'Advanced Network Analysis / Pajek: Large Networks / First Steps'

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Analysis and visulization of large networks with Pajek Vladimir Batagelj University of Ljubljana

Vienna, St. Stephen’s Cathedral

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften Universitat¨ Wien, 21-22. 6. 2007

& version: June 18, 2007 / 03 : 11% V. Batagelj: Analysis and visulization of large networks with Pajek 2

' Outline $ 1 Networks ...... 1 6 Complexity of algorithms ...... 6 7 Pajek ...... 7 11 Approaches to large networks ...... 11 12 Statistics ...... 12 19 Clusters, clusterings, partitions, hierarchies ...... 19 20 Representations of properties ...... 20 30 Example: Snyder and Kick World Trade ...... 30 35 Clustering ...... 35 38 Contraction of cluster ...... 38 42 Subgraph ...... 42 44 Important vertices in network ...... 44 52 Dense groups ...... 52 60 Connectivity ...... 60 64 Cuts ...... 64 69 Citation weights ...... 69 70 k-rings ...... 70 75 Islands ...... 75

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 3

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84 Bipartite cores ...... 84 91 Directed 4-rings ...... 91 96 Pattern searching ...... 96 101 Multiplication of networks ...... 101 105 Networks from data tables ...... 105 107 EU projects on simulation ...... 107 116 What else? ...... 116

http://vlado.fmf.uni-lj.si/pub/networks/doc/tut/Vienna07.pdf

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 1

' Networks $ A network is based on two sets – set of vertices (nodes), that represent the selected units, and set of lines (links), that represent ties between units. They determine a graph.A line can be directed – an arc, or undirected – an edge. Additional data about vertices or lines can be known – their properties (attributes). For example: Alexandra Schuler/ Marion Laging-Glaser: Analyse von Snoopy Comics name/label, type, value, . . . Network = Graph + Data The data can be measured or computed.

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Networks / Formally A network N = (V, L, P, W) consists of:

• a graph G = (V, L), where V is the set of vertices and L = E ∪ A is the set of lines; A is the set of arcs and E is the set of edges. n = |V|, m = |L|

• P vertex value functions / properties: p : V → A

• W line value functions / weights: w : L → B

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % *Vertices 20 1 "m01" 2 "m02" 3 "m03" 4 "m04" 5 "m05" 6 "f06" 7 "f07" 8 "f08" 9 "f09" 10 "f10" 11 "f11" 12 "f12" 13 "f13" 14 "f14" V. Batagelj: Analysis and visulization of large networks 15 "f15" with Pajek 3 16 "f16" 17 "f17" 18 "f18" 19 "f19" ' Example: 20 "f20" Wolfe Monkey Data $ *Edges 1 2 2 1 3 10 inter.net inter.net 1 4 4 sex.clu age.vec rank.per 1 5 5 *Vertices 20 *vertices 20 *vertices 20 *vertices 20 1 6 5 1 "m01" 1 15 1 1 7 9 2 "m02" 1 10 2 1 8 7 3 "m03" 1 10 3 1 9 4 4 "m04" 1 8 4 1 10 3 5 "m05" 1 7 5 1 11 3 6 "f06" 2 15 10 1 12 7 7 "f07" 2 5 11 1 13 3 8 "f08" 2 11 6 1 14 2 9 "f09" 2 8 12 1 15 5 10 "f10" 2 9 9 1 16 1 11 "f11" 2 16 7 1 17 4 12 "f12" 2 10 8 1 18 1 13 "f13" 2 14 18 2 3 5 14 "f14" 2 5 19 2 4 1 15 "f15" 2 7 20 2 5 3 16 "f16" 2 11 13 2 6 1 17 "f17" 2 7 14 2 7 4 18 "f18" 2 5 15 2 8 2 19 "f19" 2 15 16 2 9 6 20 "f20" 2 4 17 2 10 2 *Edges 2 11 5 1 2 2 2 12 4 1 3 10 2 13 3 1 4 4 2 14 2 1 5 5 2 15 2 1 6 5 2 16 6 1 7 9 2 ...17 3 1 8 7 2 18 1 1 9 4 2 19 1 1 10 3 Important notes: 0 is not 3 allowed 4 8 as vertex number. Pajek doesn’t support Unix text ﬁles – 1 11 3 3 5 9 1 12 7 3 6 5 lines should 1 13 be ended3 with CR LF. 3 7 11 1 14 2 3 8 7 1 15 5 3 9 8 1 16 1 3 10 8 Methodenforum der Fakult 1 at¨ 17 fur¨ Sozialwissenschaften, 4 Universitat¨ Wien, 21-22. 6. 2007

3 11 14 L L S L L S L L 1 18 1 G & 3 12 17 % 2 3 5 3 13 9 2 4 1 3 14 11 2 5 3 3 15 11 2 6 1 3 16 5 2 7 4 3 17 9 2 8 2 3 18 4 2 9 6 2 10 2 2 11 5 2 12 4 2 13 3 2 14 2 2 15 2 2 16 6 2 17 3 2 18 1 2 19 1 3 4 8 3 5 9 3 6 5 3 7 11 3 8 7 3 9 8 3 10 8 3 11 14 3 12 17 3 13 9 3 14 11 3 15 11 3 16 5 3 17 9 3 18 4 V. Batagelj: Analysis and visulization of large networks with Pajek 4

' Size of network $ The size of a network/graph is expressed by two numbers: number of vertices n = |V| and number of lines m = |L|.

1 In a simple undirected graph (no parallel edges, no loops) m ≤ 2 n(n − 1); and in a simple directed graph (no parallel arcs) m ≤ n2. The quotient γ = m is a density of graph. mmax Small networks (some tens of vertices) – can be represented by a picture and analyzed by many algorithms (UCINET, NetMiner). Also middle size networks (some hundreds of vertices) can still be represented by a picture (!?), but some analytical procedures can’t be used. Till 1990 most networks were small – they were collected by researchers using surveys, observations, archival records, . . . The advances in IT allowed to create networks from the data already available in the computer(s). Large networks became reality. Large networks are too big to be displayed in details; special algorithms are needed for their analysis (Pajek ).

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' Large Networks $ Large network – several thousands or millions of vertices. Can be stored in computer’s memory – otherwise huge network. Usually sparse m <

Pajek datasets.

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Complexity of algorithms From some thousands to some (tens) millions of units (vertices). Let us look to time complexities of some typical algorithms:

T(n) 1.000 10.000 100.000 1.000.000 10.000.000 LinAlg O(n) 0.00 s 0.015 s 0.17 s 2.22 s 22.2 s LogAlg O(n log n) 0.00 s 0.06 s 0.98 s 14.4 s 2.8 m √ SqrtAlg O(n n) 0.01 s 0.32 s 10.0 s 5.27 m 2.78 h SqrAlg O(n2) 0.07 s 7.50 s 12.5 m 20.8 h 86.8 d CubAlg O(n3) 0.10 s 1.67 m 1.16 d 3.17 y 3.17 ky

For the interactive use on large graphs already quadratic algorithms, O(n2), are too slow.

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' Pajek $ The main goals in the design of Pajek are: • to support abstraction by (recursive) decomposition of a large network into several smaller networks that can be treated further using more sophisticated methods; • to provide the user with some powerful visualization tools; • to implement a selection of efﬁcient subquadratic algorithms for analysis of large networks.

With Pajek we can: ﬁnd clusters (components, neighbourhoods of ‘important’ vertices, cores, etc.) 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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' $ Pajek’s data types In Pajek analysis and visualization are performed using 6 data types:

• network (graph), • partition (nominal or ordinal properties of vertices), • vector (numerical properties of vertices), • cluster (subset of vertices), • permutation (reordering of vertices, ordinal properties), and • hierarchy (general tree structure on vertices).

Pajek supports also multi-relational, temporal and two-mode networks.

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' $ ... Pajek’s data types The power of Pajek is based on several transformations that support different transitions among these data structures. Also the menu structure of the main Pajek’s window is based on them. Pajek’s main window uses a ‘calculator’ paradigm with list-accumulator for each data type. The operations are performed on the currently active (selected) data and are also returning the results through accumulators. The procedures are available through the main window menus. Frequently used sequences of operations can be deﬁned as macros. This allows also the adaptations of Pajek to groups of users from different areas (social networks, chemistry, genealogy, computer science, mathematics. . . ) for speciﬁc tasks. Pajek supports also repetitive operations on series of networks.

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' ESNA Pajek $

An introduction to social network analysis with Pajek is available in the book ESNA (de Nooy, Mrvar, Batagelj 2005). Pajek– program for analysis and visualization of large networks is freely available, for noncommercial use, at its web site.

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

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 11

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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 use the described decomposition approach – identify smaller (sub) networks that can be analyzed further using more sophisticated methods.

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' $ Statistics Input data

• numeric → vector

• ordinal → permutation

• nominal → clustering (partition) Computed properties global: number of vertices, edges/arcs, components; maximum core number, . . . local: degrees, cores, indices (betweeness, hubs, authorities, . . . ) inspections: partition, vector, values of lines, . . . Associations between computed (structural) data and input (measured) data.

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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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' $ . . . Statistics The global computed properties are reported by Pajek’s commands or can be seen using the Info option. In repetitive commands they are stored in vectors. The local properties are computed by Pajek’s commands and stored in vectors or partitions. To get information about their distribution use the Info option. As an example, let us look at The Edinburgh Associative Thesaurus network. The EAT is a network of word association as collected from subjects (students). The weight on the arcs is the count of word associations. File/Network/Read eatRS.net Info/Network/General

It has 23219 vertices and 325624 arcs (564 loops); number of lines with value=1 is 227481.

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. . . Statistics To identify the vertices with the largest degree: Net/Partitions/Degree/All Partition/Make vector Info/Vector +10 The largest degrees have the vertices: vertex deg label 1 12720 1108 ME 2 12459 1074 MAN 3 8878 878 GOOD 4 18122 875 SEX 5 13793 803 NO 6 13181 799 MONEY 7 23136 732 YES 8 15080 723 PEOPLE 9 13948 720 NOTHING 10 22973 716 WORK

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' Statistics / Pajek and R $ Pajek (0.89 and higher) supports interaction with statistical program R and the use of other external programs as tools (menu Tools). 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’)

The obtained picture can be saved with File/Save as in selected format (PDF or PS for LATEX; Windows metaﬁle format for inclusion in Word). Attention! The vertices of degree 0 are not considered by tabulate.

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' EAT all-degree distribution $

EAT all−degree distribution

● 5000 ● ● ● ● ● ●

500 ● ● ● ●●●●● ● ●●●●●●●●●● ● ●●● ●●● ● ●● ●●● ● ●●●● ● ● ●● ● ●●● ●●● ●● ● ●● freq ● ●●● ●●●●● ●● 50 ● ● ●●●● ●●●● ●● ●●● ●●●●●● ●●●●●●● ●●● ●●● ●●●●●● ●●●●● 10 ●●●● ● ●●●●●● ● ●●●●●●●● ●●●●●●●●●● 5 ●●●●●●●● ● ●●●●●●●●●●●●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●● 1

1 5 10 50 100 500

deg

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' $ Degree distribution

Random graph degree distribution, n=100000, degav=30 US Patents degree distribution

● ● ● ● 1 e+06 ● ● ● ● ● ● ● ● ● ● ●● ●● ●● ● ● ●● ● ● ●● 6000 ●● ●● ●● ● ●● ●● ● ●● ●● ●● ●● ● 1 e+04 ●● ●● ●● ●● ● ●●● ●● ●● ● ●● 4000 ● ● ●● ●

freq freq ● ●●● ● ●● ●● ●●●● ●●● ● ● ●●● ●●●● ●●●● ●●●● ● ●●● ●● ● ●● ●●● ●●●

1 e+02 ●● ●● ●● ● ● ●●●●●●

2000 ● ●●●● ●●●●●●● ●●●●●● ● ● ●● ● ●●●● ●●●● ●●●●●●●●●●● ● ●●●●●●●● ● ●●●●●●●●●● ●●●●● ● ● ● ●●●●●●●●●●●● ● ● ●●●●●●●●●●●●●●●●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●●●●●● 0 1 e+00 10 20 30 40 50 1 5 10 50 100 500 1000

deg deg

Real-life networks are usually not random in the Erdos/Renyi˝ sense. The analysis of their distributions gave a new view about their structure – Watts (Small worlds), Barabasi´ (nd/networks, Linked).

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' $ Clusters, clusterings, partitions, hierarchies A nonempty subset C ⊆ V is called a cluster (group). A nonempty set of

clusters C = {Ci} forms a clustering.

Clustering C = {Ci} is a partition iff [ ∪C = Ci = V in i 6= j ⇒ Ci ∩ Cj = ∅ i

Clustering C = {Ci} is a hierarchy iff

Ci ∩ Cj ∈ {∅,Ci,Cj}

Hierarchy C = {Ci} is complete, iff ∪C = V; and is basic if for all v ∈ ∪C also {v} ∈ C.

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' $ Representations of properties Properties of vertices P and lines W can be measured in different scales: numerical, ordinal and nominal. They can be input as data or computed from the network. In Pajek numerical properties of vertices are represented by vectors, nominal properties by partitions or as labels of vertices. Numerical property can be displayed as size (width and height) of vertex (ﬁgure), as its coordinate; and a nominal property as color or shape of the ﬁgure, or as a vertex label (content, size and color). We can assign in Pajek numerical values to links. They can be displayed as value, thickness or grey level. Nominal vales can be assigned as label, color or line pattern (see Pajek manual, section 4.3).

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 21

' Some comments $ While the technical graph drawing problems could ask for a single ’the best’ picture, the social network analysis is a part of data analysis. Its goal is to get insight into the structure and characteristics of a given network, but also how it inﬂuences related social processes. What is the goal: exploration of network data (layout editor), presentation of the obtained results (layout viewer), . . . ? What is a GD result: picture or layout ? What is the medium of the result: static picture on ’paper’, interactive layout, . . . ? What kind of user will use the result: simple, advanced, . . . ? Most methods are ’paper’ oriented. In larger/denser networks there is often too much information to be presented at once. A possible answer are interactive layouts where the user controls what (s)he wants to see.

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James Moody: Display of properties – school

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' Lothar Krempel $

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' FAS: The scientiﬁc ﬁeld of Austria $

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' Katy Borner¨ : Text analysis $

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' Jeffrey Johnson: St Marks food web $

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' Big picture, V. Batagelj, AE’04 $

subnetwork (n = 5952, m = 18008) of the symmetrized Edinburgh Associative Thesaurus

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' $ Big picture

thrust synthetic telegram syringe signal whiskey studies white collar feminine produced comprehend legion ghoul spooky totter and lime wrap praise wilderness toga roman water wings cobweb wizard rangers celtic particularly orthopaedic rayon loom remove swotting working works muslin beware rack noah ark kit soaring shudder sod industrious coup d'etat silly bitch camera trench towers lent sleeping bag wind-screen priestess oz gauze rot quartered upwards retained pied willingly

tie-pin understand wants slick weaver thicker collar taken succeed studying journalism strips topical spoil ruin offend worker mixer slabs masculine foreign lungs apparition pious petroleum paste stole witch sceptre spider web lipstick jill downwards piper gladly appendix tests especially bind whale spanner satin optics magician ghost pattern shears brussel sprout vocation intestines simon sipping slaked simplicity wiper mitre orb groan spiders halved chairs tables kept

needs jamb thinner tie weave volume hazard wound twist sat mobile lick catastrophy powerful niagara seats hardness softness stubborn hated belfry nylon cravat render showing printing woven occupied conjurer topic option made nuclear mosaic lining brussels sprouts jack putty robust lime dew wire washing up palate sugars condition shrug kilt flounder obstinate plays theatres australia sort shove apparent obvious since harmed injure alien pale moan porpoise tied loved

quenched learner sixteen necessities surgeon knot push cowboys trick wooden selectionrisk choice forthwith lambs reactor levi pope quench slake strong sallow newcastle screw screwdriver complain grumble izzy tartan whilst solving lo objection overruled revenue bats beginner type emigrate tug puncher precise rasp print rigid recently press patient naval silk triumph flying injury harm lay porcelain morrow jug ox disaster plug spark mesh liquid olive rod sacked cordial behold mule inland

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cider treasure deadly consulate postcard request maisonettes schooner soon strap july nous chez cup baa crew cuts fleece difficulty complex gulp wallpaper taste-bud epaulettes taught anthropoid tackled replenished bacteria trove unsafe text book mythology ask to be jib yield give donate gave cloth saucer when at once sure disk severe sons broader cotton stopper girls difficult protestant brown ale trodden thorn snog gibbon tarzan intestine pests chinese syrup throwing bondage tested statistics erupt or not to be empire disc toothache article wool soft

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jumping practice key-hole merchant august teacup crawly creepy falling whine inn thieves glandular protein insects homeward newt spinach tse tung origin pops rover pullover jumper hoyle legend donated extinct knickers select failed agony floor lino put placed snip pins decay tooth incisor soak robbers lips embrace pole ruins nibble dinner solution servant larva spawn volcano unhealthy al leaping weld private eye fred dwellings memoir writing seaman pass newspaper handkerchief groove worm spectacles reach attain damp hymn donkey sink kitchen servility pans

signature tops padlock sweater homes myth include factory find out choose suffer needles corduroy moisture windsor cops douse fever starve flirt gagged bound frog troubled terrified surface godliness o.k. all right stupendous raise scrape sent indirect magazine lock slug ed tar heave anchor fail presented emery exclude quest fibre fell pain scouts guides diving sever braces cows bilge wet drawbridge fortress mouth drown tummy kippers sugar lumps seascape aided recipe tadpole smut pots cleanliness journal injection passed torture weeds bulls guiness helped

valid wonderful direct lethal slack key hinges knob grip aground news pocket look for search pick tales ceiling windows erosion arid castle kings drought tremble float fishing gel talons infective morals strawberry next to vein wits flux funnels shipment mast steward sailing require until definite egg-shaped damsel distress glow stairs gash scissors trousers trews soil nip dry task toffee tray disregard ignore plankton creamy landscape silica housemaid toad croak ethics mao snipe wholesome jugular bored stationerypulp infliction herds raining alkali

reeling solder wit fantastic britain loose knocker door handle wag prow cruise sailor bulletin clip tissue need wounded unharmed endure composition stories discomfort steps wick scissor cut shave cozy bullocks dehydrated martini england falls drinking boyfriend girlfriend rights eagle malady illness ail ailing tinned maid latter cripple unreal talking nova tight slams destiny captain secure join spasm candle crease creases desert queens confession thunder lightning planets netting cuisine appears electric apes monkeys flour um ease ache gasp parched indisposed

jacket filled roam unwell adjacent staying speaking sarcasm kangaroo pouch hinge enter tail liner wreck matelot paper necessity image safe vintage ounce mutiny carver blade razor pitcher imbibe hanger sheepskin dragon agriculture leak golden personality digest vicarage raising seems meander wander nausea worried anxious mod rocker er wheel chair nit fabulous great marvellous close doors keys fate oars want reflections essay bounty suffering flue headache delicate sheath follicle blades earth breath frothy swim menu treacle civil jersey siphon soda ill crew tiredness phoney invalid sender pod pea slip slide sailors shut ship document mirror puppet quid discovery fork quake fur thistle plunge dive jangle jingle tasty sickness disease rugger poorly sick ports nearby open knock dock deck boat gazette reflect ink wine employment danger sunday migraine spoon knife wig curlers cropping shampoo pinch tap booze drink bowler mink dilute dog-collar character welfare feast refectory peas mosquito health puke neater hatch locks vessel quarto desire chimney casks thirsty eats tidier

pubic potatoes closeness sooner oath masts ended closed ajar lift funnel fairies vine anguish humid nationality british hair consume eat wing vital silence broker nauseous spew placard haemorrhoids neurology paws latest swear liners began elevator cargo dingy canoe ferry reflection blob devalued pound dagger stab comb lager trickle coca-cola bar snack fields coat scythe tunnel contract goal oesophagus french kraut state nation bluebottle kite lump nazi nauseating slime elevate snarl growl at devalue busy broom sweep coif flood german magic wand oar grape mersey larder scones stock pond proper strike odontology near later earlier commenced started hold driving berth weapon sail vest pants pen heather cloak drinker brush bottles brew wards hat sickle eating fly concord jet fishes fitness eaters healthy sssh from home polo industry harbours ships begun director scribble lung cancer sword string cement cable beards wavy pub ale saloon currants tigers sole kipper dolphin ate pantry trim shush spuds absent tablet turtle virile fountain meadows leagues

crane still rear afar away afterwards finished exams error sharpener jive carpenter ply froth cap fin food plane bomber frightened pebbles sandy toast grime shin nigh far gone with the wind mint docks ever ready pole vault grasp came rigging girders heap tropic bitten refill cartridge shaggy occupation blimey daily indigestion carving local brewing pint splash shower ripple instant cafe goalie shark bait plaice roe restaurant nuisance quiet yachts boats sharpen patience study pill ceremony planks bouncer crypt rugby lions aeroplane squalor hush snap jagged mistake meal flight beach quiescent untruth piles distant although upper going coming lying at last battery pencil poodle dance cor descending warning concrete throat sore beer hops arrows mineral infirmary tea football spiral net fish grub cater airport lake pest marmalade poster errant baron artificial ink-pot went decks moment finals corrugated ferrite reading scotch terrain haystack leash job teak carpentry tonic water ward coffee league soccer appetite spitfire scared dirt filth silent noiseless aluminium thread pup work wood

recline antimony foundry bitch ripples crackle pilot preserve tart stork methylated spirits penultimate lower pillow-case playing chivalry hang done contain final matches boxer filings pile blunder puppy draw arduous cork plank splinter tankard keg bows h2o pump topper language miners mines staircase diet cod chips mackerel nourishment chef cook tomato screech sand pebble paddy southern noisy huff higher snoring knight suspend whisky passive knit needle barking toil isles career procure nurse whistle barrels taps china scuttle fearful toothbrush paw sketch timber mutton ram butty margarine rarely lies true gulf nap mentioned fag finally conclude ending scrap cuddly steel iron brace crayon dog bark dimension acquire get beadle cottage barrel shutter alcoholic reservoir hospital headgear english blend miner depth fired gill skate meals prime sauce judo thither hither tarts jam serene nightmare truth honesty hammock nightmares sleeping armour finish dentists active sew setter hound discover canals clear sawdust sills patients coal porridge life-boat irish northern dentistry biter bottle buns obtain lie fantasies waking beginning end token cox crate sill channel fill oats kettle fib false untrue dreams dreaming fleet metal ore fables monger teeth fangs switzerland pet puss rash concentrate ascending achieve raisins shorter tumbler window boiling soiree afternoon almoner balmy wave breaker field turn minister sausage pasture lamb ewe karate loaves dough jar loaf butter bawl peacefulspread falsehood gospel snooze kittens said dentist lace cruiser handler kitten find button thatch slate matron canon rector digestion stew

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rummy gin clergyman waves proceed praying lover cigars fume swift wake coma complete edition slippy manchester ledger arrow object breadth width residence void coventry pew kirk evensong priest cartilage shanties taste flavour whisk frighten anxiety convalescence fahrenheit deep profound slice yell grains of course hater tobacco bedtime bureau toy depart washington d.c. skip warm gain twain mark barns sloshed boozed clanger frame picture moo commerce breakwater ribbons concern ha violin naturally pillowslip and few wall taylor mower index afraid diverse centigrade sought tag awake lend leave stack paint nothingness canterbury cathedral buzz effect cause salt water fret worry shallow fascist smoking lung cancer smoke rest fags beds letter envelope et office whether regulation rule exception row residing hop centimetre caution airy fairy leap liz bag wary loss outboard hay mat inebriated drunk soot gloss portrait church steeple tang score breakers necessary mistress seldom scare fear terror of fact fathoms scream tranquil pheasant lemon cigarette fracture darts brim lawn terrify cropper viola basin

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trade room parish amaze astonish market pictures leaving limit cigar hose happening abrasive choke thong squirm bedsit camping canvas chapel minor blunt cakes hood frequently broth pottage sine sheets post posted correspondence skipping connect first beg abate carry nearly squares shatter reader hurdle barges messing teach educate mileage esso board dolls wheels full bull pints unladen jigsaw puzzle crossword mists grass sharp doctors soup stodgy log edinburgh puff exclaim peck throw fling mattress gasoline shake milking tears vitamin c aircraft

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remaining rapid medic various all rice trotter limp nook left prescription hay fever cough breed chatter everyone or nothing aces drain youth comforts midst better improve talked spare bouts mole orifice decorate chalet colour azure heat fog smog epileptic contention grate lemons oranges cinders burger biscuit digestive amount core juice jaffa amiable easel hog fitted lag exist die tractor duck bicycle bean as dealt cerebrum bleed adolescence keep waggon panda basketball other flowing impediment glucose reddish cake thigh budgie pear in hand

boxing lead right correct physician consultant vendor seller spear canasta address home worse toenails communist thames burn dripping curried transport fruit orange avenue firs forestry jelly commission mire strive cha expire stall stains personally velocity talk coroner metre deal cards brain of humour bleeding retain bungalow barge mouse poppies himself blue cloud mist burst estuary speech fire coo annoy ham ebb tide joint succulent simultaneous discussion hearse bald scarf bonfire chess alternative bay sweetness sugar icing bagpipes keeper citrus persevere wrong spine winter summer section killed bereavement sentry clouds flow pip tangerine woods hedge rome shouting hypothalamus dozy matchbox very desk inanimate suicide action diamond tumour brawn instead screws commons semi-detached cranium nape casualty herself tot fete tune negroes negro sky chalk articulation hudson severn orator oration honey blaze flames ember mousse cadbury's caged cloister steak trees shrubs surgery acceleration speed haste chat speak blithe fingertips company limited trap squeak spring river sweet finder peel shock

extinguish hesitation swiftly dawdle quick gossip tries graves discuss athlete dead death life fatal reflex say manner saver nails manor house skull balloon negress arson colours ankle dove juices pips forest italy resort hasty incorrect greatest back beard guard touch feel sandal granite plaster roads streets stifling head neck down settle midlands melody africa black blackboard waiting collapse brook stream dee speaker caster spoonful hailer loud chocolate corned beef seeker departs autumn feathered attic elms orchard alive giraffe sour

gradual slow evidence hearsay extremely attempts and again blouse coffin burial rock fall rivulet hive rainbow tomatoes stroganoff bush bushes locution bias khaki churchyard stubble freeway wrath shooting looked died mortality funeral being human crying clot bible scripture tidings mansion mitten day try nigger mellow respond tumble decline arrest logs warmth sound abatement fry's sprain roast painting leaves loft shrub twins leafy front corpse lodging construct mortgage hot shrunken fingers up sit ascend white blanco cane diabetic stump peeling chicken

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rung mushroom lieutenant consequence alarm poplar who quickly confinement pedal rungs disagree weary what barracks regiment haemoglobin fable narrate mile built cool allotment menstrual shot pistol bout ugliness impossible botany tinker clotted stars milky way cosmology calamity rodent crawl creeper minutes stingy sluggish hit agree dispute rats fatigue fatigued apart giver binding arithmetic relay inch garden carnations rang rifle glue statue pollen cream bumble-bee council segment twig thicket pop group hollow glade cross-country anew again soldier transform concede coniferous pine osborne prejudice colonel hours springs stud ladder miss toadstool pride separate detatched taker soldiers sums shoe foot furlong constructed clock nostrils possible maple bough mean rapidly judicial cycle mice at all regard been army story tell william casterbridge bouquet transition period holster range bud change alter stick adhere tailor boiler song astronomy galaxy compartments daddy jane limbs prickly creep wept output branch vacation willing ivy holly wait amok run belong from repeat enlist may april dictionary time liberty devon john poker

trot stallion shorts least sock boulders pimple gelding runner throbbing portion dash abide most rocking has salvation tale mayor slipper temperature petals shop actions boom hockey suit singer mummy shares legs arms creature input ness holiday apple pie liver miserly lente mare ride filly sprinter perambulate according look dot enrol prodigy peninsula city america pax arrange words o'clock clocks aquiline bang cave cavern cowslips broken probable sing cornwall blossom cabbage trumpet cooker cob president lollipop to gentle freedom star constellation flee sap smack stable walk observe bred romper stay squint stink newyork belt buckle assistant early nose bore station stocks holidays fuzz spot gas whore american law-court east intermediate kingdom gallop carriage belonging ahoy argument ally players stench mayoress non-violence thermometer rocks beetle armies girl atomic baggage feasible ditty senior platform locomotive vacations drivers loch high-speed imply kennedy poke pony see born troops island giggle pitt london rifleman boy dam bluebell malt vinegar likely queue broad celebrity curry willow

solitary horses hoof horse refuse place acquaintance remain corps smell acquired obtained blow tornado mould yank west hooves foal stroll promenade there everybody communicate recognize perceive foe together graph chastity shoot au pair late nostril train distribute oxygen hydrogen rail monks hobby jockey fragrance castaway country town peace tranquillity chair geology angel got visage man woman games bomb napalm luggage forsyte bus conductor narrow junior cloudy technology freight morse code char thermodynamics harlot acne kidney laugh jest alderman brine wide confide rider amble will shall was is location shine breeze alone recognise lodge colleague friend comrade darn blinds fireside crescent sun salt saga rails compartmentwind raffle friar tube warden spots meter gnu gonzales ridden rode saddle bridle subtraction here companionship tock tick odour chuckle joke village radish boot war table abbey shit ray face features in-law atom pepper science railway ticket lady traffic drake miser ripe smile shanty existence westminster actress saline conducted fare inspector criminology quilt female

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promise injustice cart in addition conception conditioned member provost hatred grin corns cactus bottomless tan rays loveliness steam diesel firework exchange remittance gong performance parking lomond photosynthesis speedy necklace observed neigh shaft grave among both chewing gum love loathe palms hands currency seat bench lamps blacksmith anvil chisel father matrimony waving blast lichen armchair stalk blew ligament fame onion railroad seen not me listen pal neighbour next door breeds stair case blister bloke comic battle forwards under corn fool engaged married gale hilly lone stare gaze ramble hiding grief dead-end yourself cherish affair feet panning torch pit today amusing teller impressionism strip tease beads epsom go to has not thyself you hear carry on match buying selling dearest bit nappy cradle hate loath conjunctivitis gloves chiropody confectionery light plant to-day mallet hammer middle-aged digit ware funny circular theatre over obese single furry fortune economy hash pickle snub lean lumps tenderness cortex paris yesterday thumb spherical flakes plump quietly wrist idiot heard hastings backwards axe hearer thank mound sledge double ken salts joined magistratelistener justice court data sorrow ego self they sitter passion emotion dislike toes sweets plated dark aspidistra nanny snow fat cruel garter gorge save hart stockings wee intake timing slim broadcast hasn't me because height route of cake baby cot resurrection charge eyes inches blisters bulb tomorrow scape billy nail finger alchemy benign accordion damn charm circumference faculty arts lard softly watch tempest storm and on mate france feature cube oxo chopper

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such sly fewer computer didn't ice skates organ money endlessness december november fox programme bare figures convenience load crucifix glisters brum petal geranium perform mozart clash bid fearless cheshire finance wage spent verdict innocent minster sounds underground sprinted less premium ballet own possess have pets vanish stark conflict furious numbers cub nick theft steal thief robber stamen bull ring entry milk bottle help assist choral bach drum ban cowboy bracelet cubism corporal punishment edam cheque homo climb women valiant cheese fee

ran were examine lodgings fair bright crocus daffodil hyacinth let isosceles coins allowance invest loot walked strolled scaffolding thou edifice bond james arcade certainly amusement repetition public conveniences maker sapiens skating top base semibreves allow cylindrical auction apartment crime buses crap expenses mart infinity others architecture consider reconsider once upon a time between angry gentlemen pyramid glimmer fetched bent den tamer cop kennels steep hill men summit counterpoint bidder fairy tale unicorn dime cheddar cash neighbours york rescue thieve rink brahms nickel till

paths noun verb digs thee construction wolf pansy shining monotonous lass lad permit smashed flat due earn lily theirs retard mine punch for opposing ecstasy cogitate contemplate annoyed sect tigress tiger crooked chin eye shiner cats iris consumer communism merchandise peak mount floe bottom lid notes chief sculpture cost dollar felony triangle macaroni bill salary encountered gambling permission unkind site against think ponder courts gents ladies egypt vanity menstruation ant slope flower-pot space indian cent spend met mates old age

wink pox pronoun architect appear chemist careful lion dogs young custody price retail refund owed piggy bank gap not nice granted ours yours thine erected kith dong building jubilation ja no anti seem imagine legislate deed miles her sight roar class goods mountain everest climbing persons crowds backside boring symphony pulse ellipse prosperous dollars squaw compel national account buffalo pan friends wings structure meditate law black eye him obey command vision parents atheist belief leisure dustbin beethoven force micro constable trams pension

retreat retaliate truly believing consent ding opposed bones buttercup lioness antique rabble tuner piano forte cents famous poverty gent needy banks owe shilling kin only mind scarce joy yes slaughter solicitor lawyer barrister martial defend heavy indication order glad elated agent tulip god paternal sterling people mob accumulate county dull drab beat stretch kane coerce anthem small billion loan paid shillings horrid hothouse mercenary thrift leader his hers ancient new masses creator meeting spice unpleasant pleasure disobey part tiny

my concept indeed happiness column weighty skeleton compound pleased leo perforation deity abdicate roses keyboard straight parallel petite wagon prize saving nasty receipt economics worlds professor seeing squadron aye feeling do don't dancer fun social happy joyful daisy attack craving old aged almighty ageless worship rhythm sonata dim crowd dreary defeat arse citizen folk jumps dunce honk francs debt pence darwin repay erect lifting rare handsom calendar calculation turban entire whole farce line large gastric lonely trek uncommon big

somewhere ways destroy test laden roars primary elastic cleanse dipper evolution uphill sighted advance absent-minded nobody somebody idea means ping pong cabby taxi dispense sensation ear nelson celebration party mournful unhappy contentment unearth archaic ageing noon minus snowdon peer collect gather education half wicked dodgems brass heating central doubles badminton little flu ho shakespeare wealth packet grating pounds diffraction downhill sixpence upright imperative accordance cocktail cheerfulness gay contented lashes decrepit fellow demi india motors university campus lines expense stupid

anybody should sisters lobe sad hell kong judgement school quarter elephant accountant spades your their notion really actually tomb amnesia cab brothers set neither tory oh weight prawn miserable armed shovel age outdated divine hong headmasterfailure evil band triad tennis trunk tidy neat horn policeman stormy bob snooty crisp inspiration with gramme get-together groovy morose ammunition guns years spade dig plus lord leavers cars good-bye hello college pusher flog bars one triplet poison toot silly coin ounces inferior conservative huge strategy our thought check media mass kill occurs nor labour gram ton fornicate ridge arthur throne cole racquet unjust unfair this reaction nowhere boggle ought without free cannot shaker ago teacher pupil excavation era eyelid 10 heaven comprehensive grammar spelling success achievement darling goodbye association spoken decimal drugs bubbles two three trio wipe clean enormous riches snob peeler heathen pagan flip superior melancholy content rifles create defence chaos business tins orbit unity daft foolish bobby pennies weather

triste television judy that ideas examination reveal hounds happens within gunpowder make unload adult reign russia king lear costly dear word meaning thirty racket mucky bog potato flop whom arrival innocence legal rabbits slay rip ends lanky pray scales can grown plot orphan kid brought commandment borough humans classes prefect gazer pair of a kind four generation spotless rags loo foolhardy shopping list blight pin-stripe enemies tall sex glum napkin havoc husband actor beneficent rose bosom breast gazers dust hills mountains

guilt manufacture grown-up monarch martyr saint departure show indicate hares tear compulsory hike kneel tin enjoyment surely gender masturbation amends child lucky spouse pure cheap forty suds couple dwarf flush dirty filthy inner prosper hundred spud smith's frying what's plan solitude u tape hitch odds brief opener soul masturbating disorder 9 spoilt royalty queen wife dandelion number count good bad manners dale chaste soap cancerous growth five quartet massive million thousand notorious penny crisps farthing date grew each distaste

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everlasting sequence series unfinished memory womb dejected bastard fray annihilate bolognese drag once coronet chart geometry excellent coral possibly trains ridiculous income pieces shame meditation perpetual sufficientenough suggestion quo gladness month labyrinth chemical paradise hearing-aid spaghetti shoes glare epoch angels twice atlas goes polar bear greet greens wash devil trinity corral reef drug ugly elusive sell blows lavatory probably maybe known stands smuggle romantic strange even illegitimate eight 19 kids madam quinine starring he foreigners unknown senseless contraband

year shape bits sues suffice hence so mend illegitimacy ager boots forlorn upon a time group park nonsense sister vigour shrews oral therefore status longing odd weasel healer eternal socks lids ninety 20 clothes fashion fashionedhelper satan particle sentence nice phrase grotesque elopement recital affluence railways coons spending highest disgrace aah stanza adequate recall torn delight forgotten neuter stoat fierce envy nine charles panorama map comes banner sir apex tit pauper gravity she brother wogs per cent futile useless lowest

ben contraceptive ooh thus wordsworth positive couldn't homosexual satisfy jonathan vivid heels admit charming view panoramic garment broke geography contours jutland succour beautiful stuff flatten trivial fortitude immaterial harold wilson sadism masochism verse poem poet plenty negative release 1968 peculiar queer repair grieving kinky goliath march teen ferocious sneak confess avarice greed prince garments hinder monarchy storage washing mainland pores shade sun-tan prison methedrine pleasant metric hiss solar pilgrim gosh bonny unimportant incognito strength irrelevant

consist taming poetry elect opinion bountiful declare phallus let go unbound gratify erotica faire calcium modern greyhounds caress grow germanium poisonous breathtaking royal emblem history wed elan cell lovely unmarried system pretty luck golly faeces clyde agitate weakness grandpa rules statesmanpolitician finite prose ah nursery than saliva running 1969 liberal expect david protest optimism hope honest gloom togs pegs penniless flag intentions junction form jazz captive tyrant jail larger newton progress abuse trip excursion sanction unready unprepared grandma misuse

confirm consideration infinite transmit aft rhyme rhymes oppose symbol regret weird walking please thanks tacks lust savoir carried brows iniquity faith district cities towns venetian snake vista quarantine garb lessons flagpole union jackmode jewels graft skin lecture inmate improbably export chance treble muscle horrible stir shirts ties totally dogfish comprise regulations fore vote poll spit loth unusual maturity mid-way nursery school holy ghost tempo laundry dermis lotion prisoner warder bigger ski articles things boo insignificant twin outing rhodesia catfish

customs temper ripped apology sorry yearn opposite received pessimism wild pretender merry twenty locus regal questions molehill gaol objects possibility opportunity ablative dative beggars unemployed visible goodness thank you heeled quaint sin urban schoolroom rattle reptile wardrobe months hexagonal answers pensionsterribly give out convict tip violins stocking unlikely attractive leaps wholesale thoroughly completely follower disciple hoop nosy positively nisi merci thankful metres enquiries princess tricolour laundrette epidermis size knocks deltoid terrible awful

assume presume dole forgot gracious grateful signpost invisible stroke frank family individual coon patriotism octopus chest hemp penthouse hostage sputnik neath saves vale import la parker negativelyexcise surmise oops aches woo remembered suburb turkish anticipate masturbate wish glittering gleam reason tickle folks shooters mountaineeringmethod marry drawer power quadruped harpsichord glen giant choosers a daisy yards narcissus horrific prisoners valley

majority pains rather contrary personalstore private carbonate title motive sparkle lizard person reports snooker sari sense seventh suite satellite minority satiate unforgivable tame planning shimmer thrill long time polite wog prayer welcome virgin mushrooms shines fiendish sixth whip lash corrosion rust fiasco imprisonment warehouse no see well mannered stranger department excitement foreigner toadstools gleams Pajek

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 29

' Temporal networks / September 11 $ Steve Corman with collab- orators from Arizona State University transformed, using his Centering Resonance Anal- ysis (CRA), daily Reuters news (66 days) about September 11th into a temporal network of words coappearance. This network was a challange network for Viszards 2002 session. Pictures in SVG: 66 days.(SVG viwer) Every year (from 2002) we have at the Sunbelt conference a Viszards session presenting solutions of Viszards group to a visualizations of selected network or type of networks.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 30

' $

Example: Snyder and Kick World Trade The data are available as a Pajek’s project file SaKtrade.paj The network consists of trade relations (118 vertices, 515 arcs, 2116 edges). The source of the data is the paper: Snyder, David and Edward Kick (1979). The World System and World Trade: An Empirical Exploration of Conceptual Conflicts, Sociological Quaterly, 20,1, 23-36. The project file contains also the (sub)continents partition: 1 - Europe, 2 - North America, 3 - Latin America, 4 - South America, 5 - Asia, 6 - Africa, 7 - Oceania.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 31

' $ Draw / Partition

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tog dah lao lao mon

Draw/Draw Partition Layout/Energy/Kamada-Kawai/Free Layout/Energy/Fruchterman Reingold/2D

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 32

' $

Zoom in

Using right button on the mouse select the zoom area. To restore the standard view select Redraw.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 33

' $ Fruchterman Reingold / factor = 9

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

Layout/Energy/Fruchterman Reingold/3D

3D picture / King

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 34

' Matrix representation $

Pajek - shadow [0.00,1.00]

usa can cub hai dom jam tri mex gua hon els nic cos pan col ven ecu per bra bol par chi arg uru uki ire net bel lux fra swi spa por wge ege pol aus hun cze ita mat alb yug gre cyp bul rum usr fin swe nor den ice mli sen dah nau nir ivo gui upv lib sie gha tog cam nig gab car chd con zai uga ken bur rwa som eth saf maa mor alg tun liy sud irn tur irq egy syr leb jor isr sau yem kuw afg cha mon tai kod kor jap ind pak brm sri nep tha kmr lao vnd vnr mla phi ins aut nze usa can cub hai dom jam tri mex gua hon els nic cos pan col ven ecu per bra bol par chi arg uru uki ire net bel lux fra swi spa por wge ege pol aus hun cze ita mat alb yug gre cyp bul rum usr fin swe nor den ice mli sen dah nau nir ivo gui upv lib sie gha tog cam nig gab car chd con zai uga ken bur rwa som eth saf maa mor alg tun liy sud irn tur irq egy syr leb jor isr sau yem kuw afg cha mon tai kod kor jap ind pak brm sri nep tha kmr lao vnd vnr mla phi ins aut nze Partition/Make Hierarchy [Yes][No] Hierarchy/Make Permutation File/Network/Export Matrix to EPS/Using Permutation [SaKmatrix.EPS][No] GsView: Media/User Defined ... [1300 pt][1300 pt]

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 35

' Clustering $ Better network matrix reorderings can be obtained using clustering: Cluster/Create Complete Cluster [118] Operations/Dissimilarity*/d5 [1][SaKdendro.EPS] Hierarchy/Make Permutation [select network SaK.net] File/Network/Export Matrix to EPS/Using Permutation [SaKmatrix.EPS][No]

or blockmodeling.

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

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 36

' $ Clustering Pajek - Ward [0.00,135.13] Pajek - shadow [0.00,1.00]

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

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 37

' $ Reordering clustering

Pajek - shadow [0.00,1.00]

The order of clusters in a hier- uki fra wge jap net ita usa bel lux swe den archy is not ﬁxed and can be swi can nor spa irn irq pak ire aut hun isr sau changed. kuw aus fin por bra arg pol cze usr ege yug ind cha gre tur egy bul rum syr leb cyp ice tun cub liy mor alg nig uga ken eth brm tha sud sri gha kor vnr phi nze tai mla ins saf mex col uru per chi ven ecu lib dom zai jam tri pan sen ivo els cos gua hon nic car chd nau tog dah nir gab sie con hai gui mat bol par cam maa yem kod lao mon nep bur rwa vnd som afg mli upv alb kmr jor uki fra wge jap net ita usa bel lux swe den swi can nor spa irn irq pak ire aut hun isr sau kuw aus fin por bra arg pol cze usr ege yug ind cha gre tur egy bul rum syr leb cyp ice tun cub liy mor alg nig uga ken eth brm tha sud sri gha kor vnr phi nze tai mla ins saf mex col uru per chi ven ecu lib dom zai jam tri pan sen ivo els cos gua hon nic car chd nau tog dah nir gab sie con hai gui mat bol par cam maa yem kod lao mon nep bur rwa vnd som afg mli upv alb kmr jor We see the typical center–periphery structure.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 38

' $ Contraction of cluster Contraction of cluster C is called a graph G/C, in which all vertices of the cluster C are replaced by a single vertex, say c. More precisely: G/C = (V0, L0), where V0 = (V\ C) ∪ {c} and L0 consists of lines from L that have both end-vertices in V\ C. Beside these it contains also a ’star’ with the center c and: arc (v, c), if ∃p ∈ L, u ∈ C : p(v, u); or arc (c, v), if ∃p ∈ L, u ∈ C : p(u, v). There is a loop (c, c) in c if ∃p ∈ L, u, v ∈ C : p(u, v). In a network over graph G we have also to specify how are determined the values/weights in the shrunk part of the network. Usually as the sum or maksimum/minimum of the original values. Operations/Shrink Network/Partition

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' Contracted clusters – international trade $

Pajek - shadow [0.00,1.00]

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

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

n(Ci,Cj ) w(Ci,Cj ) = n(Ci) · n(Cj )

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' $

Computing the weights File / Pajek Project File / Read [SaKtrade.paj] Net / Transform / Remove / Loops [No] Net / Transform / Edges -> Arcs [No] Operations / Shrink Network / Partition [1][0] 1 2 3 4 5 6 7 ------#usa 1. 2 30 13 56 42 45 4 #cub 2. 30 74 25 196 20 37 12 #per 3. 12 28 33 124 16 36 5 #uki 4. 55 217 130 695 427 483 41 #mli 5. 42 8 14 406 122 117 11 #irn 6. 43 37 43 444 142 307 30 #aut 7. 4 4 5 39 9 30 2 Partition / Make Permutation [select partition (Sub)continents] Operations / Functional Composition / Partition*Permutation Partition / Count Partition / Make Vector Operations / Vector / Put loops

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' . . . Computing the weights $ In Pajek sequences of

1 2 3 4 5 6 7 commands can be com------#usa 1. 4 30 13 56 42 45 4 #cub 2. 30 89 25 196 20 37 12 bined into a macro com- #per 3. 12 28 40 124 16 36 5 #uki 4. 55 217 130 723 427 483 41 mand using #mli 5. 42 8 14 406 155 117 11 #irn 6. 43 37 43 444 142 337 30 Macro / Record #aut 7. 4 4 5 39 9 30 4 count 2 15 7 29 33 30 2 and Vector / Create Identity Vector [7] [select as second vector From partition ...] Macro / Recording... Vectors / Divide First by Second Operations / Vector / Vector # Network / input The macro can be acti- Operations / Vector / Vector # Network / output [edit partition - rename vertices] vated by 1 2 3 4 5 6 7 ------Macro / Play N.Am 1. 1.00 1.00 0.93 0.97 0.64 0.75 1.00 L.Am 2. 1.00 0.40 0.24 0.45 0.04 0.08 0.40 S.Am 3. 0.86 0.27 0.82 0.61 0.07 0.17 0.36 The sequence for com- Euro 4. 0.95 0.50 0.64 0.86 0.45 0.56 0.71 Afri 5. 0.64 0.02 0.06 0.42 0.14 0.12 0.17 puting the weights Asia 6. 0.72 0.08 0.20 0.51 0.14 0.37 0.50 Ocea 7. 1.00 0.13 0.36 0.67 0.14 0.50 1.00 w(Ci,Cj) is saved in the macro weights.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 42

' Subgraph $

A subgraph H = (V0, L0) of a given graph G = (V, L) is a graph which set of lines is a subset of set of lines of G, L0 ⊆ L, its vertex set is a subset of set of vertices of G, V0 ⊆ V, and it contains all end-vertices of L0. A subgraph can be induced by a given subset of vertices or lines. It is a spanning subgraph iff V0 = V.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 43

'Cut-out – induced subgraph: Snyder and Kick – Africa $

sie

nir gab

chd ivo maa upv gui mor cam mli

sen nig

nau gha tun con lib

saf

liy egy tog alg

zai sud dah car

uga som

ken eth

rwa

bur

Operations/Extract from Network/Partition [6]

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 44

' Cut-out: Snyder and Kick $ Latin America : South America

cos

ecu per gua col bra els mex

jam pan chi par

hon ven arg bol hai dom uru nic tri

cub

Operations/Extract from Network/Partition [3,4] Operations/Transform/Remove lines/Inside clustersPajek [3,4] The vertices can be manually put on a rectangular grid produced by [Draw] Move/Grid

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 45

' $ Important vertices in network It seems that the most important distinction between different vertex indices is based on the view/decision whether the network is considered directed or undirected. This gives us two main types of indices:

• directed case: measures of importance; with two subgroups: measures of inﬂuence, based on out-going arcs; and measures of support, based on incoming arcs;

• undirected case: measures of centrality, based on all lines.

For undirected networks all three types of measures coincide. If we change the direction of all arcs (replace the relation with its inverse relation) the measure of inﬂuence becomes a measure of support, and vice versa.

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' $

. . . Important vertices in network The real meaning of measure of importance depends on the relation described by a network. For example the most ’important’ person for the relation ’ doesn’t like to work with ’ is in fact the least popular person. Removal of an important vertex from a network produces a substantial change in structure/functioning of the network.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 47

' $ Closeness Most indices are based on the distance d(u, v) between vertices in a network N = (V, L). Two such indices are

radius r(v) = maxu∈V d(v, u) P total closeness S(v) = u∈V d(v, u) These two indices are measures of inﬂuence – to get measures of support we have to replace in deﬁnitions d(u, v) with d(v, u).

If the network is not strongly connected rmax and Smax equal ∞. Sabidussi (1966) introduced a related measure 1/S(v); or in its normalized form n − 1 closeness cl(v) = P u∈V d(v, u)

D = maxu,v∈V d(v, u) is called the diameter of network.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 48

' Betweeness $ Important are also the vertices that can control the information ﬂow in the network. If we assume that this ﬂow uses only the shortest paths (geodesics) we get a measure of betweeness (Anthonisse 1971, Freeman 1977)

1 X gu,t(v) b(v) = (n − 1)(n − 2) gu,t u,t∈V:gu,t>0 u6=v,t6=v,u6=t

where gu,t is the number of geodesics from u to t; and gu,t(v) is the number of those among them that pass through vertex v.

If we know matrices [du,v] and [gu,v] we can determine also gu,v(t) by:   gu,t · gt,v du,t + dt,v = du,v gu,v(t) =  0 otherwise

For computation of geodesic matrix see Brandes.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 49

' Hubs and authorities $ To each vertex v of a network N = (V, L) we assign two values: quality of

its content (authority) xv and quality of its references (hub) yv. A good authority is selected by good hubs; and good hub points to good authorities (see Klienberg). X X xv = yu and yv = xu u:(u,v)∈L u:(v,u)∈L Let W be a matrix of network N and x and y authority and hub vectors. Then we can write these two relations as x = WT y and y = Wx. We start with y = [1, 1,..., 1] and then compute new vectors x and y. After each step we normalize both vectors. We repeat this until they stabilize. We can show that this procedure converges. The limit vector x∗ is the principal eigen vector of matrix WT W; and y∗ of matrix WWT .

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 50

' $

. . . Hubs and authorities Similar procedures are used in search engines on the web to evaluate the importance of web pages. PageRank, PageRank / Google, HITS / AltaVista, SALSA, teorija. Examples: Krebs, Krempl.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 51

' Clustering coefﬁcient $ Let G = (V, E) be simple undirected graph. Clustering in vertex v is usually measured as a quotient between the number of lines in subgraph G1(v) = G(N 1(v)) induced by the neighbors of vertex v and the number of lines in the complete graph on these vertices:  1  2|L(G (v))|  deg(v) > 1 C(v) = deg(v)(deg(v) − 1)   0 otherwise

We can consider also the size of vertex neighborhood by the following correction deg(v) C (v) = C(v) 1 ∆ where ∆ is the maximum degree in graph G. This measure attains its largest value in vertices that belong to an isolated clique of size ∆.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 52

' $

Dense groups Several notions were proposed in attempts to formally describe dense groups in graphs.

Clique of order k is a maximal complete subgraph (isomorphic to Kk), k ≥ 3. s-plexes, LS sets, lambda sets, cores, . . . For all of them, except for cores, it turned out that they are difﬁcult to detemine.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 53

' $ Cores and generalized cores The notion of core was introduced by Seidman in 1983. Let G = (V, E) be a graph. A subgraph H = (W, E|W ) induced by the set W is a k-core or a core of order k iff

∀v ∈ W : degH(v) ≥ k, and H is a maximal subgraph with this property. The core of maximum order is also called the main core. The core number of vertex v is the highest order of a core that contains this vertex. The degree deg(v) can be: in-degree, out-degree, in-degree + out-degree, etc., determining different types of cores.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 54

' $ Properties of cores From the ﬁgure, representing 0, 1, 2 and 3 core, we can see the following properties of cores:

• The cores are nested: i < j =⇒ Hj ⊆ Hi • Cores are not necessarily connected subgraphs.

An efﬁcient algorithm for determining the cores hierarchy is based on the following property:

If from a given graph G = (V, E) we recursively delete all vertices, and edges incident with them, of degree less than k, the remaining graph is the k-core.

For details see the paper.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 55

' $ 6-core of Krebs Internet industries

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 56

' Generalized cores $ The notion of core can be generalized to networks. Let N = (V, E, w) be a network, where G = (V, E) is a graph and w : E → R is a function assigning values to edges. A vertex property function on N, or a p- function for short, is a function p(v, U), v ∈ V, U ⊆ V with real values.

Let NU (v) = N(v) ∩ U. Besides degrees, here are some examples of p-functions:

X + pS(v, U) = w(v, u), where w : E → R0

u∈NU (v)

pM (v, U) = max w(v, u), where w : E → R u∈NU (v)

pk(v, U) = number of cycles of length k through vertex v in (U, E|U)

The subgraph H = (C, E|C) induced by the set C ⊆ V is a p-core at level t ∈ R iff ∀v ∈ C : t ≤ p(v, C) and C is a maximal such set.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 57

' Generalized cores algorithm $ The function p is monotone iff it has the property

C1 ⊂ C2 ⇒ ∀v ∈ V :(p(v, C1) ≤ p(v, C2))

The degrees and the functions pS, pM and pk are monotone. For a monotone function the p-core at level t can be determined, as in the ordinary case, by successively deleting vertices with value of p lower than t; and the cores on different levels are nested

t1 < t2 ⇒ Ht2 ⊆ Ht1

The p-function is local iff p(v, U) = p(v, NU (v)) .

The degrees, pS and pM are local; but pk is not local for k ≥ 4. For a local p-function an O(m max(∆, log n)) algorithm for determining the p-core

levels exists, assuming that p(v, NC (v)) can be computed in O(degC (v)). For details see the paper.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 58

' $ pS-core at level 46 of Geombib network

E.Arkin

J.Mitchell I.Tollis A.Garg M.Bern L.Vismara D.Eppstein

G.diBattista M.Goodrich R.Tamassia

G.Liotta D.Dobkin S.Suri J.O'Rourke J.Vitter

J.Hershberger

B.Chazelle F.Preparata B.Aronov R.Seidel L.Guibas J.Snoeyink H.Edelsbrunner M.Sharir P.Agarwal R.Pollack J.Pach D.Halperin P.Gupta

M.Smid E.Welzl R.Janardan M.Overmars P.Bose J.Boissonnat M.vanKreveld O.Devillers J.Matousek J.Majhi M.Yvinec C.Yap M.deBerg J.Schwerdt O.Schwarzkopf G.Toussaint M.Teillaud

J.Czyzowicz J.Urrutia

C.Icking

R.Klein

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 59

' $ 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 Layout/Energy/Kamada-Kawai Options/Values of lines/Similarities Layout/Energy/Kamada-Kawai Operations/Extract from Network/Partition [21] Draw Layout/Energy/Kamada-Kawai Options/Values of lines/Forget Layout/Energy/Kamada-Kawai [select Geom.net] Net/Vector/PCore/Sum/All Info/Vector Vector/Make Partition/by Intervals/Selected Thresholds [45] Info/Partition Operations/Extract from Network/Partition [2] Draw Options/Values of lines/Similarities Layout/Energy/Fruchterman-Reingold

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 60

' $ 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.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 61

' $ 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 after- ward these solutions combined into ﬁnal solution.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 62

' 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).

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 63

' $ 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]

b k i e c h j a g f g l d a e #a b c

f l d h g f i k

k j #e i i e h j l a b c d g f k

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 64

' 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) = (V0, L(V0), p), determined by the set

V0 = {v ∈ V : p(v) ≥ t}

and L(V0) is the set of lines from L that have both endpoints in V0.

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.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 65

' Vertex-cut: Krebs Internet Industries, core=6 $

Lucent CommerceOne

UPS

SAP

Motorola CIBER Yahoo! Ariba EMC Oracle Peoplesoft Sun FoundryNetworks EDS divine WebMethods IBM E.piphany HP Siebel BMCSoftware Cisco Novell Intel AT&T ExodusComm KPNQwest Vignette CacheFlow

Loudcloud

Compaq RedHat RealNetworks 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.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L %

Pajek V. Batagelj: Analysis and visulization of large networks with Pajek 66

' $ Line-cut: Krebs Internet Industries, w3 ≥ 5

Motorola CIBER Ariba Oracle Sun FoundryNetworks IBM E.piphany HP Cisco Intel AT&T KPNQwest

KPMG Compaq RealNetworks Dell

Akamai MSFT Inktomi

AOL

TerraLycos

FoundryNetworks RealNetworks

KPMG

TerraLycos AT&T Pajek Compaq AOL Inktomi

MSFT Dell Sun HP

Akamai IBM Intel Cisco KPNQwest

Motorola Oracle Ariba CIBER

E.piphany

Pajek

Pajek Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 67

' Cuts / Pajek commands $ Vertex-cut: File/Pajek Project File/Read [Krebs.paj] Net/Partitions/Core/All Partition/Make Vector 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 Layout/Energy/Kamada-Kawai 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 Partition/Make Vector 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 Layout/Energy/Kamada-Kawai

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 68

' $ 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.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 69

' Citation weights $

POGGIO-T-1975-V19-P201

KOHONEN-T-1976-V21-P85 The citation network analysis

KOHONEN-T-1976-V22-P159 ANDERSON-JA-1977-V84-P413 started in 1964 with the paper of KOHONEN-T-1977-V2-P1065 PFAFFELHUBER-E-1975-V18-P217 COOPER-LN-1979-V33-P9 AMARI-SI-1977-V26-P175 WOOD-CC-1978-V85-P582 PALM-G-1980-V36-P19 Garﬁeld et al. In 1989 Hummon BIENENSTOCK-EL-1982-V2-P32 SUTTON-RS-1981-V88-P135 HOPFIELD-JJ-1982-V79-P2554 AMARI-S-1980-V42-P339 and Doreian proposed three ANDERSON-JA-1983-V13-P799 KOHONEN-T-1982-V43-P59

KNAPP-AG-1984-V10-P616 indices – weights of arcs that are MCCLELLAND-JL-1985-V114-P159 proportional to the number of CARPENTER-GA-1987-V37-P54 different source-sink paths passing GROSSBERG-S-1987-V11-P23 HECHTNIELSEN-R-1987-V26-P1892

GROSSBERG-S-1988-V1-P17 HECHTNIELSEN-R-1987-V26-P4979 through the arc. We developed SEJNOWSKI-TJ-1988-V241-P1299 HECHTNIELSEN-R-1988-V1-P131 algorithms to efﬁciently compute BROWN-TH-1988-V242-P724 KOHONEN-T-1990-V78-P1464

BROWN-TH-1990-V13-P475 these indices.

TREVES-A-1991-V2-P371 HASSELMO-ME-1994-V7-P13 Main subnetwork (arc cut at level HASSELMO-ME-1993-V16-P218

HASSELMO-ME-1994-V14-P3898 0.007) of the SOM (selforganizing BARKAI-E-1994-V72-P659 maps) citation network (4470 ver- HASSELMO-ME-1995-V67-P1

HASSELMO-ME-1995-V15-P5249 tices, 12731 arcs). See paper. GLUCK-MA-1997-V48-P481

ASHBY-FG-1999-V6-P363

Pajek

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 70

' k-rings $ A k-ring is a simple closed chain of length k. Using k-rings we can deﬁne a weight of edges as

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−2-

edge 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.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 71

' $

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).

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 72

' $ Edge-cut at level 16 of triangular network of Erdos˝ 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.

ARONOV, BORIS LINIAL, NATHAN PACH, JANOS POLLACK, RICHARD M. HENNING, MICHAEL A. without Erdos,˝ FRANKL, PETER SPENCER, JOEL H. ALON, NOGA OELLERMANN, ORTRUD R. LOVASZ, LASZLO n = 6926, KOMLOS, JANOS GODDARD, WAYNE D. FUREDI, ZOLTAN TUZA, ZSOLT ALAVI, YOUSEF BABAI, LASZLO SZEMEREDI, ENDRE CHARTRAND, GARY m = 11343 BOLLOBAS, BELA HARARY, FRANK AJTAI, MIKLOS KUBICKI, GRZEGORZ SCHWENK, ALLEN JOHN

RODL, VOJTECH NESETRIL, JAROSLAV ROSA, ALEXANDER GYARFAS, ANDRAS SCHELP, RICHARD H. STINSON, DOUGLAS ROBERT LEHEL, JENO CHEN, GUANTAO MULLIN, RONALD C. FAUDREE, RALPH J. COLBOURN, CHARLES J. JACOBSON, MICHAEL S. PHELPS, KEVIN T.

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' $

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.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 74

'Edge-cut at level 11 of transitive network of ODLIS $ dictionary graph

serial publication American Library Directory transaction log periodical suggestion box review frequency charge series issue library colophon call number Library Literature

journal layout fixed location publishing printing blanket order American Library Association /ALA/ title page Books in Print /BIP/ vendor homepage International Standard Book Number /ISBN/ entry round table published price dummy librarian condition edition catalog plate fiction Oak Knoll bibliographic record imprint abstract dust jacket work book bibliography half-title editor

library binding title table of contents /TOC/ index invoice new book text endpaper copyright book size parts of a book front matter collation publisher binding folio

cover page

Pajek Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 75

' 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. See details.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 76

' Islands - Reuters terror news $

airline united_airlines plant

american_airlines attendant Using CRA S. Corman nuclear pakistani herald flight pilot power train and K. Dooley produced arabic-language organization boston weapon manual saudi congressional the Reuters terror news contain service newspaper car passenger member chemical bin_laden network that is based on saudi-born leader rental uniform

inhale necessary all stories released dur- scare dissident taliban suspect firefighter jet fbi call afghanistan airport police knife-wielding agent ing 66 consecutive days by man anthrax world force skin thursday commercial pakistan phone case official airliner officer hijacker special the news agency Reuters arab support terrorism war cell trace hijack country united_states embassy concerning the September jonn deadly business help mighty plane wednesday twin week space strike east 11 attack on the US. The plea attack act military specialist 110-story edmund world_trade_ctr headquarters pentagon terrorist the_worst apparent action vertices of a network are air cheyenne north tower washington morning africa louisiana tuesday south anti-american words (terms); there is an news late terror wyoming city base offutt florida new_york group responsibility air_force mayor edge between two words pfc conference american mayor_giuliani nebraska barksdale team landmark exchange debris iff they appear in the same miss people

dept stock effort text unit. The weight of an rescue thousand market center edward aid buildng fire financial toll edge is its frequency. It has worker smoke plaugher large

postal emergency n = 13332 vertices and chief district death state m = 243447 edges.

Pajek

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 77

' $

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 29670 9288 3966 1827 997 578 362 250 [11] 190 125 104 71 47 37 36 33 21 23 [21] 17 16 8 7 13 10 10 5 5 5 [31] 12 3 7 3 3 3 2 6 6 2 [41] 1 3 4 1 5 2 1 1 1 1 [51] 2 3 3 2 0 0 0 0 0 1 [61] 0 0 0 0 1 0 0 2 0 0 [71] 0 0 1 1 0 0 0 1 0 0 [81] 2 0 0 0 0 1 2 0 0 7

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 78

' IslandTheme size size distribution distribution $

●

● 10000 ●

●

● ●

freq ● ● ● ●

100 ● ● ●●● ●● ●● ● ● ●● ● ● ● ● ●● ●●● ● ● ●●●● ● ●● ● ● ● ●● ● ● ●

● ●●●●● ● ● ●●● ● 1

2 5 10 20 50 100

size

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 79

' Main path and main island of Patents $

5855814 4456712

5683624 5555116

5543077 5124824 5171469 5283677

5374374 5016988 5122295 5016989 5308538

4957349 4877547 4820839 4832462 5171469

5122295 4770503 4795579 4797228 4752414 4721367

4877547 4709030 4719032 4695131 4710315 4713197 4704227 4657695

4797228 4630896 4659502 4621901

4710315 4583826 4510069 4558151 4550981 4659502

4526704 4502974 4514044 4550981

4526704 4460770 4480117 4472293 4472592 4455443

4472293 4419263 4422951

4422951 4415470 4400293 4386007

4386007 4349452 4368135 4340498 4340498

4387039 4387038 4293434 4290905 4361494 4302352 4330426 4357078 4302352

4229315 4195916 4229315 4261652

4149413 4202791 4149413 4198130

4082428 4154697 4113647 4130502 4032470 4083797 4082428 4118335

4011173 4013582 4029595 4077260 4017416 3975286 4011173 4000084 3960752

3954653 3947375 3960752 3876286 3872140 3881806

2544659 3675987 3731986 3795436 3891307 3697150 3636168 3767289 3666948 3322485 3773747 3796479 3795436 2682562 3691755

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' $

Liquid crystal display

Table 1: Patents on the liquid-crystal display Table 2: Patents on the liquid-crystal display Table 3: Patents on the liquid-crystal display

patent date author(s) and title patent date author(s) and title patent date author(s) and title 2544659 Mar 13, 1951 Dreyer. Dichroic light-polarizing sheet and the like and the 4083797 Apr 11, 1978 Oh. Nematic liquid crystal compositions 4514044 Apr 30, 1985 Gunjima, et al. 1-(Trans-4-alkylcyclohexyl)-2-(trans-4’-(p-sub formation and use thereof 4113647 Sep 12, 1978 Coates, et al. Liquid crystalline materials stituted phenyl) cyclohexyl)ethane and liquid crystal mixture 2682562 Jun 29, 1954 Wender, et al. Reduction of aromatic carbinols 4118335 Oct 3, 1978 Krause, et al. Liquid crystalline materials of reduced viscosity 4526704 Jul 2, 1985 Petrzilka, et al. Multiring liquid crystal esters 3322485 May 30, 1967 Williams. Electro-optical elements utilazing an organic 4130502 Dec 19, 1978 Eidenschink, et al. Liquid crystalline cyclohexane derivatives 4550981 Nov 5, 1985 Petrzilka, et al. Liquid crystalline esters and mixtures nematic compound 4149413 Apr 17, 1979 Gray, et al. Optically active liquid crystal mixtures and 4558151 Dec 10, 1985 Takatsu, et al. Nematic liquid crystalline compounds 3636168 Jan 18, 1972 Josephson. Preparation of polynuclear aromatic compounds liquid crystal devices containing them 4583826 Apr 22, 1986 Petrzilka, et al. Phenylethanes 3666948 May 30, 1972 Mechlowitz, et al. Liquid crystal termal imaging system 4154697 May 15, 1979 Eidenschink, et al. Liquid crystalline hexahydroterphenyl 4621901 Nov 11, 1986 Petrzilka, et al. Novel liquid crystal mixtures having an undisturbed image on a disturbed background derivatives 4630896 Dec 23, 1986 Petrzilka, et al. Benzonitriles 3675987 Jul 11, 1972 Rafuse. Liquid crystal compositions and devices 4195916 Apr 1, 1980 Coates, et al. Liquid crystal compounds 4657695 Apr 14, 1987 Saito, et al. Substituted pyridazines 3691755 Sep 19, 1972 Girard. Clock with digital display 4198130 Apr 15, 1980 Boller, et al. Liquid crystal mixtures 4659502 Apr 21, 1987 Fearon, et al. Ethane derivatives 3697150 Oct 10, 1972 Wysochi. Electro-optic systems in which an electrophoretic- 4202791 May 13, 1980 Sato, et al. Nematic liquid crystalline materials 4695131 Sep 22, 1987 Balkwill, et al. Disubstituted ethanes and their use in liquid like or dipolar material is dispersed throughout a liquid 4229315 Oct 21, 1980 Krause, et al. Liquid crystalline cyclohexane derivatives crystal materials and devices crystal to reduce the turn-off time 4261652 Apr 14, 1981 Gray, et al. Liquid crystal compounds and materials and 4704227 Nov 3, 1987 Krause, et al. Liquid crystal compounds 3731986 May 8, 1973 Fergason. Display devices utilizing liquid crystal light devices containing them 4709030 Nov 24, 1987 Petrzilka, et al. Novel liquid crystal mixtures modulation 4290905 Sep 22, 1981 Kanbe. Ester compound 4710315 Dec 1, 1987 Schad, et al. Anisotropic compounds and liquid crystal 3767289 Oct 23, 1973 Aviram, et al. Class of stable trans-stilbene compounds, 4293434 Oct 6, 1981 Deutscher, et al. Liquid crystal compounds mixtures therewith some displaying nematic mesophases at or near room 4302352 Nov 24, 1981 Eidenschink, et al. Fluorophenylcyclohexanes, the preparation ◦ 4713197 Dec 15, 1987 Eidenschink, et al. Nitrogen-containing heterocyclic compounds temperature and others in a range up to 100 C thereof and their use as components of liquid crystal dielectrics 4719032 Jan 12, 1988 Wachtler, et al. Cyclohexane derivatives 3773747 Nov 20, 1973 Steinstrasser. Substituted azoxy benzene compounds 4330426 May 18, 1982 Eidenschink, et al. Cyclohexylbiphenyls, their preparation and 4721367 Jan 26, 1988 Yoshinaga, et al. Liquid crystal device 3795436 Mar 5, 1974 Boller, et al. Nematogenic material which exhibit the Kerr use in dielectrics and electrooptical display elements 4752414 Jun 21, 1988 Eidenschink, et al. Nitrogen-containing heterocyclic compounds effect at isotropic temperatures 4340498 Jul 20, 1982 Sugimori. Halogenated ester derivatives 4770503 Sep 13, 1988 Buchecker, et al. Liquid crystalline compounds 3796479 Mar 12, 1974 Helfrich, et al. Electro-optical light-modulation cell 4349452 Sep 14, 1982 Osman, et al. Cyclohexylcyclohexanoates 4795579 Jan 3, 1989 Vauchier, et al. 2,2’-difluoro-4-alkoxy-4’-hydroxydiphenyls and utilizing a nematogenic material which exhibits the Kerr 4357078 Nov 2, 1982 Carr, et al. Liquid crystal compounds containing an alicyclic their derivatives, their production process and effect at isotropic temperatures ring and exhibiting a low dielectric anisotropy and liquid their use in liquid crystal display devices 3872140 Mar 18, 1975 Klanderman, et al. Liquid crystalline compositions and crystal materials and devices incorporating such compounds 4797228 Jan 10, 1989 Goto, et al. Cyclohexane derivative and liquid crystal method 4361494 Nov 30, 1982 Osman, et al. Anisotropic cyclohexyl cyclohexylmethyl ethers composition containing same 3876286 Apr 8, 1975 Deutscher, et al. Use of nematic liquid crystalline substances 4368135 Jan 11, 1983 Osman. Anisotropic compounds with negative or positive 4820839 Apr 11, 1989 Krause, et al. Nitrogen-containing heterocyclic esters 3881806 May 6, 1975 Suzuki. Electro-optical display device DC-anisotropy and low optical anisotropy 4832462 May 23, 1989 Clark, et al. Liquid crystal devices 3891307 Jun 24, 1975 Tsukamoto, et al. Phase control of the voltages applied to 4386007 May 31, 1983 Krause, et al. Liquid crystalline naphthalene derivatives 4877547 Oct 31, 1989 Weber, et al. Liquid crystal display element opposite electrodes for a cholesteric to nematic phase 4387038 Jun 7, 1983 Fukui, et al. 4-(Trans-4’-alkylcyclohexyl) benzoic acid 4957349 Sep 18, 1990 Clerc, et al. Active matrix screen for the color display of transition display 4’”-cyano-4”-biphenylyl esters television pictures, control system and process for producing 3947375 Mar 30, 1976 Gray, et al. Liquid crystal materials and devices 4387039 Jun 7, 1983 Sugimori, et al. Trans-4-(trans-4’-alkylcyclohexyl)-cyclohexane said screen 3954653 May 4, 1976 Yamazaki. Liquid crystal composition having high dielectric carboxylic acid 4’”-cyanobiphenyl ester 5016988 May 21, 1991 Iimura. Liquid crystal display device with a birefringent anisotropy and display device incorporating same 4400293 Aug 23, 1983 Romer, et al. Liquid crystalline cyclohexylphenyl derivatives compensator 3960752 Jun 1, 1976 Klanderman, et al. Liquid crystal compositions 4415470 Nov 15, 1983 Eidenschink, et al. Liquid crystalline fluorine-containing 5016989 May 21, 1991 Okada. Liquid crystal element with improved contrast and 3975286 Aug 17, 1976 Oh. Low voltage actuated field effect liquid crystals cyclohexylbiphenyls and dielectrics and electro-optical display brightness compositions and method of synthesis elements based thereon 5122295 Jun 16, 1992 Weber, et al. Matrix liquid crystal display 4000084 Dec 28, 1976 Hsieh, et al. Liquid crystal mixtures for electro-optical 4419263 Dec 6, 1983 Praefcke, et al. Liquid crystalline cyclohexylcarbonitrile 5124824 Jun 23, 1992 Kozaki, et al. Liquid crystal display device comprising a display devices derivatives retardation compensation layer having a maximum principal 4011173 Mar 8, 1977 Steinstrasser. Modified nematic mixtures with 4422951 Dec 27, 1983 Sugimori, et al. Liquid crystal benzene derivatives refractive index in the thickness direction positive dielectric anisotropy 4455443 Jun 19, 1984 Takatsu, et al. Nematic halogen Compound 5171469 Dec 15, 1992 Hittich, et al. Liquid-crystal matrix display 4013582 Mar 22, 1977 Gavrilovic. Liquid crystal compounds and electro-optic 4456712 Jun 26, 1984 Christie, et al. Bismaleimide triazine composition 5283677 Feb 1, 1994 Sagawa, et al. Liquid crystal display with ground regions devices incorporating them 4460770 Jul 17, 1984 Petrzilka, et al. Liquid crystal mixture between terminal groups 4017416 Apr 12, 1977 Inukai, et al. P-cyanophenyl 4-alkyl-4’-biphenylcarboxylate, 4472293 Sep 18, 1984 Sugimori, et al. High temperature liquid crystal substances of 5308538 May 3, 1994 Weber, et al. Supertwist liquid-crystal display method for preparing same and liquid crystal compositions four rings and liquid crystal compositions containing the same 5374374 Dec 20, 1994 Weber, et al. Supertwist liquid-crystal display using same 4472592 Sep 18, 1984 Takatsu, et al. Nematic liquid crystalline compounds 5543077 Aug 6, 1996 Rieger, et al. Nematic liquid-crystal composition 4029595 Jun 14, 1977 Ross, et al. Novel liquid crystal compounds and electro-optic 4480117 Oct 30, 1984 Takatsu, et al. Nematic liquid crystalline compounds 5555116 Sep 10, 1996 Ishikawa, et al. Liquid crystal display having adjacent devices incorporating them 4502974 Mar 5, 1985 Sugimori, et al. High temperature liquid-crystalline ester electrode terminals set equal in length 4032470 Jun 28, 1977 Bloom, et al. Electro-optic device compounds 5683624 Nov 4, 1997 Sekiguchi, et al. Liquid crystal composition 4077260 Mar 7, 1978 Gray, et al. Optically active cyano-biphenyl compounds and 4510069 Apr 9, 1985 Eidenschink, et al. Cyclohexane derivatives 5855814 Jan 5, 1999 Matsui, et al. Liquid crystal compositions and liquid crystal liquid crystal materials containing them display elements 4082428 Apr 4, 1978 Hsu. Liquid crystal composition and method

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 81

'Islands – The Edinburgh Associative Thesaurus $

n = 23219, m = 325624, transitivity weight

HAPPEN JUST PAYMENT RECEIPT STOLE YET PAID NOTWITHSTANDING MONIES UNPAID PAY AGAIN ALREADY COINS THRIFTY MONEY INCREASE DEALER HAPPENED LOOT NEVERTHELESS NOW DEFICIT THRIFT PROPERTY MORE MONEY OFTEN BELIEVE OFFER PROVIDE BUT REPAY WHY NO PLEASE AS SOON NOT REFUSE ANYWAY THEREFORE PROBABLY

MEANWHILE SOMETIME COULD

POWERFUL

INHUMAN BOSS

STUDYING LECTURER CHAIRMAN RESPONSIBLE TEACHER ELEGANCE PROFESSION MAN TEACHING HAIRY ENGINEERING

SCHOOL LEARNING MYSTERIOUS NICE EDUCATION CHARM BELOVED

HOMEWORK WORK

ATTRACTIVE TRAINING LOVE GIRL LECTURES DELIGHTFUL SCIENCE LESSONS FLIRT MATHS SCIENTIFIC STUDY KINDNESS BEAUTIFUL LOVELY RESEARCH ADORABLE

ACTIVITY SHAPELY

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 82

' $

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] ...

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 83

'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.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 84

' 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.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 85

' $ 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).

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 86

'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

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 87

' $ (247,2)-core and (27,22)-core

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 Taylor, Scott (IX) Vaziri, Kazrow 'WWF Smackdown!' Van Dam, Rob Valentine, Greg Vailahi, Sione Tunney, Jack Traylor, Raymond Van Dam, Rob Tenta, John Taylor, Terry (IV) Taylor, Scott (IX) 'WWE Velocity' Tanaka, Pat Tajiri, Yoshihiro Szopinski, Terry Matthews, Darren (II) Storm, Lance Steiner, Scott Steiner, Rick (I) Solis, Mercid Snow, Al 'Sunday Night Heat' Smith, Davey Boy Slaughter, Sgt. LoMonaco, Mark Simmons, Ron (I) Shinzaki, Kensuke Shamrock, Ken Senerca, Pete Scaggs, Charles Savage, Randy 'Raw Is War' Hughes, Devon Saturn, Perry Sags, Jerry Ruth, Glen Runnels, Dustin Rude, Rick Rougeau, Raymond Rougeau Jr., Jacques WWF Vengeance Huffman, Booker Rotunda, Mike Ross, Jim (III) Rock, The Roberts, Jake (II) Rivera, Juan (II) Rhodes, Dusty (I) Heyman, Paul Reso, Jason Reiher, Jim WWF Unforgiven Reed, Bruce (II) Race, Harley Prichard, Tom Powers, Jim (IV) Hebner, Earl Poffo, Lanny Plotcheck, Michael Piper, Roddy Pfohl, Lawrence WWF Rebellion Pettengill, Todd Peruzovic, Josip Palumbo, Chuck (I) McMahon, Stephanie Page, Dallas Ottman, Fred Orton, Randy Okerlund, Gene WWF No Way Out Nowinski, Chris Norris, Tony (I) Keibler, Stacy Nord, John Neidhart, Jim Nash, Kevin (I) Muraco, Don Morris, Jim (VII) Morley, Sean WWF No Mercy Wight, Paul Morgan, Matt (III) Mooney, Sean (I) Moody, William (I) Miller, Butch Mero, Marc McMahon, Vince McMahon, Shane Simmons, Ron (I) Survivor Series Matthews, Darren (II) WWF Judgment Day Martin, Andrew (II) Martel, Rick Marella, Robert Marella, Joseph A. Manna, Michael Senerca, Pete Lothario, Jose Long, Teddy LoMonaco, Mark WWF Insurrextion Lockwood, Michael Levy, Scott (III) Levesque, Paul Michael Lesnar, Brock Ross, Jim (III) Leslie, Ed Leinhardt, Rodney Layfield, John Lawler, Jerry WWF Backlash Lawler, Brian (II) Laurinaitis, Joe Rock, The Laughlin, Tom (IV) Lauer, David (II) Knobs, Brian Knight, Dennis (II) Killings, Ron Kelly, Kevin (VIII) WWE Wrestlemania XX Reso, Jason Keirn, Steve Jones, Michael (XVI) Johnson, Ken (X) Jericho, Chris Jarrett, Jeff (I) Jannetty, Marty James, Brian (II) WWE Wrestlemania X-8 McMahon, Vince Jacobs, Glen Jackson, Tiger Hyson, Matt Hughes, Devon Huffman, Booker Howard, Robert William McMahon, Shane Howard, Jamie Houston, Sam WWE Vengeance Horowitz, Barry Horn, Bobby Hollie, Dan Hogan, Hulk Hickenbottom, Michael Martin, Andrew (II) Heyman, Paul Hernandez, Ray Henry, Mark (I) WWE Unforgiven Hennig, Curt Helms, Shane Hegstrand, Michael Levesque, Paul Michael Heenan, Bobby Hebner, Earl Hebner, Dave Heath, David (I) Hayes, Lord Alfred WWE SmackDown! Vs. Raw Hart, Stu Layfield, John Hart, Owen Hart, Jimmy (I) Hart, Bret Harris, Ron (IV) Harris, Don (VII) Harris, Brian (IX) Hardy, Matt WWE No Way Out Lawler, Jerry Hardy, Jeff (I) Hall, Scott (I) Guttierrez, Oscar Gunn, Billy (II) Guerrero, Eddie Guerrero Jr., Chavo Jericho, Chris Gray, George (VI) WWE No Mercy Goldberg, Bill (I) Gill, Duane Gasparino, Peter Garea, Tony Funaki, Sho Fujiwara, Harry Jacobs, Glen Frazier Jr., Nelson Foley, Mick WWE Judgment Day Flair, Ric Finkel, Howard Fifita, Uliuli Fatu, Eddie Hardy, Matt Royal Rumble Farris, Roy Eudy, Sid Enos, Mike (I) Eaton, Mark (II) WWE Armageddon Eadie, Bill Duggan, Jim (II) Hardy, Jeff (I) Douglas, Shane DiBiase, Ted DeMott, William Davis, Danny (III) Darsow, Barry Cornette, James E. Wrestlemania X-Seven Copeland, Adam (I) Gunn, Billy (II) Constantino, Rico Connor, A.C. Cole, Michael (V) Coage, Allen Coachman, Jonathan Clemont, Pierre Wrestlemania X-8 Guerrero, Eddie Clarke, Bryan Chavis, Chris Centopani, Paul Cena, John (I) Canterbury, Mark Candido, Chris Calaway, Mark Copeland, Adam (I) Bundy, King Kong Wrestlemania 2000 Buchanan, Barry (II) Brunzell, Jim Brisco, Gerald Bresciano, Adolph Bloom, Wayne Cole, Michael (V) Bloom, Matt (I) Blood, Richard Blanchard, Tully Survivor Series Blair, Brian (I) Blackman, Steve (I) Bischoff, Eric Calaway, Mark Bigelow, Scott 'Bam Bam' Benoit, Chris (I) Batista, Dave Bass, Ron (II) Barnes, Roger (II) Summerslam Backlund, Bob Austin, Steve (IV) Bloom, Matt (I) Apollo, Phil Anoai, Solofatu Anoai, Sam Anoai, Rodney Anoai, Matt Anoai, Arthur Royal Rumble Benoit, Chris (I) Angle, Kurt André the Giant Anderson, Arn Albano, Lou Al-Kassi, Adnan Ahrndt, Jason Adams, Brian (VI) No Way Out Austin, Steve (IV) Young, Mae (I) Wright, Juanita Wilson, Torrie Vachon, Angelle Stratus, Trish Runnels, Terri Anoai, Solofatu Robin, Rockin' Psaltis, Dawn Marie King of the Ring Moretti, Lisa Moore, Jacqueline (VI) Moore, Carlene (II) Mero, Rena Angle, Kurt McMichael, Debra McMahon, Stephanie Martin, Judy (II) Martel, Sherri Invasion Laurer, Joanie Keibler, Stacy Kai, Leilani Stratus, Trish Hulette, Elizabeth Guenard, Nidia Garca, LiliÆn Ellison, Lillian Dumas, Amy Fully Loaded Dumas, Amy

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 88

' $ (2,516)-Hard core

Ribald Tales of Canterbury Young Nurses In Lust Hot Tight Asses 6 Return to Sex 5th Avenue Young Girls in Tight Jeans Cumback Pussy 8 Reincarnation of Don Juan Young and Naughty Hot Tight Asses 20 Cumback Pussy 6 Hot Sweet Honey Red Vibe Diaries 2: Dark Desires Year of the Sex Dragon, The Hot Shots Cumback Pussy 4 Get Some Rear Ended Roommates XTV 2 Cum for Me Carol Rear Busters XTV 1 Hot Nights at the Blue Note Cafe Cream of Cumback Pussy Hot In the City Raunch V X-rated Bloopers and Outtakes Crazed Raunch 6 X-rated Blondes Hospitality Sweet Covergirl Hooter Heaven Rapture X Dreams Honey Buns Country Girl Rambone the Destroyer Wrapped Up Hollywood Starlets Coming on Strong Rainwoman 6 WPINK-TV 3 Hollywood Exposed 2 Coming of Age Rainwoman 4 Woman in Pink, The Come Hither, Cum Ginger Rainbird Within and Without You Holly Does Hollywood Club Head Holiday for Angels Radio-active With Love from Susan Hindlick Maneuver, The Club Ginger Radio K-KUM With Love from Ginger Club DV8 2 Rachel Ryan RR Witching Hour, The Hienie's Heroes Cherry Cheeks Hidden Obsessions Queen of Hearts 3 Wire Desire Cheerleader Academy Pussypoppers Wings of Passion Hershe Highway 4 Cheeks 2: The Bitter End North, Peter (I) Herman's Bed Pussyman Takes Hollywood Willing Women Heads and Tails Cheek to Cheek 2: The Newest Cheeks on the Block Pussyman 2: The Prize Wild Women 61: Rachel Ryan Head Games Checkmate Pussyman Wild Women 32: Summer Rose Head Clinic Charmed and Dangerous Psychic, The Wild Women 11: Tanya Foxx Chameleon, The Prom Girls Wild Weekend Hawaii Vice Part III: Beyond the Badge Certifiably Anal Hawaii Vice 6 Project: Ginger Wild in the Wilderness Hawaii Vice 5 Centerfolds Private Teacher Wild Buck Hawaii Vice 2 Caught In the Middle Private Affairs: Vol 6 Wild Bananas On Butt Row Harlequin Affair Caught in the Act Private Affairs: Vol 2 Wild and Wicked 3 Caught From Behind 9 Pretty As You Feel Wicked Whispers Hard to Handle Caught From Behind 6 Hard Rider Precious Peaks Wicked Ways #2 Caught From Behind 4 Pouring It On Wicked One Hard as a Rock Caught From Behind 2: The Sequel Happy Endings Possessions Wicked As She Seems Guilty by Seduction Caught From Behind 10 Portrait of Dorian Whore, The Cat Alley Pornomania 1 Whore of the Worlds Greatest American Blonde Car Wash Angels Grand Opening Porn on the 4th of July Whore House Captain Butt's Beach Poonies, The Who Killed Holly Hollywood? Graduation from F.U. Canned Heat Gorgeous Pleasure Seekers White Bunbusters Good Girls Do California Native Pleasure Party Whispered Lies Cajun Heat Pleasure Hunt Part II Where the Sun Never Shines Going Pro Butts of Steel Goin' Down Slow Plaything 2 What Gets Me Hot! Butties Plaything Wet Dreams Reel Fantasies Goddess of Love Butt Sisters, The Gluteus to the Maximus Playing with a Full Dick West Coast Girls Glen or Glenda? Busted Play It Again... Samantha! We Love to Tease Glamour Girl 5 Burning Desire Pink Pussycat, The Way They Were, The Give Me Your Soul... Burgundy Blues Piece of Heaven Wacky World of X-Rated Bloopers Bun for the Money Physical II Voyeur, The Girls' Club, The Bun Busters Girls Who Love to Suck Photo Flesh Voyeur's Favorite Blowjobs and Anals 8, The Girls of the Double D 9 British Are Coming, The Perverted Passions Voodoo Lust: The Possession Girls of the Double D 13 Bringing Up the Rear Perverted 1 Visions of Desire Girls of the Double D 11 Bride, The Perks Virgin Dreams Breaking It Perfect Fit Video Tramp Girls of the A Team, The Brazilian Connection, The Girls of Paradise Peggy Sue Victoria and Company Girls of Cell Block F Brat Force Passionate Heiress Vegas: Snake Eyes Girl with the Heart-Shaped Tattoo, The Bottoms Up! Series 8 Passionate Angels Vagina Town Ginger's Private Party Bottom Line, The Passenger 69 Up Your Ass 5 Bottom Dweller Part Deux, The Passages 2 Up 'n Coming Ginger's Greatest Boy/Girl Hits Bottom Dweller 5: In Search of... Ginger Then and Now Passages 1 Unforgivable Ginger Snacks Booty Mistress Party Doll A Go-Go, Part 1 Unchain My Heart Ginger On the Rocks Booty Ho 3 Party Doll A Go-Go 2 Unbelievable Orgies Ginger Lynn: The Movie Boobs Butts and Bloopers 1 Party Doll Turnabout Boiling Point Paradise Lost True Legends of Adult Cinema: The Modern Video Era Ginger Lynn Non-Stop Boiling Desires Ginger Lynn and Co. Paler Shade of Blue, A True Legends of Adult Cinema: The Erotic 80's Body of Innocence Overtime: Oral Hijinx Trashy Lady Ginger in Ecstasy Body Music Ginger Effect, The Oval Office, The Tracie Lords Ghost Town Bod Squad, The Outrageous Orgies 5 Toys 4 Us 2 Blowin' the Whistle Outlaw, The Touch of Mischief Gettin' Ready Bloopers 2 Gang Bangs II Out of Love Touch Me Bloopers Orgies Torrid Without a Cause Gang Bangs Blondes Who Blow Gang Bang Wild Style 2 Oral Majority 9 Top It Off Gang Bang Nymphette Blondage Oral Majority 8 Top 25 Adult Stars of All Time, The Gang Bang Jizz Queens Blame It On Ginger Oral Majority 7 Too Good to Be True Gang Bang Jizz Jammers Black Valley Girls 2 Oral Majority 4 Tomboy Black Valley Girls Oral Majority 3 To the Rear Gang Bang Girl 22 Black Throat Gang Bang Girl 20 Oral Majority 10 Tits Ahoy Gang Bang Girl 17 Black Stockings Oral Majority Tip of the Tongue Gang Bang Girl 13 Billionaire Girls Club Open Up Traci Tight Squeeze Gang Bang Girl 12 Bigger They Come Only the Very Best On Video Tight Ends in Motion Big Pink, The Only the Best of the 80's Thrill Street Blues Gang Bang Face Bath 4 Big Melons 4 Gang Bang Face Bath 3 One Night Stand Three-way Lust Gang Bang Face Bath 2 Big Melons 31 On the Loose Three by Three Gang Bang Face Bath Big Melons 26 On Golden Blonde Those Lynn Girls Gang Bang Cummers Big Mellons 25 Office Girls This Is Your Sex Life Beyond Thunderbone Obsession Texas Crude Games Couples Play Beyond Reality: Mischief in the Making Future Voyeur Nurse Nancy Terms of Endowment Full Throttle Girls 1: Boredom Pulled the Trigger Between the Cheeks 3 Nurse Fantasies Terminal Case of Love Full Nest Between the Cheeks 2 Norma Jeane Anal Legend Temptation Eyes Full Moon Fever Between the Cheeks Nobody's Looking Teasers Best Rears of Our Lives, The No Tell Motel Tease, The Friends and Lovers: The Sequel Best of the Vivid Girls #30 Fresh Meat Nightbreed Tawnee Be Good Best of the Dark Bros., Vol. 2, The Night Temptress Taste of Victoria Paris French Doll Best of the Dark Bros., The Forbidden Cravings Night Tales Taste of Tawnee, A Forbidden Bodies Best of Talk Dirty, Vol. 1, The Night Deposit Taste of Ariel Best of Shane 1 New Wave Hookers 4 Tarnished Knight For Your Thighs Only Best of Loose Ends For the Money 1 New Wave Hookers 2 Talk Dirty to Me, Part III Best of Double Penetration New Wave Hookers Talk Dirty to Me 9 Fluffer, The Best of Diamond Collection 11 Flesh Shopping Network Never Say Never Takin' It to the Limit Flashback Best of Christy Canyon Naughty Thoughts Take My Wife, Please! First Annual XRCO Adult Film Awards Best of Caught from Behind 2 Naughty 90's Take Me Firm Offer Best of Caught from Behind Nasty Nymphos 3 Tailspin 1 Best of Amber Lynn Nasty Lovers Tails of Perversity 3 Firefoxes Beefeaters Fire in the Hole Naked Truth, The Tails of Perversity 2 Fine Art of Cunnilingus, The Beaverly Hills Cop Naked Ambition Tails of Perversity Film Buff Beaver and Buttcheeks Naked and Nasty Tailiens 2 Filet-o-Breast Beat Goes On, The Mystic Pieces Tailiens Bazooka County 3 Wallice, Marc Mystery of the Golden Lotus Tailhouse Rock Femmes érotiques, Les Battle of the Titans Femme Vanessa, La Muff 'n' Jeff Tailgunners Fast Girls Battle of the Superstars Motel Sex Swedish Erotica 74 Farmer's Daughter 2 Bare Market More Than Friends Swedish Erotica 56 Fantasy Inc. Bare Elegance Moonstroked Swedish Erotica 54 Barbii Unleashed Model Wife Surfside Sex Fame Is a Whore On Butt Row Barbara Dare's Bad Eyewitness Nudes Miscreants Superstars of Sex: Racquel Darrian Extreme Sex 4: The Experiment Ball Street Mirage 2 Super Tramp Extreme Sex 2: The Dungeon Badgirls 2: Strip Search Mirage Super Groupie Extreme Sex 1: The Club Bad Mind Shadows 2 Sunny After Dark Backroad to Paradise Mind Shadows Summer Break Exhibitionist, The Backing in 3 Executive Suites Midslumber's Night Dream Sugarpussy Jeans Every Woman Has a Fantasy 3 Backfield in Motion Midnight Pink Suburban Swingers 2 Eternity Backdoor to Hollywood 11 Midnight Hour, The Street Walkers Eternal Lust 2 Backdoor Summer II Megasex Strange Sex in Strange Places Backdoor Brides Part 2 Matter of Size, A Stiff Competition 2 Escort to Ecstasy Backdoor Brides Erotic Starlets 12: Crystal Lee Masque Stiff Competition Backdoor Bonanza 9 Mark of Zara Starting Over Erotic Newcummers 4 Backdoor Bonanza 13 Erotic Explosions 2 Marilyn Whips Wallstreet Starr Entertainment L.A. Style Back to Nature Manbait 2 Star, The Back Doors, The Manbait Star Cuts 4: Ginger Lynn Encore Bachelor Party Enchantress Man Who Loves Women, The Star Cuts 39: Trinity Loren Baby Face 2 Make My Wife, Please Star Cuts 37: Buffy Davis Edge of Heat 2 Babe Watch Edge of Heat Make My Night Star 85 Ecstasy Aussie Exchange Girls Make Me Want It Splendor in the Ass Easy Way, The Asspiring Actresses Magic Shower, The Splash Shots Earth Girls Are Sleazy Ass Openers 8 Lust in the Fast Lane Spies Ass Openers 6 Lust College Spermbusters E. TV Ass Openers 4 DØj Vu Lust Bug, The Spellbound Dreams of Candace Hart Ass Openers 3 Lust at the Top Spectacular Orgasms Dreams in the Forbidden Zone Ass Openers 10 Luscious Lucy in Love Sorority Pink 2: The Initiation Dream Machine, The Ass Openers 1 Lucky Break Sophisticated Lady Ass Lovers Special Lovin' USA Sodomania: The Baddest of the Best Dream Lust Ass Busters Inc. Dragon Lady 4: Tales from the Bed 3, The Lovers, The Sodomania: Slop Shots 1 Double Penetrations 7 Ass Backwards Love Lessons Sodomania 18 Double Penetrations 6 Art of Desire Love Ghost Sodomania 13 Double Penetrations 2 Aroused Love Bites Snatched Army Brat 2 Loose Morals Smart Ass, The Double Penetration 5 Arizona Gold Double Penetration 4 Loose Ends III Smart Ass Returns, The Double Penetration 2 Anything Goes Loose Ends II Slumber Party Double Penetration Another Rear View Loose Ends Sloppy Seconds Dirty Prancing Animal in Me Loads of Fun 4 Slip of the Tongue Angels of Mercy Little Romance Slip Into Ginger and Amber Dirty Pictures Angelica Dirty Movies Like a Virgin Slightly Used Angel Rising Life and Loves of Nikki Charm Sleeping with Everybody Dirty Looks Angel Puss Dirty Dreams Let's Play Doctor Slave to Love Dickman and Throbbin Analizer, The Legend of Barbi-Q and Little Fawn, The Sky Foxes Anal Trashy Ass Laying the Ghost Skin Games Diamond in the Rough Anal Thunder 2 Diamond Collection Double X 74 Latin Lust Sister Dearest Anal Taboo Last Temptation, The Sindy Does Anal Again Diamond Collection Double X 10 Anal Sweetheart Diamond Collection 79 Lascivious Ladies of Dr. Lipo, The Simply Kia Diamond Collection 67 Anal Sluts and Sweethearts Laid Off Simply Blue Diamond Collection 64 Anal Secrets Lady in Red, The Shot From Behind Diamond Collection 61 Anal Riders 106 KSEX 106.9 Sheila's Deep Desires Anal Queen Kiss, The Shayla's Gang Dial F for Fantasy Anal Princess Dial a Nurse Kiss My Asp Shaved Pink Dial A for Anal Anal Mystique Kinky Vision 2 Shane's World Devil Made Her Do It, The Anal Lover Kinky Couples Sexy Secrets N 1 Devil in Miss Jones 5: The Inferno, The Anal Justice Kinky Sexy and 18 Anal Innocence 2 Keyhole Video #114: Christy Canyon Special Sexual Fantasies Devil in Miss Jones 4: The Final Outrage Anal Inferno Devil in Miss Jones 3: A New Beginning, The Kascha and Friends Sextectives Desktop Dolls Anal Hounds and Bitches Just Another Pretty Face Sexpertease DeRenzy Tapes Anal Hellraiser 2 Juicy Sex Scandals Sex Toys Delinquents On Butt Row Anal Encounters 2 Juicy Lucy Sex Stories Anal Encounters 1 Jezebel Sex Sluts in the Slammer Deeper, Harder, Faster Anal Ecstasy Deep Throat Girls Jaded Love Sex Shoot Deep Obsession Anal Delights 3 It's My Body Sex Plays Deep Inside Victoria Paris Anal Deep Rider Interactive Sex Maniacs Deep Inside Vanessa del Rio Anal Crack Master Insatiable Sex Fifth Avenue Anal Climax 3 Inferno Sex Busters Deep Inside Traci Anal Attitude Deep Inside Shanna McCullough Indecent Itch Sex Beat Deep Inside Samantha Strong Anal Anarchy Indecent Exposures Sex Appraisals Deep Inside Racquel Darrian Anal Adventures of Suzy Super Slut Inches for Keisha Sex Academy 2: The Art of Talking Dirty Deep Inside P.J. Sparxx American Pie In Search of the Golden Bone Sex 3: After Seven American Beauty Immaculate Erection Sensual Exposure Deep Inside Nina Hartley Amber Lynn: The Totally Awesome Deep Inside Missy Images of Desire Seeing Red Amazing Tails 5 I Want It All Seducers, The Deep Inside Kelly O'Dell Amazing Tails 4 Deep Inside Ginger Lynn Byron, Tom I Touch Myself Secret of Her Suckcess Deep Inside Brittany O'Connell Amazing Tails 3 I Like to Be Watched Secret Life of Nina Hartley, The Amazing Tails 2 I Dream of Christy Secret Fantasies 4 Deep Inside Barbii Amazing Tails 1 Deep Inside Ariana Hunger, The Secret Fantasies 3 All the Best, Barbara House On Chasey Lane Screaming Rage Deep In Angel's Ass Alice in Hollyweird Deep Cover House of the Rising Sun Scarlet Woman, The Deep Cheeks 3 Al Terego's Double Anal Alternatives House of Sleeping Beauties 2 Scarlet Bride, The Decadence Aja House of Sleeping Beauties Savanah Unleased Debutante, The After Midnight House of Blue Dreams Satyr Afro Erotica 15 Hottest Ticket Satin Seduction Dear Bridgette Adventures of Tracy Dick: The Case of the Missing Stiff Darker Side of Shayla, The Hothouse Rose Part 1 Sabotage Darker Side of Shayla 2, The Adventures of Billy Blues, The Hotel Sodom Ruthless Affairs Curse of the Catwoman Adult 45 Hotel Paradise Royals: Ginger Lynn Cumshot Revue 5 Above the Knee Hotel Fantasy Roll-x Girls A-List, The Hot Wired Rocky Porno Video Show, The Cumshot Revue 3 A Is for Asia Cumshot Revue 2 Hot Tight Asses 9 Rising, The 4F Dating Service Hot Tight Asses 8 Rise of the Roman Empress 2 Cumming of Ass 40 Something Cumback Pussy 9: Your Ass Is Mine! 1-800-934-Boob

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 89

' $ 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

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 90

' $

4-rings and analysis of 2-mode networks In bipartite (2-mode) network there are no 3-rings. The densest substruc-

tures are complete bipartite subgraphs Kp,q. They contain many 4-rings.

pq w (K ) = 4 p,q 2 2 The 4-rings weights were implemented in Pajek only recently, in August 2005.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 91

' $ 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.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 92

' $

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 ------

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 93

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Example: Islands for w4 / Charlie Brown and Adult

Morgan, Jonathan (I) Kesten, Brad Brando, Kevin Schoenberg, Jeremy Boy, T.T. Davis, Mark (V)

Hauer, Brent Robbins, Peter (I) Voyeur, Vince Shea, Christopher (I) Charlie Brown and Snoopy Show Altieri, Ann Reilly, Earl 'Rocky' Charlie Brown Celebration Dough, Jon 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 Sanders, Alex (I) It's the Great Pumpkin, Charlie Brown North, Peter (I) Charlie Brown's All Stars! Life Is a Circus, Charlie Brown Charlie Brown Christmas Michaels, Sean Race for Your Life, Charlie Brown

Be My Valentine, Charlie Brown Mendelson, Karen Horner, Mike It's Magic, Charlie Brown Dryer, Sally Stratford, Tracy Melendez, Bill You're a Good Sport, Charlie Brown Drake, Steve (I) Boy Named Charlie Brown It's a Mystery, Charlie Brown It's an Adventure, Charlie Brown Byron, Tom Silvera, Joey It's Flashbeagle, Charlie Brown Momberger, Hilary Play It Again, Charlie Brown Is This Goodbye, Charlie Brown? West, Randy (I) There's No Time for Love, Charlie BrownCharlie Brown Thanksgiving You're Not Elected, Charlie Brown Jeremy, Ron Snoopy Come Home It's the Easter Beagle, Charlie Brown Wallice, Marc Savage, Herschel

Thomas, Paul (I) Shea, Stephen

Pajek Pajek

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 94

' $ Example: Island for w4 / Polizeiruf 110 and Starkes Team

Maranow, Maja Polizeiruf 110 - Ein Bild von einem Mrder Starkes Team, Ein Polizeiruf 110 - Kopf in der Schlinge ’Affre Semmeling, Die’ Starkes Team - Eins zu Eins, Ein Polizeiruf 110 - Zerstrte Trume Starkes Team - Kollege Mrder, Ein Polizeiruf 110 - Angst um Tessa Blow Starkes Team - Sicherheitsstufe 1, Ein Martens, Florian Polizeiruf 110 - Rosentod Starkes Team - Das Bombenspiel, Ein Starkes Team - Erbarmungslos, Ein 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 Polizeiruf 110 - Todsicher Starkes Team - Auge um Auge, Ein Schwarz, Jaecki Lansink, Leonard Starkes Team - Lug und Trug, Ein Polizeiruf 110 - Der Spieler

Starkes Team - Der letzte Kampf, Ein Polizeiruf 110 - Mordsfreunde Starkes Team - Kleine Fische, groe Fische, Ein Starkes Team - Roter Schnee, Ein Starkes Team - Der Todfeind, Ein Polizeiruf 110 - Kurschatten Starkes Team - Mordlust, Ein Polizeiruf 110 - Tote erben nicht Starkes Team - Das groe Schweigen,Winkler, WolfgangEin Starkes Team - Der schne Tod, Ein Polizeiruf 110 - Der Pferdemrder Bademsoy, Tayfun Starkes Team - Trume und Lgen, Ein Starkes Team - Der Verdacht, 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

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % Pajek V. Batagelj: Analysis and visulization of large networks with Pajek 95

' $

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 ???? ????

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 96

' $ 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. Three connected relinking marriages in the Michael/Zrieva/ Junius/Georgio/ Nicola/Ragnina/ Marinus/Zrieva/ Francischa/Georgio/ Anucla/Zrieva/ Nicoleta/Zrieva/ Maria/Ragnina/ genealogy (represented as a p-graph) of ra- gusan noble families. A solid arc indicates is a son of Junius/Zrieva/ Lorenzo/Ragnina/ the relation, and a dotted arc Damianus/Georgio/ Margarita/Bona/ Legnussa/Babalio/ Slavussa/Mence/ indicates the is a daughter of relation. Nicolinus/Gondola/ Franussa/Bona/ Sarachin/Bona/ Nicoletta/Gondola/ In all three patterns a brother and a sister from one family found their partners in the

Marin/Gondola/ Marinus/Bona/ Magdalena/Grede/ Phylippa/Mence/ same other family.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 97

' $ Ore-graph

m-grandmother m-grandfather f-grandfather f-grandmother

In Ore-graph every person is repre- mother father stepmother sented by a vertex, marriages, relation is a spouse of , are repre-

sister-in-law brother I wife sister sented with edges and relations is a mother of and is a father of as arcs pointing from parents

daughter-in-law son son-in-law daughter to their children.

grandson

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 98

' $ p-graph

grandson In p-graph vertices represent indi- viduals or couples. In the case that a person is not married yet (s)he is

son & daughter-in-law son-in-law & daughter represented by a vertex, otherwise person is represented with the part- ner in a common vertex. There are

sister I & wife brother & sister-in-law only arcs in p-graphs – they point from children to their parents, representing the relations FiC is a

father & stepmother father & mother daughter of and MiC is a son of ; where FiC ≡ female in the couple; and MiC ≡ male in the

f-grandfather & f-grandmother m-grandfather & m-grandmothercouple.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 99

' $ Relinking patterns in p-graphs All possible relinking marriages in p-

A2 A3 graphs with 2 to 6 vertices. Patterns are labeled as follows:

A4.1 B4 A4.2 • ﬁrst character – number of ﬁrst vertices: A – single, B – two, C – three. A5.2 A5.1 B5 • second character: number of vertices in pattern (2, 3, 4, 5, or 6).

A6.3 • last character: identiﬁer (if the two A6.2 A6.1 C6 ﬁrst characters are identical). Patterns denoted by A are exactly the

B6.4 B6.1 blood marriages. In every pattern the B6.2 B6.3 number of ﬁrst vertices equals to the number of last vertices.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 100

' $ Frequencies normalized with number of couples in p-graph × 1000.

pattern Loka Silba Ragusa Turcs Royal A2 0.07 0.00 0.00 0.00 0.00 A3 0.07 0.00 0.00 0.00 2.64 A4.1 0.85 2.26 1.50 159.71 18.45 B4 3.82 11.28 10.49 98.28 6.15 A4.2 0.00 0.00 0.00 0.00 0.00 A5.1 0.64 3.16 2.00 36.86 11.42 A5.2 0.00 0.00 0.00 0.00 0.00 B5 1.34 4.96 23.48 46.68 7.03 A6.1 1.98 12.63 1.00 169.53 11.42 A6.2 0.00 0.90 0.00 0.00 0.88 A6.3 0.00 0.00 0.00 0.00 0.00 C6 0.71 5.41 9.49 36.86 4.39 B6.1 0.00 0.45 1.00 0.00 0.00 B6.2 1.91 17.59 31.47 130.22 10.54 B6.3 3.32 13.53 40.96 113.02 11.42 B6.4 0.00 0.00 2.50 7.37 0.00 Sum 14.70 72.17 123.88 798.53 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.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 101

' 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 ci,j = ai,k · bk,j k∈K In the case when I = K = J we are dealing with ordinary one-mode networks (with square matrices).

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 102

' 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 In general the multiplication of large sparse networks is a ’dangerous’ operation since the result can ’explode’ – it is not sparse.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 103

'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.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 104

' $

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 (1) T (1) P T determined by the matrix A = AA , auv = z∈V auz · azv. 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 . (2) T The network N2 is determined in a similar way by the matrix A = A A.

The networks N1 and N2 are analyzed using standard methods.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 105

' 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.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 106

' $ . . . 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)}). T We deﬁne [qi × qj] = qj × qi. T It holds qi × qj = [K × qi] ∗ [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].

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 107

' $ 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 Jurgen¨ Pfeffer’s Text2Pajek program:

• project.net – idents × projects = P

• country.net – idents × countries = C

• institution.net – idents × institutions = U

|idents| = 8869, |projects| = 933, |institutions| = 3438, |countries| = 60.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 108

' $

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

• ...

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 109

' $

EU projects – deleted projects Some projects (27) from original data set have to be deleted – in the ﬁnal data set RuthDELmain they were marked as deleted. When producing two-mode networks we could ﬁrst physicaly delete them. Instead of this,

we used another approach: we produced the cluster CD of deleted idents and from it a two-mode matrix D (idents × idents; not implemented yet in Pajek). Matrix D is a ’diagonal’ matrix with value 1 for idents not

belonging to CD and 0 otherwise. Using matrix D we can determine the network ProjInst.net by W = PT ? D ? U – the deleted idents don’t contribute to the network.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 110

' $

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.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 111

' Analysis of ProjInst.net $

ARMINES PSI FUR PRODUKTE UND TQT SRL SYS.E DER INFORMATIONSTECH.

BICC GENERAL CABLE ESI SOFTWARE SA 28283 CHALMERS TEKNISKA HOEGSKOLA COLOPLAST A/S MTU AERO ENGINES 25525 DAIMLER CHRYSLER AG BUURSKOV VOLKSWAGEN AG FRAUENHOFER INST. FUER DE ZENTRUM FUER LUFT UND RAUMFAHRT E.V. EA TECH. LTD PRODUKTIONSTECH. UND AUTOMATISIERUNG EADS DE 506503 MECALOG SARL LMS UMWELTSYS.E, DIPL. ING. DR. HERBERT BACK BAE SYSTEMS 506257 EUROCOPTER S. INST. NAT. DE RECHERCHE AIRBUS UK LIMITED SUR LES TRANSPORTS ET LEUR SCURIT TESSITURA LUIGI SANTI SPA IST-2000-29207 DASSAULT AVIATION INST. FUER TEXTIL UND AIRBUS DEUTSCHLAND SNECMA MOTEURS SA INST. SUPERIOR TECNICO VERFAHRENSTECH. DENKENDORF 502917 C. R. FIAT S.C.P.A. KBC MANUFAKTUR, KOECHLIN, NAT. TEC. UNIV.502909 OF ATHENS NL ORG. FOR APPLIED BAUMGARTNER UND CIE. AG SCIENTIFIC RESEARCH - TNO 502842 29817 AIRBUS FRANCE SAS BARTENBACH TRUMPF-BLUSEN-KLEIDER ALENIA AERONAUTICA SPA 501084 WALTER GIRNER UND CO. KG POLYMAGE SARL BARCO NV G4RD-CT-2002-00836 G4MA-CT-2002-00022 STICHTING NATIONAAL LUCHT MSO CONCEPT INNOVATION + SOFTWARE OFFICE NAT. DETUDES ET ROSENHEIMER GLASTECH. DE REC. AEROSPATIALES BRPR987001 G4RD-CT-2000-00178 ENK6-CT-2002-30023 502896 7210-PR/163 G4RD-CT-2001-00403 G4RD-CT-2002-00795 RUDOLF BRAUNS AND CO. KG CENTRE DE RECH. METALLURG. 502889 SHERPA ENGINEERING SARL 7215-PP/031 G4RD-CT-2000-00395 CATALYSE SARL 7210-PR/233 VOEST-ALPINE STAHL EVG3-CT-2002-80012 INST. DE RECHERCHES THYSSENKRUPP STAHL A.G. DE LA SIDERURGIE FR T3.2/99 DISENO DE SISTEMAS EN SILICIO CENTRE FOR EUROP. ECONOMIC SMT4982223 ILEVO AB FONDAZIONE ENI - ENRICO MATTEI 7210-PR/095 IST-2001-35358 CSTB JERNKONTORET HPSE-CT-2002-00108 UNIV. DER BUNDESWEHR MUENCHEN BUILDING RESEARCH CHIPIDEA - MICROELECTRONICA, S.A. ENEL.IT LANDIS & GYR - EUROPE AG UNIV. PANTHEON-ASSAS - PARIS II OESTERREICHISCHER BERGRETTUNGSDIENST SSAB TUNNPLÅT IFEN GES. FUER SATELLITENNAVIGATION 7215-PP/034 RESEARCH INST. OF THE FINNISH ECONOMY JOE3980089 WYKES ENGINEERING COMPANY LH AGRO EAST S.R.O. QLK6-CT-2002-02292 IST-2000-30158 TECHNOFARMING S.R.L. T3.5/99 THE AARHUS SCHOOL OF BUSINESS MEFOS, FOUNDATION FOR HELP SERVICE REMOTE SENSING INST. CARTOGRAFIC DE CATALUNYA CINAR LTD. METALLURGICAL RESEARCH HPSE-CT-2002-00143 LESPROJEKT SLUZBY S.R.O. BAYER. ROTES KREUZ ENERGY RESEARCH CENTRE NL IST-2000-28177 BRITISH STEEL UNIV. OF MACEDONIA 7210-PR/142 JOR3980200 FRAUENHOFER INST. FUER AGRO-SAT CONSULTING MATERIALFLUSS UND LOGISTIK ENK5-CT-2000-00335 DATASYS S.R.O. UNIV. OF ABERDEEN ORAD HI TEC SYS. POLAND CRE GROUP LTD. MJM GROUP, A.S. FRIMEKO INT. AB CENTRE DE ROBOTIQUE INOX PNEUMATIC AS BBL DFA DE FERNSEHNACHRICHTEN AGENTUR TPS TERMISKA PROCESSER AB KOMMANDITGES. HAMBURG 1 PROLEXIA FERNSEHEN BETEILIGUNGS & CO A.S.M. S.A. IST-1999-56418 ZAMISEL D.O.O DPME ROBOTICS AB INGENIORHOJSKOLEN HELSINGOR TEKNIKUM GATE5 AG INDUSTRIAS ROYO 511758 LKSOFTWARE UAB LKSOFT BALTIC BRST985352 SUPERELECTRIC DI SVETS & TILLBEHOR AB IST-2000-30082 ALBERTSEN & HOLM AS CARLO PAGLIALUNGA & C. SAS WISDOM TELE VISION IST-1999-57451 SPORTART OK GAMES DI ALESSANDRO CARTA ASM - DIMATEC INGENIERIA FFT ESPANA TECH. DE AUTOMOCION, ENERGITEKNIK HEATEX AB UNIV. DE ZARAGOZA YAHOO! DE OSAUHING EETRIUKSUS BROD THOMASSON EDAG ENGINEERING + DESIGN GUNNESTORPS SMIDE & MEKANISKA AB Pajek

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 112

' Analysis of Countries.net $ To obtain picture in which the

Kazakhstan stronger lines cover weaker lines we Japan Afghanistan

Azerbaijan Georgia Morocco have to sort them Liechtenstein Ecuador India Iceland Net/Transform/Sort Uzbekistan Belarus Tunisia Jordan Lebanon lines/Line values/Ascending

Armenia Canada France Algeria United Kingdom For dense (sub)networks we get Russian F. Italia Finland The Netherlands Malta Moldavia China Turkey better visualization by using matrix Germany Greece Thailand Portugal Spain Switzerland Israel display. In this case we also recoded Turkmenistan Sweden Denmark Austria Cyprus Estonia Serbia-Montenegro Slovakia Ukraine Norway values (2,10,50). To determine USA Belgium Macedonia Poland Slovenia Croatia Hungary clusters we used Ward’s clustering Luxembourg Ireland Latvia Romania Bulgaria Czech R. Lithuania Albania 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.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 113

' Analysis of Countries.net $ Pajek - shadow [0.00,4.00]

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 Pajek - Ward [0.00,4785.14] Latvia Lithuania Luxembourg Ecuador Cyprus Thailand Armenia Turkey Turkmenist Uzbekistan Bulgaria Moldavia Ukraine Japan Kazakhstan Slovenia Azerbaijan India Romania Macedonia Albania Slovakia Liechtenst USA Serbia-Mon Iceland Russian F. Canada Estonia Israel China Belarus Hungary Georgia Ireland Tunisia Lebanon Czech R. Jordan Algeria Norway Malta Morocco Poland Afghanista Luxembourg Finland Croatia Portugal Latvia Lithuania Denmark Cyprus Turkey Switzerlan Bulgaria Ukraine Austria Slovenia Sweden Romania Slovakia Greece USA Portugal Belgium Denmark Poland Spain Finland The Nether Switzerlan Austria Italia Czech R. Ireland France Norway Hungary United Kin Israel Germany 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

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 114

' $ 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.UNITARYDAEDALUS ENTERPRISE INFORMATICS LTD FL-SOFT V/JENS ALL-RUSSIAN SCIENTIFICU.PARIS CENTER VI PIERRE ETJOERGEN MARIE CURIE OESTERGAARD BELIMO AUTOMATIONU.LA LAGUNA SOFIISKI U.SVETI KLIMENT OHRIDSKI THE U.COURT OF THE U.OF ABERDEEN SENTIENT MACHINE RESEARCH B.V. SIEMENS BUILDING TECH.S AG U.OULU I.OF INFORMATION TECH.S AS.CONOCIMIENTO DATAMED HEALTHCARE INF.SYS.STICHTING NEURALE NETWERKEN NOTTINGHAM TRENT U. U.E DE COIMBRA T.U.CLAUSTHAL MOMATEC U.CRETE U.ULSTER CITY U.LONDON 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. AND METALLURGY ASS.RECH.SCIENTIFIQUE BOURNEMOUTH U. ENTE PER LE ELITE EUROP.LAB KINGS COLLEGE LONDON STICHTING U.NYENRODE NUOVE TECNOLOGIE To identify the most important institu- FOR INTELLIGENT TECH. I.FUER NATURSTOFF-FORSCHUNG E.V. I.NAT.POLITEC.DE TOULOUSE U.GIRONA U.AMSTERDAM U.GENT AUSTRIAN I.AI START ENGINEERING JSCO T.U.DELFT ENERGY RESEARCH C.NL I.NAT.DE RECHERCHE SUR LES TRANSPORTS ET LEUR SECURITE tions we ﬁrst computed p -cores vec- U.GRANADA S TEKNILLINEN KORKEAKOULU HELSINKI T.U. NAT.U.IRELAND,MAYNOOTH U.TWENTE TSS-TRANSPORT SIMULATION SYS.S.L. U.KLINIKUM AACHEN KATHOLIEKE U.LEUVEN U.BRISTOL FRIEDRICH-SCHILLER-U.JENA tor and use it to determine the cor- ERASMUS U.ROTTERDAM CONSEJO SUP.DE INVEST.CIENTIFICAS QINETIQ DEP.OF ENVIRONMENT, AABO AKADEMI U JOZEF STEFAN I. GKSS TRANSPORT- FORSCHUNGSZENTRUM AND THE REGIONS GEESTHACHT U.MARIBOR U.P.MADRID MANNESMANN VDO AG U.PAUL SABATIER DE TOULOUSE III EUROP.SPACE AGENCY U.PAISLEY TECHSOFT ENGINEERING S.R.O. U.VALLADOLID U.P.CATALUNYA U.STRATHCLYDE U.LEEDS TECNOLOGIAS CAE AVANZADAS S.L. U.S.GENOVA PT.TORINO U.NOTTINGHAM C.SVILUPPO MATERIALI HERMSDORFER I.FUER TECH. responding vertex islands. We got PT.BARI DAIMLER CHRYSLER AG U.MANCHESTER OXFORD BROOKES U. U.DORTMUND BAE SYSTEMS U.S.PADOVA SAFE TECH. LOUGHBOROUGH T.U. NOKIA MOBILE PHONES LTD CZECH T.U.PRAGUE AVIO S.P.A. BRITISH TELEC. NAT.T.U.ATHENS FOKKER SPACE BV T.U.V KOSICIACH I.SUPERIOR TECNICO ANAKON U.SHEFFIELD FUNDACION LABEIN NCODE INT. POLISH ACAD.OF SCIENCES FINITE ELEMENT ANALYSIS LTD. RISOE NAT.LAB TUN ABDUL RAZAK RESEARCH C.LTD. essentially one large island. Again DANMARKS T.U. U.GREENWICH PRINCIPIA INGENIEROS CONSULTORES U.C.LOUVAIN FUNDACION INASMET STAVANGER U.COLLEGE CRANFIELD U. SULZER MARKETS AND TECH.AG, IFP SICOMP AB SULZER INNOTEC CHALMERS TEKNISKA HOEGSKOLA DAMT LTD the corresponding subnetwork is very SKF R&D COMPANY B.V. U.S.NAPOLI CAESAR SYSTEMS LTD NAFEMS LTD. A.U.THESSALONIKI INTES - INGENIEURGES. FUER TECH.SOFTWARE ENGIN SOFT TRADING SRL C.INT.LENGINYERIA U.DURHAM MARITIME HYDRAULICS AS NL ORG.FOR APPLIED INBIS TECH.LTD dense. We prepared also a matrix dis- SCIENTIFIC RESEARCH-TNO FEMSYS LTD U.S.TRIESTE C.R.FIAT S.C.P.A. CAD - FEM SOFISTK AG MSC SOFTWARE QUEENS U.BELFAST ABS CONSULTING ALTAIR ENGINEERING SAMTECH SA NLSE VERENIGDE SCHEEPSBOUW BUREAUS B.V. LEUVEN MEASUREMENTS AND SYS.INT.NV MERITOR HEAVY VEHICLE play. CREA CONSULTANTSBRAKING LTD SYS.- UK 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 C.NAT.DE LA ST MECANICA APLICADA S.L. GERMAN AEROSPACE CENTRE RECHERCHE SCIENTIFIQUE FRAUENHOFER I.FUER INGENIEURBUERO FUER BIOMEDICAL ENGINEERING TRAGWERKSPLANUNG ROYAL I.OF TECH. DUNLOP STANDARD KATHOLIEKE HOGESCHOOL SINT-LIEVEN AEROSPACE GROUP U.HANNOVER GIFFORD AND PARTNERS LTD. VOLVO AERO CORP.AB MECAS S.R.O. ATOS ORIGIN ENG. LULEAA T.U. STRUCTURAL INTEGRITY ASSESSMENTS LTD CORK I.OF TECHNOLOGY NORUT TEKNOLOGIHAHN-SCHICKARD-GES. A.S. WS ATKINS CONSULTANTS LTD. EASI ENGINEERING U.E DO MINHO U.SPLIT NUMERICAL ANALYSIS WILDE AND TECHNISCHPARTNERS LTD ADVIESBUREAU N.V.AND DESIGN&CO KG INTEGRATED DESIGN & RANDOM LOADING DESIGN FEGS AWEANALYSIS PLC CONSULTANTS LTD MERKLE UND PARTNERD C WHITE&PARTNERS LTD DR THELLEN EATEC LTD

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 115

' Analysis of Institutions.net $

Pajek - Ward [0.00,1376.93] Pajek - shadow [0.00,6.00] ALLOGG AB AS. CONOCI ASS. RECH. AUSTRIAN I BELIMO AUT ALLOGG AB COVENTRY U AS. CONOCI DAEDALUS I ASS. RECH. DATAMED H AUSTRIAN I FACULTY OF BELIMO AUT FED. UNITA COVENTRY U FL-SOFT V/ DAEDALUS I INST. OF I DATAMED H GOETHE UNI FACULTY OF MIT-MANAGE FED. UNITA MOMATEC FL-SOFT V/ NAT. UNIV. INST. OF I NOTTINGHAM GOETHE UNI POLITECNIC MIT-MANAGE SENTIENT M MOMATEC SIEMENS BU NAT. UNIV. SOFIISKI U NOTTINGHAM START ENGI POLITECNIC STICHTING SENTIENT M STICHTING SIEMENS BU THE UNIV. SOFIISKI U UNIV. DE L START ENGI UNIV.SKLIN STICHTING UNIV. DE G STICHTING UNIV. PARI THE UNIV. UNIV. OF A UNIV. DE L UNIV. OF C UNIV.SKLIN UNIV. OF C UNIV. DE G UNIV. OF W UNIV. PARI UNIV. OF Z UNIV. OF A INST. DALL UNIV. OF C RAUTARUUKK UNIV. OF C UNIV.E DE UNIV. OF W UNIV. OF U UNIV. OF Z SOFTECO SI INST. DALL UNIV. GENT RAUTARUUKK TSS - TRAN UNIV.E DE UNIV. DE G UNIV. OF U UNIV. DE V SOFTECO SI UNIVERZA V UNIV. GENT UNIV. PAUL TSS - TRAN TECH. UNIV UNIV. DE G UNIV. WIEN UNIV. DE V UNIV. VAN UNIVERZA V ENERGY RES UNIV. PAUL TEKNILLINE TECH. UNIV DE MONTFOR UNIV. WIEN CITY UNIVE UNIV. VAN UNIV. OF J ENERGY RES AABO AKADE TEKNILLINE RISOE NAT. DE MONTFOR KINGS COLL CITY UNIVE UNIV. DORT UNIV. OF J FRIEDRICH- AABO AKADE UNIV. OF C RISOE NAT. INST. NAT. KINGS COLL BULGARIAN UNIV. DORT ENTE PER L FRIEDRICH- LOUGHBOROU UNIV. OF C HELSINKI U INST. NAT. CRANFIELD BULGARIAN UNIV. CATH ENTE PER L OTTO VON G LOUGHBOROU UNIV. DEGL HELSINKI U UNIV. OF O CRANFIELD UNIV. OF T UNIV. CATH ELITE EURO OTTO VON G ERASMUS UN UNIV. DEGL INST. FUER UNIV. OF O UNIV. PARI UNIV. OF T BRITISH TE ELITE EURO BOURNEMOUT ERASMUS UN UNIV. OF B INST. FUER UNIV. OF S UNIV. PARI DANMARKS T BRITISH TE DAIMLER CH BOURNEMOUT INST. NAT. UNIV. OF B INST. SUPE UNIV. OF S POLITECNIC DANMARKS T POLISH ACA DAIMLER CH UNIV. POLI INST. NAT. NAT. TEC. INST. SUPE CONSEJO SU POLITECNIC KATHOLIEKE POLISH ACA UNIV. TWEN UNIV. POLI TECH. UNIV NAT. TEC. UNIV. POLI CONSEJO SU CENTRE NAT KATHOLIEKE TEC. UNIV. UNIV. TWEN UNIV. OF P TECH. UNIV FUNDACION UNIV. POLI JOZEF STEF CENTRE NAT CZECH TECH TEC. UNIV. UNIV. OF N UNIV. OF P UNIV. OF S FUNDACION BAE SYSTEM JOZEF STEF UNIV. OF M CZECH TECH C. R. FIAT UNIV. OF N NL ORG. FO UNIV. OF S CHALMERS T BAE SYSTEM SAMTECH SA UNIV. OF M VOLVO AERO ABS CONSUL AVIO S.P.A ALTAIR ENG MSC SOFTWA ANAKON LULEAA UNI ATOS ORIGI QUEENS UNI AWE PLC AIRBUS FRA BEHR & CO CAD - FEM CAESAR SYS C. SVILUPP CORK INST. TRL CREA CONSU LEUVEN MEA D C WHITE A. UNIV. T DAMT LTD GERMAN AER DEP. OF E CENTRE INT DR THELLEN UNIV. DEGL DUNLOP STA QINETIQ EASI ENGIN UNIV. OF L EATEC LTD FUNDACION FEMSYS LTD ACCESS E.V FOKKER SPA EUROP. SPA FORSCHUNGS UNIV. OF G GIFFORD AN UNIV. DEGL HAHN-SCHIC UNIV. OF G HERMSDORFE UNIV. OF N INBIS TECH FINITE ELE INGENIEURB ROCKFIELD INTEGRATED WS ATKINS KATHOLIEKE ROYAL INST MANNESMANN UNIV. HANN MARITIME H FRAUENHOFE MECAS S.R. MERITOR HE GKSS - FOR MERKLE UND NAT. NUCLE NAFEMS LTD UNIV. OF D NCODE INT. ENGIN SOFT NLSE VEREN FEGS NEW TECH. IFP SICOMP NOKIA MOBI INTES - IN NORUT TEKN UNIV. DEGL NUMERICAL PRINCIPIA OXFORD BRO ABS CONSUL PD & E AUT ALTAIR ENG RANDOM LOA ANAKON SAFE TECH. ATOS ORIGI SKF R & D AWE PLC SOFISTK AG BEHR & CO ST MECANIC CAESAR SYS STAVANGER CORK INST. STRUCTURAL CREA CONSU SULZER MAR D C WHITE TECHNISCH DAMT LTD TECHSOFT E DEP. OF E TECNOLOGIA DR THELLEN TUN ABDUL DUNLOP STA UNIV.E DO EASI ENGIN UNIV. OF S EATEC LTD WILDE AND FEMSYS LTD FRAUENHOFE FOKKER SPA GKSS - FOR FORSCHUNGS NAT. NUCLE GIFFORD AN UNIV. OF D HAHN-SCHIC ENGIN SOFT HERMSDORFE FEGS INBIS TECH IFP SICOMP INGENIEURB INTES - IN INTEGRATED UNIV. DEGL KATHOLIEKE PRINCIPIA MANNESMANN FINITE ELE MARITIME H ROCKFIELD MECAS S.R. WS ATKINS MERITOR HE ROYAL INST MERKLE UND UNIV. HANN NAFEMS LTD UNIV. DEGL NCODE INT. UNIV. OF G NLSE VEREN UNIV. OF N NEW TECH. CAD - FEM NOKIA MOBI C. SVILUPP NORUT TEKN TRL NUMERICAL LEUVEN MEA OXFORD BRO A. UNIV. T PD & E AUT GERMAN AER RANDOM LOA CENTRE INT SAFE TECH. UNIV. DEGL SKF R & D QINETIQ SOFISTK AG UNIV. OF L ST MECANIC FUNDACION STAVANGER ACCESS E.V STRUCTURAL EUROP. SPA SULZER MAR UNIV. OF G TECHNISCH SAMTECH SA TECHSOFT E VOLVO AERO TECNOLOGIA AVIO S.P.A TUN ABDUL MSC SOFTWA UNIV.E DO LULEAA UNI UNIV. OF S QUEENS UNI WILDE AND AIRBUS FRA C. R. FIAT NL ORG. FO CHALMERS T ALLOGG AB AS. CONOCI ASS. RECH. AUSTRIAN I BELIMO AUT COVENTRY U DAEDALUS I DATAMED H FACULTY OF FED. UNITA FL-SOFT V/ INST. OF I GOETHE UNI MIT-MANAGE MOMATEC NAT. UNIV. NOTTINGHAM POLITECNIC SENTIENT M SIEMENS BU SOFIISKI U START ENGI STICHTING STICHTING THE UNIV. UNIV. DE L UNIV.SKLIN UNIV. DE G UNIV. PARI UNIV. OF A UNIV. OF C UNIV. OF C UNIV. OF W UNIV. OF Z INST. DALL RAUTARUUKK UNIV.E DE UNIV. OF U SOFTECO SI UNIV. GENT TSS - TRAN UNIV. DE G UNIV. DE V UNIVERZA V UNIV. PAUL TECH. UNIV UNIV. WIEN UNIV. VAN ENERGY RES TEKNILLINE DE MONTFOR CITY UNIVE UNIV. OF J AABO AKADE RISOE NAT. KINGS COLL UNIV. DORT FRIEDRICH- UNIV. OF C INST. NAT. BULGARIAN ENTE PER L LOUGHBOROU HELSINKI U CRANFIELD UNIV. CATH OTTO VON G UNIV. DEGL UNIV. OF O UNIV. OF T ELITE EURO ERASMUS UN INST. FUER UNIV. PARI BRITISH TE BOURNEMOUT UNIV. OF B UNIV. OF S DANMARKS T DAIMLER CH INST. NAT. INST. SUPE POLITECNIC POLISH ACA UNIV. POLI NAT. TEC. CONSEJO SU KATHOLIEKE UNIV. TWEN TECH. UNIV UNIV. POLI CENTRE NAT TEC. UNIV. UNIV. OF P FUNDACION JOZEF STEF CZECH TECH UNIV. OF N UNIV. OF S BAE SYSTEM UNIV. OF M C. R. FIAT NL ORG. FO CHALMERS T SAMTECH SA VOLVO AERO AVIO S.P.A MSC SOFTWA LULEAA UNI QUEENS UNI AIRBUS FRA CAD - FEM C. SVILUPP TRL LEUVEN MEA A. UNIV. T GERMAN AER CENTRE INT UNIV. DEGL QINETIQ UNIV. OF L FUNDACION ACCESS E.V EUROP. SPA UNIV. OF G UNIV. DEGL UNIV. OF G UNIV. OF N FINITE ELE ROCKFIELD WS ATKINS ROYAL INST UNIV. HANN FRAUENHOFE GKSS - FOR NAT. NUCLE UNIV. OF D ENGIN SOFT FEGS IFP SICOMP INTES - IN UNIV. DEGL PRINCIPIA ABS CONSUL ALTAIR ENG ANAKON ATOS ORIGI AWE PLC BEHR & CO CAESAR SYS CORK INST. CREA CONSU D C WHITE DAMT LTD DEP. OF E DR THELLEN DUNLOP STA EASI ENGIN EATEC LTD FEMSYS LTD FOKKER SPA FORSCHUNGS GIFFORD AN HAHN-SCHIC HERMSDORFE INBIS TECH INGENIEURB INTEGRATED KATHOLIEKE MANNESMANN MARITIME H MECAS S.R. MERITOR HE MERKLE UND NAFEMS LTD NCODE INT. NLSE VEREN NEW TECH. NOKIA MOBI NORUT TEKN NUMERICAL OXFORD BRO PD & E AUT RANDOM LOA SAFE TECH. SKF R & D SOFISTK AG ST MECANIC STAVANGER STRUCTURAL SULZER MAR TECHNISCH TECHSOFT E TECNOLOGIA TUN ABDUL UNIV.E DO UNIV. OF S WILDE AND

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 116

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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). Still in the implementation phase is the hierarchical clustering in large networks based on Ferligoj and Batagelj (1982 and 1983).

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 117

' Selected Books on SNA $

• J. P Scott: Social Network Analysis: A Handbook. SAGE Publications, 2000. Amazon.

• A. Degenne, M. Forse:´ Introducing Social Networks. SAGE Publications, 1999. Amazon.

• S. Wasserman, K. Faust: Social Network Analysis: Methods and Applications. CUP, 1994. Amazon.

• W. de Nooy, A. Mrvar, V. Batagelj: Exploratory Social Network Analysis with Pajek, CUP, 2005. Amazon. ESNA page.

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

• E. Lazega: The Collegial Phenomenon: The Social Mechanisms of Cooperation among Peers in a Corporate Law Partnership. OUP, 2001. Amazon.

• P.J. Carrington, J. Scott, S. Wasserman (Eds.): Models and Methods in Social Network Analysis. CUP, 2005. Amazon.

• U. Brandes, T. Erlebach (Eds.): Network Analysis: Methodological Foundations. LNCS, Springer, Berlin 2005. Amazon.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 118

' Courses on NA $ • James Moody, The Ohio State University • Steve Borgatti, UCINET • Barry Wellman, University of Toronto • Douglas White, University of California Irvine • Lada Adamic, University of Michigan • Mark Newman, University of Michigan • Jon Kleinberg, Cornell University • Robert A. Hanneman, University of California, Riverside; workshop • Noah Friedkin, University of California, Santa Barbara • John Levi Martin, University of Wisconsin, Madison • Vladimir Batagelj, University of Ljubljana • Andrej Mrvar, University of Ljubljana

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L % V. Batagelj: Analysis and visulization of large networks with Pajek 119

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Software for SNA UCINET, NetDraw Pajek Netminer Visone SNA/R StOCNET Negopy InFlow GUESS NetworkX prefuse JUNG BGL/Python See also the INSNA list and recent overview by M. Huisman and M.A.J. van Duijn.

Methodenforum der Fakultat¨ fur¨ Sozialwissenschaften, Universitat¨ Wien, 21-22. 6. 2007 & L L S L G L S L L %