).
The vertex-cut of a network N = (V, L, p), p : V → R, at selected level t
is a subnetwork N(t) = (V 0 , L(V 0 ), p), determined by the set
V 0 = {v ∈ V : p(v) ≥ t}
and L(V 0 ) is the set of lines from L that have both endpoints in V 0 .
The line-cut of a network N = (V, L, w), w : V → R, at selected level t is
a subnetwork N(t) = (V(L0 ), L0 , w), determined by the set
L0 = {e ∈ L : w(e) ≥ t}
and V(L0 ) is the set of all endpoints of the lines from L0 .
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Vertex-cut: Krebs Internet Industries, core=6
Lucent
CommerceOne
UPS
SAP
CIBER
Motorola
Ariba
Yahoo!
EMC
FoundryNetworks
IBM
Siebel
HP
Peoplesoft
Oracle
EDS
Sun
WebMethods
divine
E.piphany
BMCSoftware
Cisco
Novell Intel
ExodusComm
KPNQwest
AT&T
Vignette
CacheFlow
Loudcloud
Compaq
RealNetworks
RedHat
Dell
Akamai
MSFT
Inktomi
AOL
Pajek
Each vertex represents a company that competes in the Internet industry, 1998 do 2001. n = 219, m = 631. red – content, blue – infrastructure,
green – commerce. Two companies are linked with an edge if they have announced a joint venture, strategic alliance or other partnership.
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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
MSFT
HP
Sun
Dell
Akamai
IBM
Cisco
Intel
KPNQwest
Ariba
Oracle
Motorola
CIBER
E.piphany
Pajek
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Cuts / Pajek commands
Vertex-cut:
File/Pajek Project File/Read [Krebs.paj]
Net/Partitions/Core/All
Draw/Draw-Partition-Vector
Layout/Energy/Kamada-Kawai
Operations/Extract from Network/Partition [6]
[select Types ... as First partition]
[select All core ... as Second partition]
Partitions/Extract Second from First [6]
Draw/Draw-Partition
Line-cut:
[select Krebs ... network]
Net/Count/3-Rings/Undirected
Info/Network/Line Values
Net/Transform/Remove/Lines with Values/lower than [5]
Net/Partitions/Degree/All
Operations/Extract from Network/Partition [1-*]
[select Types ... as First partition]
[select All Degree ... as Second partition]
Partitions/Extract Second from First [1-*]
Draw/Draw-Partition
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Simple analysis using cuts
We look at the components of N(t).
Their number and sizes depend on t. Usually there are many small
components. Often we consider only components of size at least k and
not exceeding K. The components of size smaller than k are discarded as
’noninteresting’; and the components of size larger than K are cut again at
some higher level.
The values of thresholds t, k and K are determined by inspecting the
distribution of vertex/arc-values and the distribution of component sizes
and considering additional knowledge on the nature of network or goals of
analysis.
We developed some new and efficiently computable properties/weights.
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Citation weights
POGGIO-T-1975-V19-P201
KOHONEN-T-1976-V21-P85
ANDERSON-JA-1977-V84-P413
PFAFFELHUBER-E-1975-V18-P217
COOPER-LN-1979-V33-P9
WOOD-CC-1978-V85-P582
AMARI-SI-1977-V26-P175
PALM-G-1980-V36-P19
BIENENSTOCK-EL-1982-V2-P32
SUTTON-RS-1981-V88-P135
HOPFIELD-JJ-1982-V79-P2554
ANDERSON-JA-1983-V13-P799
KNAPP-AG-1984-V10-P616
MCCLELLAND-JL-1985-V114-P159
CARPENTER-GA-1987-V37-P54
GROSSBERG-S-1987-V11-P23
GROSSBERG-S-1988-V1-P17
SEJNOWSKI-TJ-1988-V241-P1299
HECHTNIELSEN-R-1987-V26-P1892
BROWN-TH-1988-V242-P724
BROWN-TH-1990-V13-P475
TREVES-A-1991-V2-P371
HASSELMO-ME-1994-V7-P13
BARKAI-E-1994-V72-P659
AMARI-S-1980-V42-P339
The citation network analysis
started in 1964 with the paper of
Garfield et al. In 1989 Hummon
and Doreian proposed three
indices – weights of arcs that are
proportional to the number of
different source-sink paths passing
through the arc. We developed
algorithms to efficiently compute
these indices.
Main subnetwork (arc cut at level
0.007) of the SOM (selforganizing
maps) citation network (4470 vertices, 12731 arcs).
See paper.
GLUCK-MA-1997-V48-P481
ASHBY-FG-1999-V6-P363
Pajek
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Cores and generalized cores
E.Arkin
J.Mitchell
I.Tollis
M.Bern
A.Garg
D.Eppstein
L.Vismara
G.diBattista
R.Tamassia
M.Goodrich
G.Liotta
D.Dobkin
S.Suri
J.O’Rourke
J.Vitter
J.Hershberger
B.Chazelle
R.Seidel B.Aronov L.Guibas
H.Edelsbrunner
M.Sharir
F.Preparata
J.Snoeyink
P.Agarwal
R.Pollack
D.Halperin
J.Pach
P.Gupta
M.Smid
E.Welzl
M.Overmars
P.Bose
M.vanKreveld
J.Boissonnat
O.Devillers
J.Matousek
C.Yap
J.Majhi
M.Yvinec
M.deBerg
O.Schwarzkopf
R.Janardan
J.Schwerdt
G.Toussaint
M.Teillaud
J.Urrutia
C.Icking
J.Czyzowicz
The notion of core was introduced by Seidman in 1983.
Vertices belonging to a k-core
have to be linked to at least k
other vertices of the core. A
very efficient algorithm exists
for determining cores.
The notion of core can be extended to other vertex functions and for several of them
the corresponding cores can be
efficiently determined.
R.Klein
Figure presents the pS -core at level 46 of the collaboration network (7343 vertices, 11898
edges, edge weight counts the number of common works) in the field of computational
geometry.
See paper.
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Cores and generalized cores / Core 10
C.Zelle
H.A.El-Gindy
M.E.Houle
M.L.Demaine
J.Czyzowicz
V.Sacristan
K.R.Romanik
D.H.Rappaport
F.Hurtado
H.Meijer
D.Bremner
G.Liotta
A.Lubiw
T.C.Shermer
W.J.Lenhart
S.S.Skiena
I.Streinu
H.Everett
B.Zhu
D.M.Avis
T.C.Biedl
M.J.vanKreveld
J.Urrutia
S.M.Robbins
M.Yvinec
J-M.Robert
S.Lazard
M.Teillaud
S.P.Fekete
P.Belleville
G.T.Toussaint
P.K.Bose
J.S.B.Mitchell
S.H.Whitesides
O.Devillers
Te.Asano
M.T.deBerg
E.D.Demaine
D.L.Souvaine
T.Roos
M.H.Overmars
J-R.Sack H.Alt
G.Rote
J.O’Rourke
R.Seidel
J-D.Boissonnat
J.Erickson
K.Mehlhorn
R.Wenger
R.Pollack
S.Suri
M.Sharir
O.Schwarzkopf
J.S.Snoeyink
D.M.Mount
E.M.Arkin
G.T.Wilfong
D.Halperin
B.Chazelle
J.E.Hershberger
O.Aichholzer
I.G.Tollis
N.Katoh
H.Imai
M.T.Goodrich
J.S.Vitter
S-W.Cheng
N.M.Amato
D.Z.Chen
R.Tamassia R.L.S.Drysdale
Q.Huang
F.P.Preparata
L.J.Guibas
K.Kedem
S.J.Fortune
J.Matousek
J.C.Clements
H.S.Sawhney
D.G.Kirkpatrick
C-K.Yap
D.Eppstein
B.Aronov
J.Ashley
S.A.Mitchell
E.Trimble
D.White
D.P.Dobkin
H.Edelsbrunner
F.Aurenhammer D.T.Lee
M.W.Bern
D.Steele
W.J.Bohnhoff
A.Aggarwal
L.P.Chew
R.R.Lober
S.R.Kosaraju
G.D.Sjaardema
T.K.Dey N.Amenta
P.Yanker
D.Petkovic
G.Lerman
J.Hass
L.Lopez-Buriek
T.J.Wilson
P.Plassmann
J.R.Hipp
C.K.Johnson
E.Sedgwick
M.Flickner M.Gorkani
J.Pach
W.R.Oakes
S.Parker
T.J.Tautges
P.K.Agarwal
E.Welzl
J.Harer
T.L.Edwards
S.E.Benzley
T.D.Blacker M.Whitely
D.Letscher
D.Zorin
A.Hicks
C.Grimm
J.Weeks
W.Niblack J.Hafner
B.Dom
s
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%
* 6
21
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$
Cores and generalized cores / Pajek commands
File/Network/Read [Geom.net]
Net/Partitions/Core/All
Info/Partition
Operations/Extract from Network/Partition [13-*]
Draw/Draw-Partition
Options/Values of lines/Similarities
Draw
Options/Values of lines/Forget
[select Geom.net]
Net/Vector/PCore/Sum/All
Info/Vector
Vector/Make Partition/by Intervals/Selected Thresholds [45]
Info/Partition
Draw
Options/Values of lines/Similarities
Layout/Energy/Fruchterman-Reingold
s
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y
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* 6
22
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$
k-rings
A k-ring is a simple closed chain of length k. Using k-rings we can define
a weight of edges as
s
s
s
s
s
s
wk (e) = # of different k-rings containing the edge e ∈ E
Since for a complete graph Kr , r ≥ k ≥ 3 we have
wk (Kr ) = (r − 2)!/(r − k)!, the edges belonging to
cliques have large weights. Therefore these weights
can be used to identify the dense parts of a network.
For example: all r-cliques of a network belong to r−2edge cut for the weight w3 .
We can assign to a given graph a triangular network in
which every line of the original graph gets as its weight
the number of triangles that contain it. The triangular
weights provide us, combined with islands, with a very
efficient way to identify dense parts of a graph.
&
%
y l y
* 6
23
'
$
Triangular connectivity
Related to triangular network is the notion of triangular connectivity
that can be used to operationalize the notion of strong ties.
These notions can be generalized to short cycle connectivity (see paper).
s
s
l y
s
y
s
s
s
&
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* 6
24
'
$
Edge-cut at level 16 of triangular network of Erdős
collaboration graph
WORMALD, NICHOLAS C.
LASKAR, RENU C.
SHELAH, SAHARON
MCKAY, BRENDAN D.
HEDETNIEMI, STEPHEN T.
MAGIDOR, MENACHEM
KLEITMAN, DANIEL J.
CHUNG, FAN RONG K.
GRAHAM, RONALD L.
SAKS, MICHAEL E.
LINIAL, NATHAN
ARONOV, BORIS
PACH, JANOS
POLLACK, RICHARD M.
HENNING, MICHAEL A.
SPENCER, JOEL H.
ALON, NOGA
OELLERMANN, ORTRUD R.
LOVASZ, LASZLO
KOMLOS, JANOS
GODDARD, WAYNE D.
FRANKL, PETER
FUREDI, ZOLTAN
ALAVI, YOUSEF
CHARTRAND, GARY
HARARY, FRANK
KUBICKI, GRZEGORZ
SCHWENK, ALLEN JOHN
TUZA, ZSOLT
BABAI, LASZLO
SZEMEREDI, ENDRE
BOLLOBAS, BELA
AJTAI, MIKLOS
RODL, VOJTECH
NESETRIL, JAROSLAV
without Erdős,
n = 6926,
m = 11343
ROSA, ALEXANDER
GYARFAS, ANDRAS
SCHELP, RICHARD H.
LEHEL, JENO
STINSON, DOUGLAS ROBERT
CHEN, GUANTAO
MULLIN, RONALD C.
FAUDREE, RALPH J.
COLBOURN, CHARLES J.
JACOBSON, MICHAEL S.
PHELPS, KEVIN T.
s
s
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s
y
s
s
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&
%
* 6
25
'
$
Directed 3-rings
In directed networks there are two types of 3-rings:
cyclic
transitive
The 3-rings weights were implemented in Pajek in May 2002.
s
s
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s
y
s
s
s
&
%
* 6
26
'
$
Edge-cut at level 11 of transitive network of ODLIS
dictionary graph
serial
publication
American Library Directory
transaction log
periodical
suggestion box
frequency
review
charge
series
issue
library
call number
colophon
Library Literature
journal
fixed location
layout
publishing
printing
American Library Association /ALA/
blanket order
Books in Print /BIP/
vendor
title page
homepage
entry
International Standard Book Number /ISBN/
published price
round table
catalog
bibliographic record
dummy
condition
librarian
edition
fiction
plate
Oak Knoll
imprint
dust jacket
abstract
work
book
bibliography
half-title
editor
title
library binding
table of contents /TOC/
invoice
new book
text
parts of a book
book size
publisher
index
binding
cover
front matter
copyright
endpaper
collation
folio
page
s
s
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s
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&
%
* 6
Pajek
27
'
$
Islands
If we represent a given or computed value of vertices / lines as a height of
vertices / lines and we immerse the network into a water up to selected level
we get islands. Varying the level we get different islands. Islands are very
general and efficient approach to determine the ’important’ subnetworks in
a given network.
We developed very efficient algorithms to determine the islands hierarchy
and to list all the islands of selected sizes.
s
s
l y
s
y
s
s
s
See details.
&
%
* 6
28
'
$
Islands - Reuters terror news
united_airlines
plant
flight
train
arabic-language
power
pilot
manual
contain
bin_laden
saudi-born
uniform
inhale
scare
firefighter
dissident
jet
leader
airport
afghanistan
police
knife-wielding
anthrax
skin
phone
airliner
officer
support
country
hijack
trace
jonn
help
special
terrorism
war
united_states
embassy
business
wednesday
deadly
plane
mighty
force
thursday
pakistan
official
hijacker
arab
cell
agent
world
commercial
case
necessary
taliban
fbi
call
man
congressional
newspaper
chemical
member
rental
suspect
saudi
service
passenger
boston
organization
weapon
car
herald
pakistani
twin
week
strike
space
plea
specialist
110-story
world_trade_ctr
edmund
pentagon
air
north
cheyenne
tower
wyoming
offutt
news
late
new_york
city
florida
action
africa
anti-american
terror
group
responsibility
mayor
air_force
pfc
nebraska
barksdale
mayor_giuliani
landmark
team
exchange
american
conference
debris
miss
effort
thousand
rescue
market
center
aid
edward
fire
smoke
people
stock
dept
buildng
financial
toll
worker
plaugher
large
postal
emergency
chief
district
state
&
death
Pajek
l y
s
y
s
s
east
headquarters
morning
tuesday
south
military
terrorist
apparent
the_worst
washington
louisiana
base
act
attack
Using CRA S. Corman
and K. Dooley produced
the Reuters terror news
network that is based on
all stories released during 66 consecutive days by
the news agency Reuters
concerning the September
11 attack on the US. The
vertices of a network are
words (terms); there is an
edge between two words
iff they appear in the same
text unit. The weight of an
edge is its frequency. It has
n = 13332 vertices and
m = 243447 edges.
s
nuclear
s
american_airlines
attendant
s
airline
%
* 6
29
'
$
Islands – US patents
As an example, let us look at Nber network of US Patents. It has 3774768
vertices and 16522438 arcs (1 loop). We computed SPC weights in it and
determined all (2,90)-islands. The reduced network has 470137 vertices,
307472 arcs and for different k: C2 =187610, C5 =8859,C30 =101,
C50 =30 islands. Rolex
[1]
0 139793
[11] 190
125
[21] 17
16
[31] 12
3
[41]
1
3
[51]
2
3
[61]
0
0
[71]
0
0
[81]
2
0
29670 9288 3966 1827 997 578 362 250
104
71
47
37 36 33 21 23
8
7
13
10 10
5
5
5
7
3
3
3
2
6
6
2
4
1
5
2
1
1
1
1
3
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
1
2
0
0
7
s
s
l y
s
y
s
s
s
&
%
* 6
30
'
$
distribution
Island Theme
size size
distribution
●
10000
●
●
●
●
●
freq
●
●
●
●
100
●
●
●
●
● ●●
●●
●●
●
●●
●
●
●
●
●●●
●●
● ●●●
●
●
●
●
●●
●
●
● ●●
1
● ● ●●
●
●
2
5
10
20
●
●●
●● ●
●● ●
50
100
size
s
s
l y
s
y
s
s
s
&
%
* 6
31
'
$
Main path and main island of Patents
5855814
4456712
5683624
5555116
5543077
5124824
5171469
5283677
5122295
5016989
5374374
5016988
5308538
4957349
4877547
4820839
4832462
4797228
4752414
4721367
4704227
4657695
5171469
5122295
4770503
4795579
4877547
4709030
4719032
4695131
4710315
4713197
4659502
4621901
4797228
4630896
4710315
4583826
4510069
4558151
4550981
4659502
4526704
4502974
4514044
4480117
4472293
4472592
4455443
4419263
4422951
4550981
4460770
4526704
4472293
4422951
4415470
4400293
4386007
4330426
4357078
4386007
4349452
4368135
4293434
4290905
4340498
4340498
4387039
4387038
4361494
4302352
4302352
4195916
4229315
4149413
4229315
4202791
4261652
4149413
4198130
4082428
4154697
4113647
4013582
4029595
4130502
4032470
4083797
4082428
4118335
4011173
4077260
4017416
3975286
4011173
4000084
3960752
3954653
3872140
2544659
3675987
3947375
3960752
3876286
3881806
3731986
3795436
3891307
3697150
3636168
3767289
3666948
3322485
3773747
3796479
3795436
2682562
3691755
s
s
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s
y
s
s
s
&
%
* 6
32
'
$
Liquid crystal display
Table 1: Patents on the liquid-crystal display
patent
2544659
2682562
3322485
3636168
3666948
3675987
3691755
3697150
3731986
3767289
3773747
3795436
3796479
3872140
3876286
3881806
3891307
3947375
3954653
3960752
3975286
4000084
4011173
4013582
4017416
4029595
4032470
4077260
4082428
date author(s) and title
Mar 13, 1951 Dreyer. Dichroic light-polarizing sheet and the like and the
formation and use thereof
Jun 29, 1954 Wender, et al. Reduction of aromatic carbinols
May 30, 1967 Williams. Electro-optical elements utilazing an organic
nematic compound
Jan 18, 1972 Josephson. Preparation of polynuclear aromatic compounds
May 30, 1972 Mechlowitz, et al. Liquid crystal termal imaging system
having an undisturbed image on a disturbed background
Jul 11, 1972 Rafuse. Liquid crystal compositions and devices
Sep 19, 1972 Girard. Clock with digital display
Oct 10, 1972 Wysochi. Electro-optic systems in which an electrophoreticlike or dipolar material is dispersed throughout a liquid
crystal to reduce the turn-off time
May 8, 1973 Fergason. Display devices utilizing liquid crystal light
modulation
Oct 23, 1973 Aviram, et al. Class of stable trans-stilbene compounds,
some displaying nematic mesophases at or near room
temperature and others in a range up to 100◦ C
Nov 20, 1973 Steinstrasser. Substituted azoxy benzene compounds
Mar 5, 1974 Boller, et al. Nematogenic material which exhibit the Kerr
effect at isotropic temperatures
Mar 12, 1974 Helfrich, et al. Electro-optical light-modulation cell
utilizing a nematogenic material which exhibits the Kerr
effect at isotropic temperatures
Mar 18, 1975 Klanderman, et al. Liquid crystalline compositions and
method
Apr 8, 1975 Deutscher, et al. Use of nematic liquid crystalline substances
May 6, 1975 Suzuki. Electro-optical display device
Jun 24, 1975 Tsukamoto, et al. Phase control of the voltages applied to
opposite electrodes for a cholesteric to nematic phase
transition display
Mar 30, 1976 Gray, et al. Liquid crystal materials and devices
May 4, 1976 Yamazaki. Liquid crystal composition having high dielectric
anisotropy and display device incorporating same
Jun 1, 1976 Klanderman, et al. Liquid crystal compositions
Aug 17, 1976 Oh. Low voltage actuated field effect liquid crystals
compositions and method of synthesis
Dec 28, 1976 Hsieh, et al. Liquid crystal mixtures for electro-optical
display devices
Mar 8, 1977 Steinstrasser. Modified nematic mixtures with
positive dielectric anisotropy
Mar 22, 1977 Gavrilovic. Liquid crystal compounds and electro-optic
devices incorporating them
Apr 12, 1977 Inukai, et al. P-cyanophenyl 4-alkyl-4’-biphenylcarboxylate,
method for preparing same and liquid crystal compositions
using same
Jun 14, 1977 Ross, et al. Novel liquid crystal compounds and electro-optic
devices incorporating them
Jun 28, 1977 Bloom, et al. Electro-optic device
Mar 7, 1978 Gray, et al. Optically active cyano-biphenyl compounds and
liquid crystal materials containing them
Apr 4, 1978 Hsu. Liquid crystal composition and method
patent
4083797
4113647
4118335
4130502
4149413
Apr 11,
Sep 12,
Oct 3,
Dec 19,
Apr 17,
date
1978
1978
1978
1978
1979
4154697 May 15, 1979
4195916
Apr 1, 1980
4198130 Apr 15, 1980
4202791 May 13, 1980
4229315 Oct 21, 1980
4261652 Apr 14, 1981
4290905
4293434
4302352
Sep 22, 1981
Oct 6, 1981
Nov 24, 1981
4330426 May 18, 1982
4340498
4349452
4357078
Jul 20, 1982
Sep 14, 1982
Nov 2, 1982
4361494
4368135
Nov 30, 1982
Jan 11, 1983
4386007 May 31, 1983
4387038
Jun 7, 1983
4387039
Jun 7, 1983
4400293
4415470
Aug 23, 1983
Nov 15, 1983
4419263
Dec 6, 1983
4422951
4455443
4456712
4460770
4472293
Dec
Jun
Jun
Jul
Sep
27,
19,
26,
17,
18,
1983
1984
1984
1984
1984
4472592
4480117
4502974
Sep 18, 1984
Oct 30, 1984
Mar 5, 1985
4510069
Apr 9, 1985
author(s) and title
Oh. Nematic liquid crystal compositions
Coates, et al. Liquid crystalline materials
Krause, et al. Liquid crystalline materials of reduced viscosity
Eidenschink, et al. Liquid crystalline cyclohexane derivatives
Gray, et al. Optically active liquid crystal mixtures and
liquid crystal devices containing them
Eidenschink, et al. Liquid crystalline hexahydroterphenyl
derivatives
Coates, et al. Liquid crystal compounds
Boller, et al. Liquid crystal mixtures
Sato, et al. Nematic liquid crystalline materials
Krause, et al. Liquid crystalline cyclohexane derivatives
Gray, et al. Liquid crystal compounds and materials and
devices containing them
Kanbe. Ester compound
Deutscher, et al. Liquid crystal compounds
Eidenschink, et al. Fluorophenylcyclohexanes, the preparation
thereof and their use as components of liquid crystal dielectrics
Eidenschink, et al. Cyclohexylbiphenyls, their preparation and
use in dielectrics and electrooptical display elements
Sugimori. Halogenated ester derivatives
Osman, et al. Cyclohexylcyclohexanoates
Carr, et al. Liquid crystal compounds containing an alicyclic
ring and exhibiting a low dielectric anisotropy and liquid
crystal materials and devices incorporating such compounds
Osman, et al. Anisotropic cyclohexyl cyclohexylmethyl ethers
Osman. Anisotropic compounds with negative or positive
DC-anisotropy and low optical anisotropy
Krause, et al. Liquid crystalline naphthalene derivatives
Fukui, et al. 4-(Trans-4’-alkylcyclohexyl) benzoic acid
4’”-cyano-4”-biphenylyl esters
Sugimori, et al. Trans-4-(trans-4’-alkylcyclohexyl)-cyclohexane
carboxylic acid 4’”-cyanobiphenyl ester
Romer, et al. Liquid crystalline cyclohexylphenyl derivatives
Eidenschink, et al. Liquid crystalline fluorine-containing
cyclohexylbiphenyls and dielectrics and electro-optical display
elements based thereon
Praefcke, et al. Liquid crystalline cyclohexylcarbonitrile
derivatives
Sugimori, et al. Liquid crystal benzene derivatives
Takatsu, et al. Nematic halogen Compound
Christie, et al. Bismaleimide triazine composition
Petrzilka, et al. Liquid crystal mixture
Sugimori, et al. High temperature liquid crystal substances of
four rings and liquid crystal compositions containing the same
Takatsu, et al. Nematic liquid crystalline compounds
Takatsu, et al. Nematic liquid crystalline compounds
Sugimori, et al. High temperature liquid-crystalline ester
compounds
Eidenschink, et al. Cyclohexane derivatives
patent
4514044
4526704
4550981
4558151
4583826
4621901
4630896
4657695
4659502
4695131
4704227
4709030
4710315
4713197
4719032
4721367
4752414
4770503
4795579
4797228
4820839
4832462
4877547
4957349
5016988
5016989
5122295
5124824
5171469
5283677
5308538
5374374
5543077
5555116
5683624
5855814
date author(s) and title
Apr 30, 1985 Gunjima, et al. 1-(Trans-4-alkylcyclohexyl)-2-(trans-4’-(p-sub
stituted phenyl) cyclohexyl)ethane and liquid crystal mixture
Jul 2, 1985 Petrzilka, et al. Multiring liquid crystal esters
Nov 5, 1985 Petrzilka, et al. Liquid crystalline esters and mixtures
Dec 10, 1985 Takatsu, et al. Nematic liquid crystalline compounds
Apr 22, 1986 Petrzilka, et al. Phenylethanes
Nov 11, 1986 Petrzilka, et al. Novel liquid crystal mixtures
Dec 23, 1986 Petrzilka, et al. Benzonitriles
Apr 14, 1987 Saito, et al. Substituted pyridazines
Apr 21, 1987 Fearon, et al. Ethane derivatives
Sep 22, 1987 Balkwill, et al. Disubstituted ethanes and their use in liquid
crystal materials and devices
Nov 3, 1987 Krause, et al. Liquid crystal compounds
Nov 24, 1987 Petrzilka, et al. Novel liquid crystal mixtures
Dec 1, 1987 Schad, et al. Anisotropic compounds and liquid crystal
mixtures therewith
Dec 15, 1987 Eidenschink, et al. Nitrogen-containing heterocyclic compounds
Jan 12, 1988 Wachtler, et al. Cyclohexane derivatives
Jan 26, 1988 Yoshinaga, et al. Liquid crystal device
Jun 21, 1988 Eidenschink, et al. Nitrogen-containing heterocyclic compounds
Sep 13, 1988 Buchecker, et al. Liquid crystalline compounds
Jan 3, 1989 Vauchier, et al. 2,2’-difluoro-4-alkoxy-4’-hydroxydiphenyls and
their derivatives, their production process and
their use in liquid crystal display devices
Jan 10, 1989 Goto, et al. Cyclohexane derivative and liquid crystal
composition containing same
Apr 11, 1989 Krause, et al. Nitrogen-containing heterocyclic esters
May 23, 1989 Clark, et al. Liquid crystal devices
Oct 31, 1989 Weber, et al. Liquid crystal display element
Sep 18, 1990 Clerc, et al. Active matrix screen for the color display of
television pictures, control system and process for producing
said screen
May 21, 1991 Iimura. Liquid crystal display device with a birefringent
compensator
May 21, 1991 Okada. Liquid crystal element with improved contrast and
brightness
Jun 16, 1992 Weber, et al. Matrix liquid crystal display
Jun 23, 1992 Kozaki, et al. Liquid crystal display device comprising a
retardation compensation layer having a maximum principal
refractive index in the thickness direction
Dec 15, 1992 Hittich, et al. Liquid-crystal matrix display
Feb 1, 1994 Sagawa, et al. Liquid crystal display with ground regions
between terminal groups
May 3, 1994 Weber, et al. Supertwist liquid-crystal display
Dec 20, 1994 Weber, et al. Supertwist liquid-crystal display
Aug 6, 1996 Rieger, et al. Nematic liquid-crystal composition
Sep 10, 1996 Ishikawa, et al. Liquid crystal display having adjacent
electrode terminals set equal in length
Nov 4, 1997 Sekiguchi, et al. Liquid crystal composition
Jan 5, 1999 Matsui, et al. Liquid crystal compositions and liquid crystal
display elements
s
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* 6
33
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$
Islands – The Edinburgh Associative Thesaurus
n = 23219, m = 325624, transitivity weight
HAPPEN
JUST
NOTWITHSTANDING
PAYMENT
YET
MONIES
STOLE
UNPAID
PAY
ALREADY
AGAIN
RECEIPT
PAID
THRIFTY
COINS
MONEY
INCREASE
HAPPENED
DEALER
LOOT
NOW
NEVERTHELESS
DEFICIT THRIFT
OFTEN
PROVIDE
OFFER
BUT
WHY
PROPERTY
MORE MONEY
BELIEVE
REPAY
NO
PLEASE
AS
SOON
THEREFORE
ANYWAY
NOT
REFUSE
PROBABLY
MEANWHILE
SOMETIME
COULD
POWERFUL
INHUMAN
LECTURER
BOSS
STUDYING
CHAIRMAN
RESPONSIBLE
TEACHER
ENGINEERING
LEARNING
ELEGANCE
MAN
PROFESSION
TEACHING
HAIRY
SCHOOL
EDUCATION
MYSTERIOUS
CHARM
BELOVED
HOMEWORK
NICE
WORK
TRAINING
LOVE
ATTRACTIVE
GIRL
LECTURES
DELIGHTFUL
SCIENCE
LESSONS
STUDY
SCIENTIFIC
FLIRT
MATHS
KINDNESS
ADORABLE
RESEARCH
ACTIVITY
BEAUTIFUL
LOVELY
SHAPELY
s
s
l y
s
y
s
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Islands / Pajek commands
File/Network/Read [eatRS.net]
Net/Partitions/Islands/Generate Network with Islands [On]
Net/Partitions/Islands/Line Weights Simple [2 50]
Partition/Canonical Partition - Decreasing Frequencies
Info/Partition
Operations/Extract from Network/Partition [1-38]
Draw/Draw-Partition-Vector
Layout/Energy/Kamada-Kawai/Free
[manually distribute components over the available space]
Options/Transform/Fit area
The procedure for ’triangular islands’ is similar
File/Network/Read [eatRS.net]
Net/Count/3-Rings/Directed/Transitive
Net/Partitions/Islands/Generate Network with Islands [On]
Net/Partitions/Islands/Line Weights Simple [2 50]
...
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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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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 ∈ N}. If all nonempty elements of C are different
it is a lattice.
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Algorithm for bipartite cores
To determine a (p, q)-core the procedure similar to the ordinary core
procedure can be used:
repeat
remove from the first set all vertices of degree less than p,
and from the second set all vertices of degree less than q
until no vertex was deleted
It can be implemented to run in O(m) time.
Interesting (p, q)-cores? Table of cores’ characteristics n1 = |C1 (p, q)|,
n2 = |C2 (p, q)| and k – number of components in K(p, q):
• n1 + n2 ≤ selected threshold
• big jumps from C(p − 1, q) and C(p, q − 1) to C(p, q).
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Table (p, q : n1 , n2 ) for Internet Movie Database
1 1590: 1590
1 | 22 24: 1854 1153 | 43 14: 29 83
2 516: 788
3 | 23 23:
47
56 | 44 14: 29 83
3 212: 1705
18 | 24 23:
34
39 | 45 13: 30 95
4 151: 4330 154 | 25 22:
42
53 | 46 13: 29 94
5 131: 4282 209 | 26 22:
31
38 | 47 12: 29 101
6 115: 3635 223 | 27 22:
31
38 | 48 12: 28 100
7 101: 3224 244 | 28 20:
36
53 | 49 12: 26 95
8
88: 2860 263 | 29 20:
35
52 | 50 11: 27 111
9
77: 3467 393 | 30 19:
35
59 | 51 11: 26 110
10
69: 3150 428 | 31 19:
35
59 | 52 11: 16 79
11
63: 2442 382 | 32 19:
34
57 | 53 10: 35 162
12
56: 2479 454 | 33 18:
34
62 | 54 10: 35 162
13
50: 3330 716 | 34 18:
34
62 | 55 10: 34 162
14
46: 2460 596 | 35 18:
33
61 | 56 10: 34 162
15
42: 2663 739 | 36 17:
33
65 | 57 9: 35 187
16
39: 2173 678 | 37 16:
33
75 | 58 9: 33 180
17
35: 2791 995 | 38 16:
30
73 | 59 9: 33 180
18
32: 2684 1080 | 39 16:
29
70 | 60 9: 32 178
19
30: 2395 1063 | 40 15:
29
77 | 61 9: 31 177
20
28: 2216 1087 | 41 15:
28
76 | 62 9: 31 177
21
26: 1988 1087 | 42 15:
28
76 | 63 8: 31 202
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(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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(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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IMDB cores / Pajek commands
See How to deal with very large networks?
Options/Read-Write/Read-Save vertices labels [Off]
Read/Network [IMDB.net] 1:40
Info/Memory
Net/Partitions/Core/2-Mode Review
Net/Partitions/Core/2-Mode [27 22]
Info/Partition
Operations/Extract from Network/Partition [Yes 1]
Net/Partitions/2-Mode
Net/Transform/Add/Vertices Labels from File [IMDB.nam]
Draw/Draw-Partition
Layers/in y direction
Options/Transform/Rotate 2D [90]
Different result (because of multiple lines)
Net/Components/Weak [2]
Draw/Draw-Partition
Net/Transform/Remove/Multiple lines/Single line
Net/Partitions/Core/2-Mode [27 22]
Operations/Extract from Network/Partition [Yes 1]
Draw/Draw-Partition
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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.
p q
w4 (Kp,q ) =
2 2
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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5-rings
In the future we intend to implement in Pajek also weights w5 . Again
there are only 4 types of directed 5-rings.
cyclic
transitive
????
????
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Pattern searching
If a selected pattern determined by a given graph does not occur frequently
in a sparse network the straightforward backtracking algorithm applied for
pattern searching finds all appearences of the pattern very fast even in the
case of very large networks. Pattern searching was successfully applied to
searching for patterns of atoms in molecula (carbon rings) and searching for
relinking marriages in genealogies.
Michael/Zrieva/
Francischa/Georgio/
Damianus/Georgio/
Legnussa/Babalio/
Nicolinus/Gondola/
Franussa/Bona/
Marin/Gondola/
Magdalena/Grede/
Junius/Georgio/
Anucla/Zrieva/
Nicola/Ragnina/
Nicoleta/Zrieva/
Junius/Zrieva/
Margarita/Bona/
Sarachin/Bona/
Nicoletta/Gondola/
Marinus/Bona/
Phylippa/Mence/
Marinus/Zrieva/
Maria/Ragnina/
Lorenzo/Ragnina/
Slavussa/Mence/
Three connected relinking marriages in the
genealogy (represented as a p-graph) of ragusan noble families. A solid arc indicates
the is a son of relation, and a dotted arc
indicates the is a daughter of relation.
In all three patterns a brother and a sister
from one family found their partners in the
same other family.
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Ore-graph
m-grandmother
m-grandfather
f-grandfather
mother
sister-in-law
brother
daughter-in-law
father
I
son
f-grandmother
stepmother
wife
son-in-law
sister
daughter
In Ore-graph every person is represented by a vertex, marriages, relation is a spouse of , are represented with edges and relations is
a mother of
and is a father
of as arcs pointing from parents
to their children.
grandson
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p-graph
grandson
son & daughter-in-law
sister
father & stepmother
son-in-law & daughter
I & wife
brother & sister-in-law
father & mother
f-grandfather & f-grandmother
m-grandfather & m-grandmother
In p-graph vertices represent individuals or couples. In the case that
a person is not married yet (s)he is
represented by a vertex, otherwise
person is represented with the partner in a common vertex. There are
only arcs in p-graphs – they point
from children to their parents, representing the relations FiC is a
daughter of and MiC is a son
of ; where FiC ≡ female in the
couple; and MiC ≡ male in the
couple.
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Relinking patterns in p-graphs
A2
All possible relinking marriages in pgraphs with 2 to 6 vertices. Patterns are
labeled as follows:
A3
A4.1
B4
• first character – number of first
vertices: A – single, B – two, C
– three.
A4.2
A5.2
A5.1
• second character: number of vertices in pattern (2, 3, 4, 5, or 6).
B5
A6.3
A6.2
A6.1
C6
B6.4
B6.1
B6.2
B6.3
• last character: identifier (if the two
first characters are identical).
Patterns denoted by A are exactly the
blood marriages. In every pattern the
number of first vertices equals to the
number of last vertices.
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Frequencies normalized with number of couples in
p-graph × 1000.
pattern
A2
A3
A4.1
B4
A4.2
A5.1
A5.2
B5
A6.1
A6.2
A6.3
C6
B6.1
B6.2
B6.3
B6.4
Sum
Loka
0.07
0.07
0.85
3.82
0.00
0.64
0.00
1.34
1.98
0.00
0.00
0.71
0.00
1.91
3.32
0.00
14.70
Silba
0.00
0.00
2.26
11.28
0.00
3.16
0.00
4.96
12.63
0.90
0.00
5.41
0.45
17.59
13.53
0.00
72.17
Ragusa
0.00
0.00
1.50
10.49
0.00
2.00
0.00
23.48
1.00
0.00
0.00
9.49
1.00
31.47
40.96
2.50
123.88
Turcs
0.00
0.00
159.71
98.28
0.00
36.86
0.00
46.68
169.53
0.00
0.00
36.86
0.00
130.22
113.02
7.37
798.53
Royal
0.00
2.64
18.45
6.15
0.00
11.42
0.00
7.03
11.42
0.88
0.00
4.39
0.00
10.54
11.42
0.00
84.36
Most of the relinking marriages happened in the genealogy of Turkish nomads; the second is
Ragusa while in other genealogies they are much less frequent.
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Multiplication of networks
To a simple two-mode network N = (I, J, E, w); where I and J are sets
of vertices, E is a set of edges linking I and J, and w : E → R (or some
other semiring) is a weight; we can assign a network matrix W = [wi,j ]
with elements: wi,j = w(i, j) for (i, j) ∈ E and wi,j = 0 otherwise.
Given a pair of compatible networks NA = (I, K, EA , wA ) and NB =
(K, J, EB , wB ) with corresponding matrices AI×K and BK×J we call a
product of networks NA and NB a network NC = (I, J, EC , wC ), where
EC = {(i, j) : i ∈ I, j ∈ J, ci,j 6= 0} and wC (i, j) = ci,j for (i, j) ∈ EC .
The product matrix C = [ci,j ]I×J = A ∗ B is defined in the standard way
X
ai,k · bk,j
ci,j =
k∈K
s
s
s
s
s
s
In the case when I = K = J we are dealing with ordinary one-mode
networks (with square matrices).
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Fast sparse matrix multiplication
The standard matrix multiplication has the complexity O(|I| · |K| · |J|) – it
is (usually) too slow to be used for large networks.
For sparse large networks we can multiply faster considering only nonzero
elements:
for k in K do
for i in NA (k) do
for j in NB (k) do
if ∃ci,j then ci,j := ci,j + ai,k ∗ bk,j
else new ci,j := ai,k ∗ bk,j
NA (k): neighbors of vertex k in network A
NB (k): neighbors of vertex k in network B
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s
s
s
s
s
In general the multiplication of large sparse networks is a ’dangerous’
operation since the result can ’explode’ – it is not sparse.
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Complexity of fast sparse matrix multiplication
Let A and B be matrices of networks NA = (I, K, EA , wA ) and NB =
(K, J , EB , wB ).
Assume that the body of the loops can be computed in the constant time c.
Then we can prove:
If at least one of the sparse networks NA and NB has small maximal degree
on K then also the resulting product network NC is sparse.
And after more detailed complexity analysis:
Let dmin (k) = min(degA (k), degB (k)), ∆min = maxk∈K dmin (k),
dmax (k) = max(degA (k), degB (k)), K(d) = {k ∈ K : dmax (k) ≥ d},
d∗ = argmind (|K(d)| ≤ d) and K ∗ = K(d∗ ).
If for the sparse networks NA and NB the quantities ∆min and d∗ are small
then also the resulting product network NC is sparse.
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2-mode network analysis by conversion to 1-mode network
Often we transform a 2-mode network into an ordinary (1-mode) network
N1 = (U, E1 , w1 ) or/and N2 = (V, E2 , w2 ), where E1 and w1 are
P
(1)
(1)
T
determined by the matrix A = AA , auv = z∈V auz · aTzv . Evidently
(1)
(1)
auv = avu . There is an edge {u, v} ∈ E1 in N1 iff N (u) ∩ N (v) 6= ∅. Its
(1)
weight is w1 (u, v) = auv .
The network N2 is determined in a similar way by the matrix A(2) = AT A.
The networks N1 and N2 are analyzed using standard methods.
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Networks from data tables
A data table T is a set of records T = {Tk : k ∈ K}, where K is the set of
keys. A record has the form Tk = (k, q1 (k), q2 (k), . . . , qr (k)) where qi (k)
is the value of the property (attribute) qi for the key k.
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. . . Networks from data tables
Suppose that the property q has the range Q. If Q is finite (it can always be
transformed in such set by partitioning the set Q and recoding the values)
we can assign to the property q a two-mode network K × q = (K, Q, E, w)
where (k, v) ∈ E iff q(k) = v, and w(k, v) = 1.
Also, for properties qi and qj we can define a two-mode network qi × qj =
(Qi , Qj , E, w) where (u, v) ∈ E iff ∃k ∈ K : (qi (k) = u ∧ qj (k) = v),
and w(u, v) = card({k ∈ K : (qi (k) = u ∧ qj (k) = v)}).
We define [qi × qj ]T = qj × qi .
It holds qi × qj = [K × qi ]T ∗ [K × qj ] = [qi × K] ∗ [K × qj ].
We can join a pair of properties qi and qj also with respect to the third
property qs : we get a two-mode network [qi ×qj ]/qs = [qi ×qs ]∗[qs ×qj ].
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EU projects on simulation
For the meeting The Age of Simulation at Ars Electronica in Linz, January
2006 a dataset of EU projects on simulation was collected by FAS research,
Vienna and stored in the form of Excel table (RuthDELmain.csv).
The rows are the projects participants (idents) and colomns correspond to
different their properties. We produced from this table three two-mode
networks using Jürgen Pfeffer’s Text2Pajek program:
• project.net – idents × projects = P
• country.net – idents × countries = C
• institution.net – idents × institutions = U
|idents| = 8869, |projects| = 933,
|countries| = 60.
|institutions| = 3438,
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EU projects – network multiplication
Since all three networks have the common set (idents) we can derive from
them using network multiplication several interesting networks:
• ProjInst.net – projects × institutions W = PT ? U
• Countries.net – countries × countries S = CT ? C
• Institutions.net – institutions × institutions Q = WT ? W
• ...
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Analysis of ProjInst.net
For identifying important parts of ProjInst.net we first computed the
4-rings weights and in the obtained network we determined the line islands
Net/Count/4-rings/Undirected
Net/Partitions/Islands/Line Weights[Simple [2,200]
We obtain 101 islands. We extracted 18 islands of the size at least 5. There
are two most important islands: aviation companies and car companies.
In labels we used a new option \n.
For analysis of two-mode networks we can use also (p, q)−cores.
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Analysis of ProjInst.net
ARMINES
PSI FUR PRODUKTE UND
SYS.E DER INFORMATIONSTECH.
BICC GENERAL CABLE
TQT SRL
ESI SOFTWARE SA
CHALMERS TEKNISKA HOEGSKOLA
28283
COLOPLAST A/S
MTU AERO ENGINES
25525
FRAUENHOFER INST. FUER
PRODUKTIONSTECH. UND AUTOMATISIERUNG
EADS DE
LMS UMWELTSYS.E, DIPL. ING. DR. HERBERT BACK
BAE SYSTEMS
29817
DASSAULT AVIATION
C. R. FIAT S.C.P.A.
NL ORG. FOR APPLIED
SCIENTIFIC RESEARCH - TNO
BARTENBACH
501084
POLYMAGE SARL
G4RD-CT-2002-00836
G4MA-CT-2002-00022
STICHTING NATIONAAL LUCHT
OFFICE NAT. DETUDES ET
DE REC. AEROSPATIALES
BRPR987001
G4RD-CT-2000-00178
502896
G4RD-CT-2001-00403
G4RD-CT-2002-00795
MSO CONCEPT INNOVATION + SOFTWARE
7210-PR/163
ROSENHEIMER GLASTECH.
ENK6-CT-2002-30023
RUDOLF BRAUNS AND CO. KG
SHERPA ENGINEERING SARL
502889
CENTRE DE RECH. METALLURG.
506503
MECALOG SARL
506257
INST. NAT. DE RECHERCHE
SUR LES TRANSPORTS ET LEUR SCURIT
INST. SUPERIOR TECNICO
502842
AIRBUS FRANCE SAS
ALENIA AERONAUTICA SPA
TRUMPF-BLUSEN-KLEIDER
WALTER GIRNER UND CO. KG
BARCO NV
7215-PP/031
EA TECH. LTD
SNECMA MOTEURS SA
AIRBUS DEUTSCHLAND
502917
502909
NAT. TEC. UNIV.
OF ATHENS
INST. FUER TEXTIL UND
VERFAHRENSTECH. DENKENDORF
KBC MANUFAKTUR, KOECHLIN,
BAUMGARTNER UND CIE. AG
VOLKSWAGEN AG
EUROCOPTER S.
AIRBUS UK LIMITED
IST-2000-29207
TESSITURA LUIGI SANTI SPA
DAIMLER CHRYSLER AG
BUURSKOV
DE ZENTRUM FUER LUFT
UND RAUMFAHRT E.V.
G4RD-CT-2000-00395
7210-PR/233
INST. DE RECHERCHES
DE LA SIDERURGIE FR
T3.2/99
CATALYSE SARL
VOEST-ALPINE STAHL
EVG3-CT-2002-80012
THYSSENKRUPP STAHL A.G.
DISENO DE SISTEMAS EN SILICIO
CENTRE FOR EUROP. ECONOMIC
SMT4982223
ILEVO AB
7210-PR/095
FONDAZIONE ENI - ENRICO MATTEI
IST-2001-35358
CSTB
JERNKONTORET
UNIV. DER BUNDESWEHR MUENCHEN
CHIPIDEA - MICROELECTRONICA, S.A.
BUILDING RESEARCH
LANDIS & GYR - EUROPE AG
OESTERREICHISCHER BERGRETTUNGSDIENST
IFEN GES. FUER SATELLITENNAVIGATION
JOE3980089
WYKES ENGINEERING COMPANY
IST-2000-30158
ENEL.IT
UNIV. PANTHEON-ASSAS - PARIS II
SSAB TUNNPL¯T
7215-PP/034
LH AGRO EAST S.R.O.
TECHNOFARMING S.R.L.
T3.5/99
LESPROJEKT SLUZBY S.R.O.
BAYER. ROTES KREUZ
ENERGY RESEARCH CENTRE NL
RESEARCH INST. OF THE FINNISH ECONOMY
QLK6-CT-2002-02292
HELP SERVICE REMOTE SENSING
CINAR LTD.
INST. CARTOGRAFIC DE CATALUNYA
HPSE-CT-2002-00108
THE AARHUS SCHOOL OF BUSINESS
MEFOS, FOUNDATION FOR
METALLURGICAL RESEARCH
HPSE-CT-2002-00143
IST-2000-28177
BRITISH STEEL
UNIV. OF MACEDONIA
7210-PR/142
JOR3980200
FRAUENHOFER INST. FUER
AGRO-SAT CONSULTING
MATERIALFLUSS UND LOGISTIK
DATASYS S.R.O.
UNIV. OF ABERDEEN
ENK5-CT-2000-00335
ORAD HI TEC SYS. POLAND
CENTRE DE ROBOTIQUE
FRIMEKO INT. AB
CRE GROUP LTD.
MJM GROUP, A.S.
INOX
PNEUMATIC
AS
BBL
DFA DE FERNSEHNACHRICHTEN AGENTUR
TPS TERMISKA PROCESSER AB
PROLEXIA
KOMMANDITGES. HAMBURG 1
A.S.M. S.A. ZAMISEL D.O.O
IST-1999-56418
FERNSEHEN BETEILIGUNGS & CO
INGENIORHOJSKOLEN HELSINGOR TEKNIKUM
DPME ROBOTICS AB
GATE5 AG
511758
INDUSTRIAS ROYO
LKSOFTWARE
IST-2000-30082
WISDOM TELE VISION
SPORTART
YAHOO! DEOSAUHING EETRIUKSUS
BRST985352
UAB LKSOFT BALTIC
ALBERTSEN & HOLM AS
ASM - DIMATEC INGENIERIA
FFT ESPANA TECH. DE AUTOMOCION,
EDAG ENGINEERING + DESIGN
SVETS & TILLBEHOR AB
SUPERELECTRIC DI
CARLO PAGLIALUNGA & C. SAS
IST-1999-57451
OK GAMES DI ALESSANDRO CARTA
ENERGITEKNIK HEATEX AB
UNIV. DE ZARAGOZA
BROD THOMASSON
GUNNESTORPS SMIDE & MEKANISKA AB
Pajek
s
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&
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* 6
63
'
$
Analysis of Countries.net
To obtain picture in which the
stronger lines cover weaker lines we
have to sort them
Kazakhstan
Afghanistan
Japan
Azerbaijan
Georgia
Morocco
Liechtenstein
Ecuador
India
Uzbekistan
Armenia
Net/Transform/Sort
Iceland
Belarus
Tunisia
Jordan
Canada
Lebanon
France
lines/Line values/Ascending
Algeria
United Kingdom
Italia
The Netherlands
Russian F.
Finland
Moldavia
China
Turkmenistan
Malta
Turkey
Greece
Germany
Portugal
Spain
Switzerland
Cyprus
Sweden
Denmark
Thailand
Israel
Austria
Estonia
Slovakia
USA
Belgium
Poland
Croatia
Luxembourg
Latvia
Norway
Slovenia
Ireland
Ukraine
Serbia-Montenegro
Macedonia
Hungary
Romania
Bulgaria Czech R.
Lithuania
Albania
For dense (sub)networks we get
better visualization by using matrix
display. In this case we also recoded
values (2,10,50).
To determine
clusters we used Ward’s clustering
procedure with dissimilarity measure
d5 (corrected Euclidean distance).
Pajek
The permutation determined by hierarchy can often be improved by
changing the positions of clusters – for the New Year 2006 Andrej added
this option in Pajek. We get a typical center-periphery structure.
s
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Analysis of Countries.net
Ecuador
Thailand
Armenia
Turkmenist
Uzbekistan
Moldavia
Japan
Kazakhstan
Azerbaijan
India
Macedonia
Albania
Liechtenst
Serbia-Mon
Iceland
Canada
Estonia
China
Belarus
Georgia
Tunisia
Lebanon
Jordan
Algeria
Malta
Morocco
Afghanista
Luxembourg
Croatia
Latvia
Lithuania
Cyprus
Turkey
Bulgaria
Ukraine
Slovenia
Romania
Slovakia
USA
Portugal
Denmark
Poland
Finland
Switzerlan
Austria
Czech R.
Ireland
Norway
Hungary
Israel
Russian F.
Sweden
Greece
Belgium
Spain
The Nether
France
United Kin
Germany
Italia
Ecuador
Thailand
Armenia
Turkmenist
Uzbekistan
Moldavia
Japan
Kazakhstan
Azerbaijan
India
Macedonia
Albania
Liechtenst
Serbia-Mon
Iceland
Canada
Estonia
China
Belarus
Georgia
Afghanista
Morocco
Malta
Tunisia
Lebanon
Jordan
Algeria
Croatia
Latvia
Lithuania
Luxembourg
Cyprus
Turkey
Bulgaria
Ukraine
Slovenia
Romania
Slovakia
USA
Russian F.
Israel
Hungary
Ireland
Czech R.
Norway
Poland
Finland
Portugal
Denmark
Switzerlan
Austria
Sweden
Greece
Belgium
Spain
The Nether
Italia
France
United Kin
Germany
Pajek - Ward [0.00,4785.14]
Ecuador
Thailand
Armenia
Turkmenist
Uzbekistan
Moldavia
Japan
Kazakhstan
Azerbaijan
India
Macedonia
Albania
Liechtenst
Serbia-Mon
Iceland
Canada
Estonia
China
Belarus
Georgia
Afghanista
Morocco
Malta
Tunisia
Lebanon
Jordan
Algeria
Croatia
Latvia
Lithuania
Luxembourg
Cyprus
Turkey
Bulgaria
Ukraine
Slovenia
Romania
Slovakia
USA
Russian F.
Israel
Hungary
Ireland
Czech R.
Norway
Poland
Finland
Portugal
Denmark
Switzerlan
Austria
Sweden
Greece
Belgium
Spain
The Nether
Italia
France
United Kin
Germany
s
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* 6
65
'
$
Analysis of Institutions.net
U.A.S.ZITTAU/GOERLITZ
U.THE AEGEAN
MIT-MANAGEMENT INTELLIGENTER TECH.N
U.PARIS-DAUPHINE
OTTO VON GUERICKE MAGDEBURG U.
COVENTRY U.
FACULTY OF ELECTRICAL ENG.
FED.UNITARY
ENTERPRISE
FL-SOFT V/JENS
DAEDALUS
INFORMATICS LTD
ALL-RUSSIAN SCIENTIFIC
CENTER
OESTERGAARD
U.PARIS
VI PIERRE ETJOERGEN
MARIE CURIE
BELIMO AUTOMATIONU.LA LAGUNA
SOFIISKI U.SVETI KLIMENT OHRIDSKI
THE U.COURT OF THE U.OF ABERDEEN
SIEMENS
BUILDING TECH.S AG
SENTIENT MACHINE RESEARCH B.V.
AS.CONOCIMIENTO
U.OULU
I.OF INFORMATION TECH.S
STICHTING NEURALE NETWERKEN
DATAMED HEALTHCARE INF.SYS.
NOTTINGHAM TRENT U.
U.E DE COIMBRA
T.U.CLAUSTHAL
MOMATEC
U.CRETE
CITY U.LONDON
U.ULSTER
GOETHE U.FRANKFURT AM MAIN
U.WIEN
ALLOGG AB
RAUTARUUKKI OY
SOFTECO SISMAT
U.WALES, ABERYSTWYTH
DE MONTFORT U.
I.DALLE MOLLE DI STUDI SULLIA
U.JYVASKYLA
BULGARIAN ACAD.
U.ZAGREB
U.CYPRUS
OF SCIENCES
U.OF CHEMICAL TECH.
BOURNEMOUTH U.
ASS.RECH.SCIENTIFIQUE
AND METALLURGY
KINGS COLLEGE LONDONENTE PER LE
ELITE EUROP.LAB
NUOVE TECNOLOGIE
STICHTINGTECH.
U.NYENRODE
FOR INTELLIGENT
I.NAT.POLITEC.DE TOULOUSE
I.FUER NATURSTOFF-FORSCHUNG E.V.
U.AMSTERDAM
U.GIRONA
U.GENT
AUSTRIAN I.AI
START ENGINEERING JSCO
T.U.DELFT
I.NAT.DE RECHERCHE SUR
ENERGY RESEARCH C.NL
LES TRANSPORTS ET LEUR SECURITE
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U.TWENTE
TSS-TRANSPORT SIMULATION SYS.S.L.
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AND THE REGIONS
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GEESTHACHT
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U.P.MADRID
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U.MARIBOR
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U.PAUL SABATIER DE TOULOUSE III
U.PAISLEY
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U.STRATHCLYDE
U.VALLADOLID
U.P.CATALUNYA
U.LEEDS
U.S.GENOVA
U.NOTTINGHAM
C.SVILUPPO MATERIALI HERMSDORFER I.FUER TECH.
PT.TORINO
PT.BARI
U.MANCHESTER
OXFORD BROOKES U.
DAIMLER CHRYSLER AG
U.DORTMUND
U.S.PADOVA
SAFE TECH.
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LOUGHBOROUGH T.U.
NOKIA MOBILE PHONES LTD
CZECH T.U.PRAGUE
AVIO S.P.A.
FOKKER SPACE BV
BRITISH TELEC.
NAT.T.U.ATHENS
T.U.V KOSICIACH
ANAKON
I.SUPERIOR TECNICO
NCODE INT.
U.SHEFFIELD
FUNDACION LABEIN
POLISH ACAD.OF SCIENCES
FINITE ELEMENT ANALYSIS LTD.
RISOE NAT.LAB
TUN ABDUL RAZAK RESEARCH C.LTD.
U.GREENWICH
DANMARKS T.U.
PRINCIPIA INGENIEROS CONSULTORES
U.C.LOUVAIN
FUNDACION INASMET
STAVANGER U.COLLEGE
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SULZER MARKETS AND TECH.AG,
IFP SICOMP AB
SULZER INNOTEC
CHALMERS TEKNISKA HOEGSKOLA
DAMT LTD
SKF R&D COMPANY B.V.
CAESAR SYSTEMS LTD
U.S.NAPOLI
A.U.THESSALONIKI
INTES - INGENIEURGES.
FUER TECH.SOFTWARE
U.DURHAM
C.INT.LENGINYERIA
NL ORG.FOR APPLIED
SCIENTIFIC RESEARCH-TNO
C.R.FIAT S.C.P.A.
U.S.TRIESTE
CAD - FEM
ENGIN SOFT TRADING SRL
MARITIME HYDRAULICS AS
INBIS TECH.LTD
FEMSYS LTD
SOFISTK AG
MSC SOFTWARE
QUEENS U.BELFAST
ABS CONSULTING
ALTAIR ENGINEERING
NLSE VERENIGDE SCHEEPSBOUW BUREAUS B.V.
MERITOR HEAVY VEHICLE
BRAKING
SYS.UK LTD
CREA CONSULTANTS LTD
TRL
PD&E AUTOMOTIVE B.V.
ACCESS E.V.
NEW TECH.ENGINEERING LTD
ROCKFIELD SOFTWARE LTD.
U.NEWCASTLE UPON TYNE
BEHR &CO.
AIRBUS FRANCE SAS
NAT.NUCLEAR CORP.LTD.
U.GLASGOW
FEMCOS INGENIEURBUERO MBH
ST MECANICA APLICADA S.L.
GERMAN AEROSPACE CENTRE
FRAUENHOFER I.FUER
INGENIEURBUERO FUER
BIOMEDICAL ENGINEERING
TRAGWERKSPLANUNG
KATHOLIEKE HOGESCHOOL SINT-LIEVEN
ROYAL I.OF TECH.
DUNLOP STANDARD
AEROSPACE GROUP
U.HANNOVER
GIFFORD AND PARTNERS LTD.
MECAS S.R.O.
VOLVO AERO CORP.AB
ATOS ORIGIN ENG.
LULEAA T.U.
STRUCTURAL INTEGRITY
CORK I.OF TECHNOLOGY
ASSESSMENTS LTD
HAHN-SCHICKARD-GES.
NORUT TEKNOLOGI
A.S.
WS ATKINS CONSULTANTS LTD. EASI ENGINEERING
U.E DO MINHO
NUMERICAL ANALYSIS
U.SPLIT
AND DESIGN&CO KG
ADVIESBUREAU N.V.
WILDE AND TECHNISCH
PARTNERS LTD
INTEGRATED DESIGN &
RANDOM LOADINGANALYSIS
DESIGN CONSULTANTS LTD
FEGS
AWE PLC
D C WHITE&PARTNERS LTD
MERKLE UND PARTNER
DR THELLEN
EATEC LTD
SAMTECH SA
LEUVEN MEASUREMENTS AND SYS.INT.NV
C.NAT.DE LA
RECHERCHE SCIENTIFIQUE
NAFEMS LTD.
To identify the most important institutions we first computed pS -cores vector and use it to determine the corresponding vertex islands. We got
essentially one large island. Again
the corresponding subnetwork is very
dense. We prepared also a matrix display.
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Analysis of Institutions.net
s
l y
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&
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ASS. RECH.
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UNIV. OF J
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EATEC LTD
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HAHN-SCHIC
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INTEGRATED
KATHOLIEKE
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MECAS S.R.
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DAEDALUS I
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Pajek - Ward [0.00,1376.93]
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Clustering with relational constraints
We can define different types of sets of feasible clusterings for the same
relation R. Some examples of types of relational constraint Φ i (R) are
type of clusterings
type of connectedness
Φ 1 (R)
weakly connected units
Φ 2 (R)
weakly connected units that contain at most one center
Φ 3 (R)
strongly connected units
Φ 4 (R)
clique
Φ 5 (R)
the existence of a trail containing all the units of the cluster
Trail – all arcs are distinct.
A set of units L ⊆ C is a center of cluster C in the clustering of type Φ 2 (R)
iff the subgraph induced by L is strongly connected and R(L)∩(C \L) = ∅.
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Some graphs of different types
3s
4s
A
A A
A As
s
1
2
a clique
4s
5s
A
A
A
A
A
A
A A
U
A
Us
A
s
- s
1
2
3
4s
5s
A
A
A
A
A
A
A
A AU s
U
A
s
s
1
2
3
strongly connected units
4s
5s
A
A
A
A
AU s
s
s
1
2
3
with a center {1, 2, 4}
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Agglomerative method for relational constraints
We can use both hierarchical and local optimization methods for solving
some types of problems with relational constraint (Ferligoj, Batagelj 1983).
1.
2.
2.1.
2.2.
2.3.
2.4.
2.4.
3.
k := n; C(k) := {{X} : X ∈ U};
while ∃Ci , Cj ∈ C(k): (i 6= j ∧ ψ(Ci , Cj )) repeat
(Cp , Cq ) := argmin{D(Ci , Cj ): i 6= j ∧ ψ(Ci , Cj )};
C := Cp ∪ Cq ; k := k − 1;
C(k) := C(k + 1) \ {Cp , Cq } ∪ {C};
determine D(C, Cs ) for all Cs ∈ C(k)
adjust the relation R as required by the clustering type
m := k
The fusibility condition ψ(Ci , Cj ) is equivalent to Ci RCj for tolerant,
leader and strict method; and to Ci RCj ∧ Cj RCi for two-way method.
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Adjusting relation after joining
Φ 1 – tolerant
Φ 2 – leader
Φ 4 – two-way
Φ 5 – strict
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Dissimilarities between clusters
In the original approach a complete dissimilarity matrix is needed. To
obtain fast algorithms we propose to consider only the dissimilarities
between linked units.
Let (U, R), R ⊆ U × U be a graph and ∅ ⊂ S, T ⊂ U and S ∩ T = ∅.
We call a block of relation R for S and T its part R(S, T ) = R ∩ S × T .
The symmetric closure of relation R we denote with R̂ = R ∪ R−1 . It
holds: R̂(S, T ) = R̂(T, S).
For all dissimilarities between clusters D(S, T ) we set:

 d(s, t) sR̂t
D({s}, {t}) =
 ∞
otherwise
where d is a selected dissimilarity between units.
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Minimum
Dmin (S, T ) =
min
d(s, t)
(s,t)∈R̂(S,T )
Dmin (S, T1 ∪ T2 ) =
min
d(s, t) =
(s,t)∈R̂(S,T1 ∪T2 )
=
min(
min
(s,t)∈R̂(S,T1 )
=
d(s, t),
min
d(s, t)) =
(s,t)∈R̂(S,T2 )
min(Dmin (S, T1 ), Dmin (S, T2 ))
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Maximum
Dmax (S, T ) =
max
d(s, t)
(s,t)∈R̂(S,T )
Dmax (S, T1 ∪ T2 )
=
max
d(s, t) =
(s,t)∈R̂(S,T1 ∪T2 )
=
max(
max
(s,t)∈R̂(S,T1 )
=
d(s, t),
max
d(s, t)) =
(s,t)∈R̂(S,T2 )
max(Dmax (S, T1 ), Dmax (S, T2 ))
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Average
w : V → R – is a weight on units; for example w(v) = 1, for all v ∈ U.
Da (S, T ) =
1
X
w(R̂(S, T ))
d(s, t)
(s,t)∈R̂(S,T )
w(R̂(S, T1 ∪ T2 )) = w(R̂(S, T1 )) + w(R̂(S, T2 ))
P
w(R̂(S, T1 ∪ T2 ))Da (S, T1 ∪ T2 ) = (s,t)∈R̂(S,T1 ∪T2 ) d(s, t) =
P
P
= (s,t)∈R̂(S,T1 ) d(s, t) + (s,t)∈R̂(S,T2 ) d(s, t) =
= w(R̂(S, T1 )) · Da (S, T1 ) + w(R̂(S, T2 )) · Da (S, T2 ))
Da (S, T1 ∪T2 ) =
w(R̂(S, T1 ))
w(R̂(S, T1 ∪ T2 ))
Da (S, T1 )+
w(R̂(S, T2 ))
w(R̂(S, T1 ∪ T2 ))
Da (S, T2 )
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Reducibility
The dissimilarity D has the reducibility property (Bruynooghe, 1977) iff
D(Cp , Cq ) ≤ min(D(Cp , Cs ), D(Cq , Cs )) ⇒
min(D(Cp , Cs ), d(Cq , Cs )) ≤ D(Cp ∪ Cq , Cs )
or equivalently
D(Cp , Cq ) ≤ t, D(Cp , Cs ) ≥ t, D(Cq , Cs ) ≥ t ⇒ D(Cp ∪ Cq , Cs ) ≥ t
Theorem 1 If a dissimilarity D has the reducibility property then hD is a
level function.
All three disimilarities have the reducibility property. In this case also the
nearest neighbor network for a given network is preserved after joining
the nearest clusters. This allows us to develop a very fast agglomerative
hierarchical clustering procedure.
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Dodge
Dooly
MontgomeryEvans
Franklin
Rusk
WheelerToombs
Caldwell
De Soto
Bullock
Stewart
Webster
Navarro
Red River
Hidalgo
Sumter
Tattnall
Wilcox
Chatham
Claiborne
Smith Jasper Clarke Choctaw
Tensas
Wilcox Telfair
Hill
Bryan
Comanche
Winn
Crisp
Bosque
Coke
BarbourQuitman
Winkler Ector
Midland Glasscock
Copiah Simpson
Liberty
Pike
Runnels
Loving
Sterling
Jeff Davis
AndersonCherokee
TerrellLee
Randolph
Long
Shelby
Ben Hill
Natchitoches
Coleman Brown
Butler Crenshaw
Jefferson
Hamilton
Appling
Freestone
Turner
El Paso
Clay
Jones Wayne
Irwin Coffee
Covington
Catahoula
Grant La Salle
Clarke
Jefferson
Davis
Worth
Wayne
Bacon
McLennan Limestone
Henry
Nacogdoches
Lincoln Lawrence
CalhounDougherty
Monroe
McIntosh
Sabine
Mills
Adams Franklin
Conecuh
Tift
Ward
Washington
Coffee Dale
Tom Green
Coryell
Reeves
San Augustine
Sabine
Crane Upton
Concordia
Pierce
Reagan
Concho
Culberson
Hudspeth
Leon
Irion
Atkinson
Early
Angelina
Baker
Covington
Houston
Mitchell
Falls
Berrien
Glynn
McCulloch San SabaLampasas
MarionLamar
Greene
Rapides
Brantley
Wilkinson Amite Pike Walthall
Cook
Colquitt
Forrest
Perry
Houston Miller
Escambia
Vernon
Trinity
Geneva
Avoyelles
Chase
Atchison
JohnsonNemaha
Grand
Butte
Polk
MadisonWarren Marion MahaskaKeokuk Washington
Louisa
Montgomery
Adams Union
Rio Blanco
Sutter
Kent
JeffersonWaukesha
Milwaukee
Ottawa
Lafayette Green
Otoe
Phillips
Weld
Morgan
Uintah
Mills
Waldo
Kennebec
Androscoggin
Lewis
Oswego
Sanilac
Saginaw
Jo Daviess Stephenson
Winnebago
Boone McHenryLake
Jones
Benton Linn
Stark
Sarpy
Cass
Logan
Larimer
Routt
Duchesne
Wasatch
Utah
Eureka
Pottawattamie
Cass
Douglas
Saunders
Butler
Hamilton
York
Lancaster
Jackson
Moffat
Washoe
Colusa
Dane
Iowa
Clayton Grant
Bremer
Tama
Colfax Dodge Washington
Platte
Polk
Merrick
Lincoln
Jefferson
Huron
Montcalm Gratiot
Black Hawk
Buchanan
Delaware Dubuque
Marshall
Clinton
Nance
ShermanHoward
Keith
Deuel
Arenac
Tuscola
Muscatine
Kimball
Morgan
Davis
Glenn
Chickasaw
Franklin Butler
HamiltonHardin Grundy
Harrison Shelby Audubon
Guthrie Dallas
Greeley
Custer
Laramie
Uinta
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Elko
Pershing
Webster
Crawford Carroll Greene Boone Story
Burt
Boone
Garden
Rich
Box Elder
Humboldt
MadisonStantonCuming
Garfield Wheeler
Calhoun
Gladwin
Bay
Muskegon
Niagara
Cedar
Sweetwater
Modoc
Siskiyou
Blaine
Sac
Osceola Clare
Mecosta Isabella Midland
Newaygo
Washington
Ozaukee
Jackson
Monona
Grant
Lake
Mason Lake
Oceana
Dodge
Richland Sauk
Thurston
Oxford
Essex
Manitowoc
Winnebago
Calumet
Marquette
Green Lake
Fond du Lac
Sheboygan
Houston
Fayette
Humboldt
CherokeeBuena Vista
Pocahontas
Wright
Plymouth
Dakota Woodbury Ida
Hancock
EssexCoos
Caledonia
Chittenden
Winneshiek
Allamakee
Crawford
Wayne
Goshen
Scotts Bluff
Mendocino
Waushara
Juneau
Adams
Monroe
La Crosse
Fillmore
Mitchell Howard
Hancock Cerro Gordo
Floyd
Washington
Orleans
Lamoille
Franklin
St. Lawrence
Washington
Winona
Olmsted
Freeborn Mower
Winnebago
Worth
Dixon
Pierce
Antelope
Box Butte
Franklin
Platte
Lander
Faribault
Palo Alto
Franklin
Grand Isle
Clinton
Alcona
Manistee Wexford Missaukee
Roscommon
Ogemaw Iosco
Cedar
Holt
Rock
Bear Lake
Oneida
Lassen
Martin
OBrien’ Clay
Kossuth
Union
Dawes
Bannock
Twin Falls
Plumas
Jackson
Osceola DickinsonEmmet
Sioux
Yankton
Bon Homme
Clay
Natrona
Sublette
Minidoka
Owyhee
Tehama
Nobles
Lyon
Lincoln
Niobrara
Harney
Lake
Jackson
Josephine
Trinity
Hutchinson
Turner
Franklin
Alpena
Otsego Montmorency
Grand Traverse
KalkaskaCrawfordOscoda
Kewaunee
Jackson
Buffalo Trempealeau
Wabasha
Blue Earth
Cottonwood
Waseca
Steele Dodge
Watonwan
Moody PipestoneMurray
MinnehahaRock
Waupaca
Brown
Outagamie
Columbia
Fall River
Fremont
Humboldt
Lake
Davison
Hanson McCook
Portage
Vernon
Tripp
Shannon
Bingham
LeelanauAntrim
Benzie
Lyman
Weston
Washakie
Hot Springs
Bonneville
Blaine
Klamath
Buffalo
Jones
Jefferson
Madison Teton
Butte
Elmore
Malheur
Cheboygan
Charlevoix
Door
Oconto
Menominee
Wood
Camas
Ada
Douglas
Coos
Penobscot
Presque Isle
Langlade
Shawano
Le SueurRice
Brown Nicollet
Somerset
Marathon
Eau Claire Clark
Pepin
Goodhue
Redwood
Lincoln Lyon
Brookings
Kingsbury
Piscataquis
Emmet
Marinette
Lincoln
Taylor
Chippewa
Dunn
Pierce
Dakota
Scott
Renville
Delta
Rusk
Barron
Anoka
St. Croix
Washington
Hennepin
Ramsey
Yellow Medicine
Campbell
Pennington
Payette
Canyon
Florence
Forest
Oneida
Menominee
Sibley
Hughes
Sawyer
McLeod Carver
Deuel
Hamlin
Hand
Beadle
Haakon
Washburn
Chisago
Polk
Sherburne
Wright
Kandiyohi
Meeker
Lac qui Parle
Chippewa
Codington
Clark
Hyde
Burnett
Price
Swift
Park
Lane
Chippewa
Mackinac
Dickinson
Kanabec
Mille Lacs
Isanti
Schoolcraft
Vilas
Pine
Morrison
Stearns
Big Stone
Day
Faulk
Spink
Meade
Gem
Crook
Edmunds
Potter
Sully
Crook
Stanley
Clark
Pope
Grant
Dewey
Ziebach
Custer
Douglas
Stevens
Benton
Roberts
Perkins
Butte
Sheridan
Big Horn
Alger
Iron
Todd
Grant
Traverse
Marshall
Aroostook
Luce
Marquette
Gogebic
Ashland
Iron
Sargent
Carbon
Beaverhead
Washington
Deschutes
Dickey
McPherson
Brown
Lemhi
Yellowstone National
Curry
Campbell
Powder River
Gallatin
Madison
Baraga
Bayfield
Douglas
Otter Tail
Emmons
Valley
Baker
Grant
Carlton
Aitkin
Crow Wing
Ransom
Sioux
Corson
Adams
Wheeler
Jefferson
Houghton
Ontonagon
LaMoure
Harding
Carter
Union
Clackamas
Cass
Wilkin
Richland
Adams
Sweet Grass
Stillwater
Big Horn
Marion
Linn
Becker
Clay
Rosebud
Yellowstone
Park
Wasco
Yamhill
Cass
Silver Bow
Wallowa
Polk
Barnes
Wadena
Logan
Fallon
Bowman
Deer Lodge
Idaho
Tillamook
Stutsman
Grant
Klickitat
Multnomah
Hood River
Lincoln
Benton
Hettinger
Treasure
Jefferson
Ravalli
Skamania
Clark
Kidder
Stark
Slope
Musselshell
Broadwater
Cowlitz
Columbia
Washington
Keweenaw
Mahnomen
Hubbard
Burleigh
Morton
Wheatland
Granite
Garfield
Walla WallaColumbia
Asotin
Lake
Itasca
Traill
Norman
Billings
Golden Valley
Meagher
Clearwater
Franklin
Clatsop
Wibaux
Prairie
Yakima
Steele
Oliver
Judith Basin
Powell
Pacific
Griggs
Mercer
Fergus
Lewis and Clark
Missoula
Mineral
Adams
St. Louis
Clearwater
Foster
Dunn
Dawson
Grant
Kittitas
Pierce
Thurston
Wells
Sheridan
McLean
Garfield
Mason
Cook
Eddy
Shoshone
King
Grays Harbor
Beltrami
Chouteau
Teton
Douglas
Kitsap
Grand Forks
Bee
Live Oak
La Salle McMullen
Refugio
Aransas
Volusia
Matagorda
Citrus
Lake
Seminole
Sumter
Hernando
Orange
Pasco
Brevard
Polk
San Patricio
Osceola
PinellasHillsborough
Nueces
Webb
Duval
Indian River
Jim Wells
Hardee
Kleberg
Manatee
St. Lucie
Highlands
Okeechobee
Sarasota DeSoto
Martin
Jim Hogg
Brooks
Zapata
Kenedy
Glades
Charlotte
Hendry
Palm Beach
Lee
Starr
Hidalgo
Willacy
Cameron
Collier
Broward
Dade
Monroe
Pajek
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What else?
In 2005 we introduced in Pajek also support for multi-relational networks
that combined with temporal networks enable analysis of new kinds of
networks – such as KEDS networks (Kansas Event Data System or Tabari).
You can use URLs in description of vertices (Nov 2005).
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References
1. Batagelj, V. and Mrvar, A.(1996-): Pajek– program for analysis and visualization of
large network, home page, data sets.
2. Batagelj, V. and Zaveršnik, M.(2002): Generalized Cores, arxiv cs.DS/0202039
3. Batagelj, V. and Zaveršnik, M.(2003): Short cycle connectivity. arxiv cs.DS/0308011
4. Batagelj V., Ferligoj A. (2000): Clustering relational data. Data Analysis (Eds.: W. Gaul,
O. Opitz, M. Schader), Springer, Berlin, 3–15.
5. Bruynooghe, M. (1977), Méthodes nouvelles en classification automatique des données
taxinomiques nombreuses. Statistique et Analyse des Données, 3, 24–42.
6. Doreian, P., Batagelj, V., Ferligoj, A. (2000), Symmetric-acyclic decompositions of
networks. J. classif., 17(1), 3–28.
7. Ferligoj A., Batagelj V. (1982): Clustering with relational constraint. Psychometrika,
47(4), 413–426.
8. Ferligoj A., Batagelj V. (1983): Some types of clustering with relational constraints.
Psychometrika, 48(4), 541–552.
9. Mrvar, A. and Batagelj, V. (2004): Relinking Marriages in Genealogies. Metodološki
zvezki - Advances in Methodology and Statistics, 1, Ljubljana: FDV, 407-418.
10. Murtagh, F. (1985), Multidimensional Clustering Algorithms, Compstat lectures, 4,
Vienna: Physica-Verlag.
11. de Nooy, W., Mrvar, A. and Batagelj V. (2005): Exploratory Social Network Analysis
with Pajek, CUP. Amazon. ESNA page.
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12. J. P Scott: Social Network Analysis: A Handbook. SAGE Publications, 2000. Amazon.
13. S. Wasserman, K. Faust: Social Network Analysis: Methods and Applications. CUP,
1994. Amazon.
14. White, D.R., Batagelj, V., and Mrvar, A. (1999): Analyzing Large Kinship and Marriage
Networks with Pgraph and Pajek. Social Science Computer Review – SSCORE, 17,
245-274.
15. Zaveršnik, M. and Batagelj, V. (2004): Islands. Slides from Sunbelt XXIV, Portorož,
Slovenia, 12.-16. May 2004, PDF
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Analysis of Large Networks with Pajek

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