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Large Networks V. Batagelj Analysis of Large Networks Pajek with Pajek Network visualization Properties Important Vladimir Batagelj subnetworks Multiplication University of Ljubljana ESNA Pajek ESSIR 2011 8th European Summer School

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Large Networks

V. Batagelj

Pajek Network visualization Properties Important subnetworks Multiplication ESNA Pajek

Analysis of Large Networks with Pajek

Vladimir Batagelj

University of Ljubljana

ESSIR 2011 – 8th European Summer School on Information Retrieval 29 Aug - 02 Sep 2011, Koblenz, Germany

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Outline

1 Pajek 2 Network visualization 3 Properties 4 Important subnetworks 5 Multiplication 6 ESNA Pajek

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Pajek and large networks

Pajek is a program for analysis and visu- alization of large networks. large ≡ the network can be stored in the computer memory. Network = Graph + Data Pajek is mostly a two men (A. Mrvar and V. Batagelj) project. We started to develop Pajek in 1996. It was assembled from experiences and code from my projects on graph algorithms in eighties and first half of nineties, and Andrej’s master thesis on graph

visualization. It is programmed in Delphi Pascal for Windows 32. A

64-bit Windows Delphi version is ready for release. In November 2010 we also started to develop a new basic network analysis library (64-bit, C++). Large networks are sparse (Dunbar number). For large structures already quadratic algorithms are too slow.

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Pajek’s backround

cut-out reduction local global hierarchy context inter-links

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.

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New algorithms

vertex and line cuts,
vertex and line islands,
(generalized) cores,
triadic spectrum; 3-rings and 4-rings weights,
fragment (motif) searching,
hierarchical clustering with relational constraints,
Doreian & Hummon weights in acyclic networks,
multiplication of networks,
fast Pathfinder algorithm, . . .
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Pajek is a network ’calculator’

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. Low level granularity of operations – a sequence of operations is usually needed to do a task (macros); but it is also more flexible.

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Pajek’s network description language

Multi-relational temporal network – KEDS/WEIS

% Recoded by WEISmonths, Sun Nov 28 21:57:00 2004 % from http://www.ku.edu/~keds/data.dir/balk.html *vertices 325 1 "AFG" [1-*] 2 "AFR" [1-*] 3 "ALB" [1-*] 4 "ALBMED" [1-*] 5 "ALG" [1-*] ... 318 "YUGGOV" [1-*] 319 "YUGMAC" [1-*] 320 "YUGMED" [1-*] 321 "YUGMTN" [1-*] 322 "YUGSER" [1-*] 323 "ZAI" [1-*] 324 "ZAM" [1-*] 325 "ZIM" [1-*] *arcs :0 "*** ABANDONED" *arcs :10 "YIELD" *arcs :11 "SURRENDER" *arcs :12 "RETREAT" ... *arcs :223 "MIL ENGAGEMENT" *arcs :224 "RIOT" *arcs :225 "ASSASSINATE TORTURE" *arcs 224: 314 153 1 [4] 890402 YUG KSV 224 (RIOT) RIOT-TORN 212: 314 83 1 [4] 890404 YUG ETHALB 212 (ARREST PERSON) ALB ETHNIC JAILED 224: 3 83 1 [4] 890407 ALB ETHALB 224 (RIOT) RIOTS 123: 83 153 1 [4] 890408 ETHALB KSV 123 (INVESTIGATE) PROBING ... 42: 105 63 1 [175] 030731 GER CYP 042 (ENDORSE) GAVE SUPPORT 212: 295 35 1 [175] 030731 UNWCT BOSSER 212 (ARREST PERSON) SENTENCED TO PRISON 43: 306 87 1 [175] 030731 VAT EUR 043 (RALLY) RALLIED 13: 295 35 1 [175] 030731 UNWCT BOSSER 013 (RETRACT) CLEARED 121: 295 22 1 [175] 030731 UNWCT BAL 121 (CRITICIZE) CHARGES 122: 246 295 1 [175] 030731 SER UNWCT 122 (DENIGRATE) TESTIFIED 121: 35 295 1 [175] 030731 BOSSER UNWCT 121 (CRITICIZE) ACCUSED

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Network visualization

Standard network visualization methods can produce readable results for not too large and relatively sparse networks. For denser networks the matrix representation is usually the right choice. In network analysis it is very important to support also visualization of additional data. It seems that interactive layouts are the future of network visualization. In Pajek the following visualization tools are available:

spring embedders: Kamada Kawai, Fruchterman Reingold
eigen vectors
acyclic
manual improvements
matrix representation

In nineties we won several first prizes at the Graph Drawing competitions.

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Network = Graph + Data

Display of properties – school (Moody)

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Analysis of Countries.net

France United Kingdom Belgium Germany Italia Poland Portugal Denmark Spain Finland Switzerland Norway Sweden Czech R. The Netherlands Russian F. Austria Greece Hungary Bulgaria Slovenia Estonia Israel Iceland USA Azerbaijan Latvia China Belarus Canada India Luxembourg Tunisia Lebanon Ireland Cyprus Japan Turkey Morocco Algeria Croatia Macedonia Romania Georgia Liechtenstein Slovakia Afghanistan Ukraine Albania Ecuador Malta Lithuania Kazakhstan Moldavia Thailand Jordan Turkmenistan Serbia-Montenegro Uzbekistan Armenia

To obtain picture in which the stronger lines cover weaker lines we have to sort them Net/Transform/Sort lines/Line values/Ascending For dense (sub)networks we get better visualization by using matrix display. In this case we also recoded values (2,10,50). To determine clusters we used Ward’s clustering procedure with dissimilarity measure d5 (corrected Euclidean distance). The permutation determined by hierarchy can often be improved by changing the positions of clusters. We get a typical center-periphery structure.

More: Batagelj, V.: Complex Networks, Visualization of. R.A. Meyers, ed., Encyclopedia of Complexity and Systems Science, Springer 2009: 1253-1268.

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Matrix display

Pajek - Ward [0.00,4785.14]

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 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 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

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k-rings

A k-ring is a simple closed chain of length k. Using k-rings we can define a weight of edges as wk(e) = # of different k-rings containing the edge e ∈ E The edges belonging to cliques have large weights. Therefore these weights can be used to identify the dense parts of a network. The k-rings can be efficiently determined only for small values of k – 3, 4, 5. The 3-rings (triangular) weights were implemented in Pajek in May 2002 and 4-rings in August 2005. On the k-rings we can also base the notion of short cycle connectivity which provides us with another decomposition of networks. In two-mode network there are no 3-rings. The densest substructures are complete bipartite subgraphs Kp,q. They contain many 4-rings.

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Directed 3- and 4-rings

There are 2 types of directed 3-rings:

cyclic transitive

and 4 types of directed 4-rings:

cyclic transitive genealogical diamond

In the case of transitive rings Pajek provides a special weight counting on how many transitive rings the arc is a shortcut.

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Charlie Brown island for w4 in IMDB

Be My Valentine, Charlie Brown Boy Named Charlie Brown Charlie Brown Celebration Charlie Brown Christmas Charlie Brown Thanksgiving Charlie Brown’s All Stars! He’s Your Dog, Charlie Brown Is This Goodbye, Charlie Brown? It’s a Mystery, Charlie Brown It’s an Adventure, Charlie Brown It’s Flashbeagle, Charlie Brown It’s Magic, Charlie Brown It’s the Easter Beagle, Charlie Brown It’s the Great Pumpkin, Charlie Brown Life Is a Circus, Charlie Brown Making of ’A Charlie Brown Christmas’ Play It Again, Charlie Brown Race for Your Life, Charlie Brown Snoopy Come Home There’s No Time for Love, Charlie Brown You Don’t Look 40, Charlie Brown You’re a Good Sport, Charlie Brown You’re In Love, Charlie Brown You’re Not Elected, Charlie Brown Charlie Brown and Snoopy Show Altieri, Ann Dryer, Sally Mendelson, Karen Momberger, Hilary Stratford, Tracy Brando, Kevin Hauer, Brent Kesten, Brad Melendez, Bill Ornstein, Geoffrey Reilly, Earl ’Rocky’ Robbins, Peter (I) Schoenberg, Jeremy Shea, Christopher (I) Shea, Stephen

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Hummon and Doreian weights

In an acyclic network the search path count (SPC) weights (Hum- mon and Doreian, 1989) are based

n counters n(u, v) that count the

number of different paths from s to t through the arc (u, v). To com- pute n(u, v) we introduce two aux- iliary quantities: n−(v) counts the number of different paths from s to v, and n+(v) counts the num- ber of different paths from v to t. They can be efficiently computed. n(u, v) = n−(u) · n+(v).

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Properties of SPC weights

The values of counters n(u, v) form a flow in the citation network – the Kirchoff’s vertex law holds: For every vertex u in a standardized citation network incoming flow = outgoing flow:

v:vRu

n(v, u) =

v:uRv

n(u, v) = n−(u) · n+(u) The weight n(t, s) equals to the total flow through network and provides a natural normalization of weights w(u, v) = n(u, v) n(t, s) ⇒ 0 ≤ w(u, v) ≤ 1 and if C is a minimal arc-cut-set

(u,v)∈C w(u, v) = 1.

In large networks the values of weights can grow very large. This should be considered in the implementation of the algorithms.

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Cores and generalized cores

The notion of core was intro- duced by Seidman in 1983. Let G = (V, E) be a graph. A sub- graph 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 maxi- mal 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,

ut-degree, in-degree + out-degree, etc., determining different types
f cores.

Algorithm: 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.

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Cores of orders 10–21 in Computational Geometry

L.J.Guibas M.Sharir L.P.Chew M.Flickner M.J.vanKreveld D.G.Kirkpatrick W.J.Lenhart S.P.Fekete F.Hurtado B.Chazelle D.White K.R.Romanik N.M.Amato T.D.Blacker J.S.Snoeyink T.C.Shermer D.Z.Chen D.P.Dobkin H.Alt F.P.Preparata J.Erickson J.E.Hershberger C-K.Yap M.Whitely J-D.Boissonnat S.J.Fortune R.L.S.Drysdale J.Harer D.M.Avis O.Schwarzkopf J.S.B.Mitchell D.Bremner H.A.El-Gindy D.Steele B.Dom J-R.Sack M.H.Overmars V.Sacristan O.Aichholzer R.Pollack D.H.Rappaport S.H.Whitesides D.Eppstein E.D.Demaine M.T.Goodrich D.M.Mount S-W.Cheng D.L.Souvaine S.A.Mitchell D.Petkovic P.Yanker M.W.Bern P.K.Agarwal I.G.Tollis T.J.Tautges H.Edelsbrunner T.L.Edwards H.Imai E.M.Arkin R.Wenger S.E.Benzley P.Plassmann M.T.deBerg D.Halperin T.C.Biedl W.J.Bohnhoff J.R.Hipp P.Belleville C.Grimm G.T.Toussaint M.Yvinec H.Meijer Te.Asano S.S.Skiena M.Teillaud H.S.Sawhney D.Zorin A.Lubiw S.Suri D.T.Lee R.R.Lober K.Kedem E.Welzl G.Liotta J.Pach P.K.Bose J.C.Clements S.R.Kosaraju J.Weeks D.Letscher G.Lerman J.Czyzowicz A.Aggarwal H.Everett B.Zhu T.K.Dey E.Trimble N.Amenta G.D.Sjaardema R.Tamassia M.Gorkani B.Aronov S.Lazard T.Roos G.T.Wilfong M.L.Demaine J-M.Robert T.J.Wilson S.M.Robbins R.Seidel N.Katoh G.Rote J.Urrutia J.S.Vitter I.Streinu L.Lopez-Buriek C.K.Johnson F.Aurenhammer S.Parker J.Matousek E.Sedgwick J.O’Rourke O.Devillers J.Ashley J.Hafner C.Zelle W.R.Oakes W.Niblack K.Mehlhorn M.E.Houle J.Hass A.Hicks Q.Huang

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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. Some examples of p-functions: pS(v, U) =

u∈NU(v)

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

u∈NU(v) w(v, u), where w : E → R

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.

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Additional p-functions

relative density pγ(v, C) = deg(v, C) maxu∈N(v) deg(u), if deg(v) > 0; 0, otherwise diversity pδ(v, C) = max

u∈N+(v,C) deg(u) −

min

u∈N+(v,C) deg(u)

average weight pa(v, C) = 1 |N(v, C)|

u∈N(v,C)

w(v, u), if N(v, C) = ∅; 0,

therwise
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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. 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.

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pS-core at level 46 of Geombib network

L.Guibas M.Sharir M.vanKreveld B.Chazelle J.Snoeyink A.Garg D.Dobkin F.Preparata J.Hershberger C.Yap J.Boissonnat O.Schwarzkopf J.Mitchell M.Overmars P.Gupta R.Pollack D.Eppstein M.Goodrich M.Bern P.Agarwal I.Tollis H.Edelsbrunner E.Arkin R.Janardan M.deBerg D.Halperin L.Vismara M.Smid G.Toussaint M.Yvinec M.Teillaud S.Suri R.Klein E.Welzl G.Liotta J.Pach P.Bose J.Schwerdt J.Majhi J.Czyzowicz R.Tamassia B.Aronov R.Seidel J.Urrutia J.Vitter J.Matousek C.Icking J.O’Rourke O.Devillers G.diBattista

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Cuts

The standard approach to find interesting groups inside a network is based on properties/weights – they can be measured or computed from network structure. The vertex-cut of a network N = (V, L, p), p : V → R, at selected level t is a subnetwork N(t) = (V′, L(V′), p), determined by the set V′ = {v ∈ V : p(v) ≥ t} and L(V′) is the set of lines from L that have both endpoints in V′. The line-cut of a network N = (V, L, w), w : L → R, at selected level t is a subnetwork N(t) = (V(L′), L′, w), determined by the set L′ = {e ∈ L : w(e) ≥ t} and V(L′) is the set of all endpoints of the lines from L′.

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SOM citation network

PFAFFELHUBER-E-1975-V18-P217 POGGIO-T-1975-V19-P201 KOHONEN-T-1976-V21-P85 KOHONEN-T-1976-V22-P159 AMARI-SI-1977-V26-P175 KOHONEN-T-1977-V2-P1065 ANDERSON-JA-1977-V84-P413 WOOD-CC-1978-V85-P582 COOPER-LN-1979-V33-P9 PALM-G-1980-V36-P19 AMARI-S-1980-V42-P339 SUTTON-RS-1981-V88-P135 KOHONEN-T-1982-V43-P59 BIENENSTOCK-EL-1982-V2-P32 HOPFIELD-JJ-1982-V79-P2554 ANDERSON-JA-1983-V13-P799 KNAPP-AG-1984-V10-P616 MCCLELLAND-JL-1985-V114-P159 HECHTNIELSEN-R-1987-V26-P1892 HECHTNIELSEN-R-1987-V26-P4979 GROSSBERG-S-1987-V11-P23 CARPENTER-GA-1987-V37-P54 GROSSBERG-S-1988-V1-P17 HECHTNIELSEN-R-1988-V1-P131 SEJNOWSKI-TJ-1988-V241-P1299 BROWN-TH-1988-V242-P724 BROWN-TH-1990-V13-P475 KOHONEN-T-1990-V78-P1464 TREVES-A-1991-V2-P371 HASSELMO-ME-1993-V16-P218 BARKAI-E-1994-V72-P659 HASSELMO-ME-1994-V14-P3898 HASSELMO-ME-1994-V7-P13 HASSELMO-ME-1995-V67-P1 HASSELMO-ME-1995-V15-P5249 GLUCK-MA-1997-V48-P481 ASHBY-FG-1999-V6-P363

Main subnetwork for Hum- mon and Doreian SPC weights (arc cut at level 0.007) of the SOM (self-

rganizing

maps) citation network (4470 vertices, 12731 arcs). See paper.

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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. We developed very efficient algorithms to determine the islands hierarchy and to list all the islands of selected sizes.

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Islands

Islands are very general and efficient approach to determine the important subnetworks in a given network. We have to express the goals of our analysis with a related property of the vertices or weight of the lines. Using this property we determine the islands of an appropriate size (in the interval k to K). In large networks we can get many islands which we have to inspect individually and interpret their content. An important property of the islands is that they identify locally important subnetworks on different levels. Therefore they detect also emerging groups.

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Islands

A set of vertices C ⊆ V is a regular vertex island in network N = (V, L, p), p : V → R iff it induces a connected subgraph and the vertices from the island are ’higher’ than the neighboring vertices max

u∈N(C) p(u) < min v∈c p(v)

A set of vertices C ⊆ V is a regular line island in network N = (V, L, w), w : L → R iff it induces a connected subgraph and the lines inside the island are ’stronger linked’ among them than with the neighboring vertices – in N there exists a spanning tree T over C such that max

(u,v)∈L,u / ∈C,v∈C w(u, v) <

min

(u,v)∈T w(u, v)

An island is simple iff it has a single peak. See details.

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Islands – US patents

The Nber network of US Patents has 3774768 ver- tices and 16522438 arcs (1 loop). We computed SPC weights in it and determined all (2,90)-islands. The re- duced network has 470137 vertices, 307472 arcs and for different k: C2 =187610, C5 =8859,C30 =101, C50 =30 islands.

2682562 3322485 3636168 3666948 3691755 3697150 3767289 3773747 3795436 3796479 3876286 3891307 3947375 3954653 3960752 3975286 4000084 4011173 4013582 4017416 4029595 4032470 4077260 4082428 4083797 4113647 4118335 4130502 4149413 4154697 4195916 4198130 4202791 4229315 4261652 4290905 4293434 4302352 4330426 4340498 4349452 4357078 4361494 4368135 4386007 4387038 4387039 4400293 4415470 4419263 4422951 4455443 4456712 4460770 4472293 4472592 4480117 4502974 4510069 4514044 4526704 4550981 4558151 4583826 4621901 4630896 4657695 4659502 4695131 4704227 4709030 4710315 4713197 4719032 4721367 4752414 4770503 4795579 4797228 4820839 4832462 4877547 4957349 5016988 5016989 5122295 5124824 5171469 5283677 5555116

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US patents / Liquid crystal display

Table 1: Patents on the liquid-crystal display patent date author(s) and title 2544659 Mar 13, 1951

Dreyer. Dichroic light-polarizing sheet and the like and the

formation and use thereof 2682562 Jun 29, 1954 Wender, et al. Reduction of aromatic carbinols 3322485 May 30, 1967

Williams. Electro-optical elements utilazing an organic

nematic compound 3636168 Jan 18, 1972

Josephson. Preparation of polynuclear aromatic compounds

3666948 May 30, 1972 Mechlowitz, et al. Liquid crystal termal imaging system having an undisturbed image on a disturbed background 3675987 Jul 11, 1972

Rafuse. Liquid crystal compositions and devices

3691755 Sep 19, 1972

Girard. Clock with digital display

3697150 Oct 10, 1972

Wysochi. Electro-optic systems in which an electrophoretic-

like or dipolar material is dispersed throughout a liquid crystal to reduce the turn-off time 3731986 May 8, 1973

Fergason. Display devices utilizing liquid crystal light

modulation 3767289 Oct 23, 1973 Aviram, et al. Class of stable trans-stilbene compounds, some displaying nematic mesophases at or near room temperature and others in a range up to 100◦C 3773747 Nov 20, 1973

Steinstrasser. Substituted azoxy benzene compounds

3795436 Mar 5, 1974 Boller, et al. Nematogenic material which exhibit the Kerr effect at isotropic temperatures 3796479 Mar 12, 1974 Helfrich, et al. Electro-optical light-modulation cell utilizing a nematogenic material which exhibits the Kerr effect at isotropic temperatures 3872140 Mar 18, 1975 Klanderman, et al. Liquid crystalline compositions and method 3876286 Apr 8, 1975 Deutscher, et al. Use of nematic liquid crystalline substances 3881806 May 6, 1975

Suzuki. Electro-optical display device

3891307 Jun 24, 1975 Tsukamoto, et al. Phase control of the voltages applied to

pposite electrodes for a cholesteric to nematic phase

transition display 3947375 Mar 30, 1976 Gray, et al. Liquid crystal materials and devices 3954653 May 4, 1976

Yamazaki. Liquid crystal composition having high dielectric

anisotropy and display device incorporating same 3960752 Jun 1, 1976 Klanderman, et al. Liquid crystal compositions 3975286 Aug 17, 1976

Oh. Low voltage actuated field effect liquid crystals

compositions and method of synthesis 4000084 Dec 28, 1976 Hsieh, et al. Liquid crystal mixtures for electro-optical display devices 4011173 Mar 8, 1977

Steinstrasser. Modified nematic mixtures with

positive dielectric anisotropy 4013582 Mar 22, 1977

Gavrilovic. Liquid crystal compounds and electro-optic

devices incorporating them 4017416 Apr 12, 1977 Inukai, et al. P-cyanophenyl 4-alkyl-4’-biphenylcarboxylate, method for preparing same and liquid crystal compositions using same 4029595 Jun 14, 1977 Ross, et al. Novel liquid crystal compounds and electro-optic devices incorporating them 4032470 Jun 28, 1977 Bloom, et al. Electro-optic device 4077260 Mar 7, 1978 Gray, et al. Optically active cyano-biphenyl compounds and liquid crystal materials containing them 4082428 Apr 4, 1978

Hsu. Liquid crystal composition and method

Table 2: Patents on the liquid-crystal display patent date author(s) and title 4083797 Apr 11, 1978

Oh. Nematic liquid crystal compositions

4113647 Sep 12, 1978 Coates, et al. Liquid crystalline materials 4118335 Oct 3, 1978 Krause, et al. Liquid crystalline materials of reduced viscosity 4130502 Dec 19, 1978 Eidenschink, et al. Liquid crystalline cyclohexane derivatives 4149413 Apr 17, 1979 Gray, et al. Optically active liquid crystal mixtures and liquid crystal devices containing them 4154697 May 15, 1979 Eidenschink, et al. Liquid crystalline hexahydroterphenyl derivatives 4195916 Apr 1, 1980 Coates, et al. Liquid crystal compounds 4198130 Apr 15, 1980 Boller, et al. Liquid crystal mixtures 4202791 May 13, 1980 Sato, et al. Nematic liquid crystalline materials 4229315 Oct 21, 1980 Krause, et al. Liquid crystalline cyclohexane derivatives 4261652 Apr 14, 1981 Gray, et al. Liquid crystal compounds and materials and devices containing them 4290905 Sep 22, 1981

Kanbe. Ester compound

4293434 Oct 6, 1981 Deutscher, et al. Liquid crystal compounds 4302352 Nov 24, 1981 Eidenschink, et al. Fluorophenylcyclohexanes, the preparation thereof and their use as components of liquid crystal dielectrics 4330426 May 18, 1982 Eidenschink, et al. Cyclohexylbiphenyls, their preparation and use in dielectrics and electrooptical display elements 4340498 Jul 20, 1982

Sugimori. Halogenated ester derivatives

4349452 Sep 14, 1982 Osman, et al. Cyclohexylcyclohexanoates 4357078 Nov 2, 1982 Carr, et al. Liquid crystal compounds containing an alicyclic ring and exhibiting a low dielectric anisotropy and liquid crystal materials and devices incorporating such compounds 4361494 Nov 30, 1982 Osman, et al. Anisotropic cyclohexyl cyclohexylmethyl ethers 4368135 Jan 11, 1983

Osman. Anisotropic compounds with negative or positive

DC-anisotropy and low optical anisotropy 4386007 May 31, 1983 Krause, et al. Liquid crystalline naphthalene derivatives 4387038 Jun 7, 1983 Fukui, et al. 4-(Trans-4’-alkylcyclohexyl) benzoic acid 4’”-cyano-4”-biphenylyl esters 4387039 Jun 7, 1983 Sugimori, et al. Trans-4-(trans-4’-alkylcyclohexyl)-cyclohexane carboxylic acid 4’”-cyanobiphenyl ester 4400293 Aug 23, 1983 Romer, et al. Liquid crystalline cyclohexylphenyl derivatives 4415470 Nov 15, 1983 Eidenschink, et al. Liquid crystalline fluorine-containing cyclohexylbiphenyls and dielectrics and electro-optical display elements based thereon 4419263 Dec 6, 1983 Praefcke, et al. Liquid crystalline cyclohexylcarbonitrile derivatives 4422951 Dec 27, 1983 Sugimori, et al. Liquid crystal benzene derivatives 4455443 Jun 19, 1984 Takatsu, et al. Nematic halogen Compound 4456712 Jun 26, 1984 Christie, et al. Bismaleimide triazine composition 4460770 Jul 17, 1984 Petrzilka, et al. Liquid crystal mixture 4472293 Sep 18, 1984 Sugimori, et al. High temperature liquid crystal substances of four rings and liquid crystal compositions containing the same 4472592 Sep 18, 1984 Takatsu, et al. Nematic liquid crystalline compounds 4480117 Oct 30, 1984 Takatsu, et al. Nematic liquid crystalline compounds 4502974 Mar 5, 1985 Sugimori, et al. High temperature liquid-crystalline ester compounds 4510069 Apr 9, 1985 Eidenschink, et al. Cyclohexane derivatives Table 3: Patents on the liquid-crystal display patent date author(s) and title 4514044 Apr 30, 1985 Gunjima, et al. 1-(Trans-4-alkylcyclohexyl)-2-(trans-4’-(p-sub stituted phenyl) cyclohexyl)ethane and liquid crystal mixture 4526704 Jul 2, 1985 Petrzilka, et al. Multiring liquid crystal esters 4550981 Nov 5, 1985 Petrzilka, et al. Liquid crystalline esters and mixtures 4558151 Dec 10, 1985 Takatsu, et al. Nematic liquid crystalline compounds 4583826 Apr 22, 1986 Petrzilka, et al. Phenylethanes 4621901 Nov 11, 1986 Petrzilka, et al. Novel liquid crystal mixtures 4630896 Dec 23, 1986 Petrzilka, et al. Benzonitriles 4657695 Apr 14, 1987 Saito, et al. Substituted pyridazines 4659502 Apr 21, 1987 Fearon, et al. Ethane derivatives 4695131 Sep 22, 1987 Balkwill, et al. Disubstituted ethanes and their use in liquid crystal materials and devices 4704227 Nov 3, 1987 Krause, et al. Liquid crystal compounds 4709030 Nov 24, 1987 Petrzilka, et al. Novel liquid crystal mixtures 4710315 Dec 1, 1987 Schad, et al. Anisotropic compounds and liquid crystal mixtures therewith 4713197 Dec 15, 1987 Eidenschink, et al. Nitrogen-containing heterocyclic compounds 4719032 Jan 12, 1988 Wachtler, et al. Cyclohexane derivatives 4721367 Jan 26, 1988 Yoshinaga, et al. Liquid crystal device 4752414 Jun 21, 1988 Eidenschink, et al. Nitrogen-containing heterocyclic compounds 4770503 Sep 13, 1988 Buchecker, et al. Liquid crystalline compounds 4795579 Jan 3, 1989 Vauchier, et al. 2,2’-difluoro-4-alkoxy-4’-hydroxydiphenyls and their derivatives, their production process and their use in liquid crystal display devices 4797228 Jan 10, 1989 Goto, et al. Cyclohexane derivative and liquid crystal composition containing same 4820839 Apr 11, 1989 Krause, et al. Nitrogen-containing heterocyclic esters 4832462 May 23, 1989 Clark, et al. Liquid crystal devices 4877547 Oct 31, 1989 Weber, et al. Liquid crystal display element 4957349 Sep 18, 1990 Clerc, et al. Active matrix screen for the color display of television pictures, control system and process for producing said screen 5016988 May 21, 1991

Iimura. Liquid crystal display device with a birefringent

compensator 5016989 May 21, 1991

Okada. Liquid crystal element with improved contrast and

brightness 5122295 Jun 16, 1992 Weber, et al. Matrix liquid crystal display 5124824 Jun 23, 1992 Kozaki, et al. Liquid crystal display device comprising a retardation compensation layer having a maximum principal refractive index in the thickness direction 5171469 Dec 15, 1992 Hittich, et al. Liquid-crystal matrix display 5283677 Feb 1, 1994 Sagawa, et al. Liquid crystal display with ground regions between terminal groups 5308538 May 3, 1994 Weber, et al. Supertwist liquid-crystal display 5374374 Dec 20, 1994 Weber, et al. Supertwist liquid-crystal display 5543077 Aug 6, 1996 Rieger, et al. Nematic liquid-crystal composition 5555116 Sep 10, 1996 Ishikawa, et al. Liquid crystal display having adjacent electrode terminals set equal in length 5683624 Nov 4, 1997 Sekiguchi, et al. Liquid crystal composition 5855814 Jan 5, 1999 Matsui, et al. Liquid crystal compositions and liquid crystal display elements

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Islands – The Edinburgh Associative Thesaurus

n = 23219, m = 325624, transitivity weight

AGAIN ALREADY ANYWAY AS BUT HAPPEN HAPPENED JUST MEANWHILE NEVERTHELESS NOTWITHSTANDING NOW OFTEN SOMETIME SOON THEREFORE WHY YET BELIEVE COINS COULD DEALER DEFICIT INCREASE LOOT MONEY MONIES MORE MONEY NO NOT OFFER PAID PAY PAYMENT PLEASE PROBABLY PROPERTY PROVIDE RECEIPT REFUSE REPAY STOLE THRIFT THRIFTY UNPAID ACTIVITY EDUCATION ENGINEERING HOMEWORK LEARNING LECTURER LECTURES LESSONS MATHS RESEARCH SCHOOL SCIENCE SCIENTIFIC STUDY STUDYING TEACHER TEACHING TRAINING WORK ADORABLE ATTRACTIVE BEAUTIFUL BELOVED BOSS CHAIRMAN CHARM DELIGHTFUL ELEGANCE FLIRT GIRL HAIRY INHUMAN KINDNESS LOVE LOVELY MAN MYSTERIOUS NICE POWERFUL PROFESSION RESPONSIBLE SHAPELY

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Analysis of two-mode networks

A two-mode network or affiliation network is a structure N = (U, V, A, w), where U and V are disjoint sets of vertices, A is the set of arcs with the initial vertex in the set U and the terminal vertex in the set V, and w : A → R is a weight. If no weight is defined we can assume a constant weight w(u, v) = 1 for all arcs (u, v) ∈ A. The set A can be viewed also as a relation A ⊆ U × V. A two-mode network can be formally represented by rectangular matrix W = [wuv]U×V. wuv =

w(u, v)

(u, v) ∈ A

therwise
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Analysis of two-mode networks

For direct analysis of two-mode networks we can use the eigen-vector approach – a two-mode variant of Kleinberg’s hubs and authorities. The weight vector (x, y) on U ∪ V is determined by relations y = Wx and x = WTy. In 2005 we proposed two new direct methods: two-mode cores and 4-rings. We can also use the clustering and blockmodeling in two-mode networks.

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Multiplication of networks

To a simple two-mode network N = (I, J , E, w); where I and J are sets of vertices, E is a set of edges linking I and J , and w : E → R (or some other semiring) is a weight; we can assign a network matrix W = [wi,j] with elements: wi,j = w(i, j) for (i, j) ∈ E and wi,j = 0

therwise.

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 = 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 ci,j =

k∈K

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

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Matrix multiplication

The standard matrix multiplication has the complexity O(|I| · |K| · |J |) – it is too slow to be used for large networks. For sparse large networks we can multiply faster considering

nly nonzero elements.

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

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Two-mode network analysis by conversion to

ne-mode network

Often we transform a two-mode network N = (U, V, E, w) into an ordinary (one-mode) network N1 = (U, E1, w1) or/and N2 = (V, E2, w2), where E1 and w1 are determined by the matrix W(1) = WWT, w(1)

uv = z∈V wuz · wT

zv. Evidently

w(1)

uv = w(1) vu . There is an edge (u : v) ∈ E1 in N1 iff

N(u) ∩ N(v) = ∅. Its weight is w1(u, v) = w(1)

uv .

The network N2 is determined in a similar way by the matrix W(2) = WTW. The networks N1 and N2 are analyzed using standard methods.

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Networks from data tables

A data table T is a set of records T = {Tk : k ∈ K}, where K is the set of

keys. A record has the form Tk = (k, q1(k), q2(k), . . . , qr(k)) where qi(k)

is the value of the property (attribute) qi for the key k.

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Networks from data tables

Suppose that the property q has the range 2Q. For example: Authors[WasFau] = { S. Wasserman, K. Faust }, PubYear[WasFau] = { 1994 }, . . . 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 v ∈ q(k), 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)}). It holds [qi × qj]T = qj × qi and qi × qj = [K × qi]T ∗ [K × qj] = [qi × K] ∗ [K × qj]. We can join a pair of properties qi and qj also with respect to the third property qs: we get a two-mode network [qi × qj]/qs = [qi × qs] ∗ [qs × qj].

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EU projects on simulation

For the meeting The Age of Simulation at Ars Electronica in Linz, January 2006 a dataset of EU projects on simulation was collected by FAS research, Vienna and stored in the form of Excel table (SimPro.csv). The rows are the projects participants (idents) and colomns correspond to different their properties. Three two-mode networks were produced from this table using J¨ urgen Pfeffer’s Text2Pajek program:

project.net – P = [idents × projects]
country.net – C = [idents × countries]
institution.net – U = [idents × institutions]

|idents| = 8869, |projects| = 933, |institutions| = 3438, |countries| = 60. Since all three networks have the common set (idents) we can derive from them using network multiplication several interesting networks:

ProjInst.net – W = [projects × institutions] = PT ∗ U
Countries.net – S = [countries × countries] = CT ∗ C
Institutions.net – Q = [institutions × institutions] = WT ∗ W
. . .
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Analysis of ProjInst.net

502909 IST-2000-30082 G4RD-CT-2000-00395 IST-2000-29207 502842 IST-2000-28177 G4RD-CT-2002-00795 G4RD-CT-2000-00178 BRPR987001 G4RD-CT-2002-00836 502896 502889 502917 G4RD-CT-2001-00403 G4MA-CT-2002-00022 BRST985352 506257 28283 506503 EVG3-CT-2002-80012 501084 29817 ENK6-CT-2002-30023 IST-2000-30158 511758 7210-PR/142 25525 7215-PP/034 T3.5/99 JOE3980089 SMT4982223 7210-PR/163 7210-PR/233 7215-PP/031 T3.2/99 IST-1999-56418 IST-1999-57451 HPSE-CT-2002-00108 IST-2001-35358 ENK5-CT-2000-00335 JOR3980200 QLK6-CT-2002-02292 7210-PR/095 HPSE-CT-2002-00143 A.S.M. S.A. AGRO-SAT CONSULTING AIRBUS DEUTSCHLAND AIRBUS FRANCE SAS AIRBUS UK LIMITED ALBERTSEN & HOLM AS ALENIA AERONAUTICA SPA ARMINES ASM - DIMATEC INGENIERIA BAE SYSTEMS BARCO NV BARTENBACH

BAYER. ROTES KREUZ

BBL BICC GENERAL CABLE BRITISH STEEL BROD THOMASSON BUILDING RESEARCH BUURSKOV CATALYSE SARL CENTRE DE RECH. METALLURG. CENTRE DE ROBOTIQUE CENTRE FOR EUROP. ECONOMIC CSTB

C. R. FIAT S.C.P.A.

CHALMERS TEKNISKA HOEGSKOLA CHIPIDEA - MICROELECTRONICA, S.A. CINAR LTD. COLOPLAST A/S CRE GROUP LTD. DAIMLER CHRYSLER AG DASSAULT AVIATION DATASYS S.R.O. DE ZENTRUM FUER LUFT UND RAUMFAHRT E.V. DFA DE FERNSEHNACHRICHTEN AGENTUR DISENO DE SISTEMAS EN SILICIO DPME ROBOTICS AB EA TECH. LTD EADS DE EDAG ENGINEERING + DESIGN ENEL.IT ENERGITEKNIK HEATEX AB ENERGY RESEARCH CENTRE NL ESI SOFTWARE SA EUROCOPTER S. FFT ESPANA TECH. DE AUTOMOCION, FONDAZIONE ENI - ENRICO MATTEI FRAUENHOFER INST. FUER MATERIALFLUSS UND LOGISTIK FRAUENHOFER INST. FUER

PRODUKTIONSTECH. UND AUTOMATISIERUNG

FRIMEKO INT. AB GATE5 AG GUNNESTORPS SMIDE & MEKANISKA AB HELP SERVICE REMOTE SENSING IFEN GES. FUER SATELLITENNAVIGATION ILEVO AB INDUSTRIAS ROYO INGENIORHOJSKOLEN HELSINGOR TEKNIKUM INOX PNEUMATIC AS

INST. CARTOGRAFIC DE CATALUNYA
INST. DE RECHERCHES

DE LA SIDERURGIE FR

INST. FUER TEXTIL UND
VERFAHRENSTECH. DENKENDORF
INST. NAT. DE RECHERCHE

SUR LES TRANSPORTS ET LEUR SCURIT

INST. SUPERIOR TECNICO

JERNKONTORET KBC MANUFAKTUR, KOECHLIN, BAUMGARTNER UND CIE. AG

KOMMANDITGES. HAMBURG 1

FERNSEHEN BETEILIGUNGS & CO LANDIS & GYR - EUROPE AG LESPROJEKT SLUZBY S.R.O. LH AGRO EAST S.R.O. LKSOFTWARE LMS UMWELTSYS.E, DIPL. ING. DR. HERBERT BACK MECALOG SARL MEFOS, FOUNDATION FOR METALLURGICAL RESEARCH MJM GROUP, A.S. MSO CONCEPT INNOVATION + SOFTWARE MTU AERO ENGINES

NAT. TEC. UNIV. OF ATHENS

NL ORG. FOR APPLIED SCIENTIFIC RESEARCH - TNO OESTERREICHISCHER BERGRETTUNGSDIENST OFFICE NAT. DETUDES ET DE REC. AEROSPATIALES OK GAMES DI ALESSANDRO CARTA ORAD HI TEC SYS. POLAND OSAUHING EETRIUKSUS POLYMAGE SARL PROLEXIA PSI FUR PRODUKTE UND SYS.E DER INFORMATIONSTECH. RESEARCH INST. OF THE FINNISH ECONOMY ROSENHEIMER GLASTECH. RUDOLF BRAUNS AND CO. KG SHERPA ENGINEERING SARL SNECMA MOTEURS SA SPORTART SSAB TUNNPL¯T STICHTING NATIONAAL LUCHT SUPERELECTRIC DI CARLO PAGLIALUNGA & C. SAS SVETS & TILLBEHOR AB TECHNOFARMING S.R.L. TESSITURA LUIGI SANTI SPA THE AARHUS SCHOOL OF BUSINESS THYSSENKRUPP STAHL A.G. TPS TERMISKA PROCESSER AB TQT SRL TRUMPF-BLUSEN-KLEIDER WALTER GIRNER UND CO. KG UAB LKSOFT BALTIC

UNIV. DE ZARAGOZA
UNIV. DER BUNDESWEHR MUENCHEN
UNIV. PANTHEON-ASSAS - PARIS II
UNIV. OF ABERDEEN
UNIV. OF MACEDONIA

VOEST-ALPINE STAHL VOLKSWAGEN AG WISDOM TELE VISION WYKES ENGINEERING COMPANY YAHOO! DE ZAMISEL D.O.O

Pajek

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Analysis of Institutions.net

AABO AKADEMI U ABS CONSULTING ACCESS E.V. AIRBUS FRANCE SAS ALLOGG AB ALTAIR ENGINEERING ANAKON A.U.THESSALONIKI AS.CONOCIMIENTO ASS.RECH.SCIENTIFIQUE ATOS ORIGIN ENG. AUSTRIAN I.AI AVIO S.P.A. AWE PLC BAE SYSTEMS BEHR &CO. BELIMO AUTOMATION BOURNEMOUTH U. BRITISH TELEC. BULGARIAN ACAD. OF SCIENCES CAD - FEM CAESAR SYSTEMS LTD C.INT.LENGINYERIA C.NAT.DE LA RECHERCHE SCIENTIFIQUE C.R.FIAT S.C.P.A. C.SVILUPPO MATERIALI CHALMERS TEKNISKA HOEGSKOLA CITY U.LONDON CONSEJO SUP.DE INVEST.CIENTIFICAS CORK I.OF TECHNOLOGY COVENTRY U. CRANFIELD U. CREA CONSULTANTS LTD CZECH T.U.PRAGUE D C WHITE&PARTNERS LTD DAEDALUS INFORMATICS LTD DAIMLER CHRYSLER AG DAMT LTD DANMARKS T.U. DATAMED HEALTHCARE INF.SYS. DE MONTFORT U. DEP.OF ENVIRONMENT, TRANSPORT AND THE REGIONS DR THELLEN DUNLOP STANDARD AEROSPACE GROUP EASI ENGINEERING EATEC LTD ELITE EUROP.LAB FOR INTELLIGENT TECH. ENERGY RESEARCH C.NL ENGIN SOFT TRADING SRL ENTE PER LE NUOVE TECNOLOGIE ERASMUS U.ROTTERDAM EUROP.SPACE AGENCY FACULTY OF ELECTRICAL ENG. FED.UNITARY ENTERPRISE ALL-RUSSIAN SCIENTIFIC CENTER FEGS FEMSYS LTD FINITE ELEMENT ANALYSIS LTD. FL-SOFT V/JENS JOERGEN OESTERGAARD FOKKER SPACE BV FEMCOS INGENIEURBUERO MBH FRAUENHOFER I.FUER BIOMEDICAL ENGINEERING FRIEDRICH-SCHILLER-U.JENA FUNDACION INASMET FUNDACION LABEIN GERMAN AEROSPACE CENTRE GIFFORD AND PARTNERS LTD. GKSS - FORSCHUNGSZENTRUM GEESTHACHT HAHN-SCHICKARD-GES. I.FUER NATURSTOFF-FORSCHUNG E.V. HELSINKI T.U. HERMSDORFER I.FUER TECH. IFP SICOMP AB INBIS TECH.LTD INGENIEURBUERO FUER TRAGWERKSPLANUNG I.NAT.DE RECHERCHE SUR LES TRANSPORTS ET LEUR SECURITE I.NAT.POLITEC.DE TOULOUSE I.OF INFORMATION TECH.S I.DALLE MOLLE DI STUDI SULLIA I.SUPERIOR TECNICO INTEGRATED DESIGN & ANALYSIS CONSULTANTS LTD INTES - INGENIEURGES. FUER TECH.SOFTWARE GOETHE U.FRANKFURT AM MAIN JOZEF STEFAN I. KATHOLIEKE HOGESCHOOL SINT-LIEVEN KATHOLIEKE U.LEUVEN KINGS COLLEGE LONDON LEUVEN MEASUREMENTS AND SYS.INT.NV LOUGHBOROUGH T.U. LULEAA T.U. MANNESMANN VDO AG MARITIME HYDRAULICS AS MECAS S.R.O. MERITOR HEAVY VEHICLE BRAKING SYS.- UK LTD MERKLE UND PARTNER MIT-MANAGEMENT INTELLIGENTER TECH.N MOMATEC MSC SOFTWARE NAFEMS LTD. NAT.NUCLEAR CORP.LTD. NAT.T.U.ATHENS NAT.U.IRELAND,MAYNOOTH NCODE INT. NLSE VERENIGDE SCHEEPSBOUW BUREAUS B.V. NL ORG.FOR APPLIED SCIENTIFIC RESEARCH-TNO NEW TECH.ENGINEERING LTD NOKIA MOBILE PHONES LTD NORUT TEKNOLOGI A.S. NOTTINGHAM TRENT U. NUMERICAL ANALYSIS AND DESIGN&CO KG OTTO VON GUERICKE MAGDEBURG U. OXFORD BROOKES U. PD&E AUTOMOTIVE B.V. POLISH ACAD.OF SCIENCES PT.BARI PT.TORINO PRINCIPIA INGENIEROS CONSULTORES QINETIQ QUEENS U.BELFAST RANDOM LOADING DESIGN RAUTARUUKKI OY RISOE NAT.LAB ROCKFIELD SOFTWARE LTD. ROYAL I.OF TECH. SAFE TECH. SAMTECH SA SENTIENT MACHINE RESEARCH B.V. SIEMENS BUILDING TECH.S AG SKF R&D COMPANY B.V. SOFIISKI U.SVETI KLIMENT OHRIDSKI SOFISTK AG SOFTECO SISMAT ST MECANICA APLICADA S.L. START ENGINEERING JSCO STAVANGER U.COLLEGE STICHTING NEURALE NETWERKEN STICHTING U.NYENRODE STRUCTURAL INTEGRITY ASSESSMENTS LTD SULZER MARKETS AND TECH.AG, SULZER INNOTEC T.U.V KOSICIACH TECHNISCH ADVIESBUREAU N.V. T.U.CLAUSTHAL T.U.DELFT TECHSOFT ENGINEERING S.R.O. TECNOLOGIAS CAE AVANZADAS S.L. TEKNILLINEN KORKEAKOULU THE U.COURT OF THE U.OF ABERDEEN TRL TSS-TRANSPORT SIMULATION SYS.S.L. TUN ABDUL RAZAK RESEARCH C.LTD. U.GRANADA U.LA LAGUNA U.VALLADOLID U.P.MADRID U.E DE COIMBRA U.E DO MINHO U.S.GENOVA U.S.NAPOLI U.S.PADOVA U.S.TRIESTE U.DORTMUND U.HANNOVER U.WIEN U.KLINIKUM AACHEN U.GIRONA U.P.CATALUNYA U.C.LOUVAIN U.PARIS VI PIERRE ET MARIE CURIE U.PARIS-DAUPHINE U.PAUL SABATIER DE TOULOUSE III U.GENT U.TWENTE U.AMSTERDAM U.A.S.ZITTAU/GOERLITZ U.BRISTOL U.OF CHEMICAL TECH. AND METALLURGY U.CRETE U.CYPRUS U.DURHAM U.GLASGOW U.GREENWICH U.JYVASKYLA U.LEEDS U.MANCHESTER U.NEWCASTLE UPON TYNE U.NOTTINGHAM U.OULU U.PAISLEY U.SHEFFIELD U.SPLIT U.STRATHCLYDE U.THE AEGEAN U.ULSTER U.WALES, ABERYSTWYTH U.ZAGREB U.MARIBOR VOLVO AERO CORP.AB WILDE AND PARTNERS LTD WS ATKINS CONSULTANTS LTD.

To identify the most important in- stitutions we first computed pS- cores vector and use it to deter- mine the corresponding vertex is-

lands. We got essentially one large

island. Again the corresponding subnetwork is very dense.

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WoS2Pajek

For converting WoS file into networks in Pajek’s format a program WoS2Pajek was developed (in Python). It produces the following files:

citation network: works × works;
authorship (two-mode) network: works × authors, for works

without complete description only the first author is known;

keywords (two-mode) network: works × keywords, only for

works with complete description;

journals (two-mode) network: works × journals, field J9;
partition of works by the publication year;
partition of works – complete description (1) / ISI name only

(0);

vector number of pages, PG or EP − BP +1.
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WoS2Pajek/ derived networks

Let us denote the citation network with Ci , u Ci v ≡ u cites v, and the authorship network with WA. Then Co = WAT ∗ WA is the collaboration network;

r better

Co′ = WAT ∗ diag(

1 deg v ) ∗ WA

Ca = WAT ∗ Ci ∗ WA is a network of citations between authors. biCo = Ci ∗ CiT is the bibliographic coupling network coCi = CiT ∗ Ci is the co-citation network coCi Since the network can be quite large we first eliminate the only-cited

works. The weight w(a, p) in the author citation network

ACi = WAT ∗ Ci counts the number of times author a cited work p. Let b(A) denotes the binarized version of A. The author co-citation network can be obtained as ACo = b(ACi) ∗ b(ACi)T

V. Batagelj

Large Networks

SLIDE 43

Large Networks

V. Batagelj

Pajek Network visualization Properties Important subnetworks Multiplication ESNA Pajek

Main island in citation network for SPC in Social networks

K L E I N _ K { 2 4 } 4 7 : 9 5 2 G R A N O V E T { 1 9 7 3 } 7 8 : 1 3 6 B O R G A T T I _ S { 2 3 } 2 9 : 9 9 1 N E W M A N _ M { 2 3 } 4 5 : 1 6 7 D E Z S O _ Z { 2 2 } 6 5 : 5 5 1 3 E U B A N K _ S { 2 4 } 4 2 9 : 1 8 M E Y E R S _ L { 2 5 } 2 3 2 : 7 1 N E W M A N _ M { 2 3 } 6 8 : 2 6 1 2 1 B U R T _ R { 2 4 } 1 1 : 3 4 9 M C P H E R S O _ M { 2 1 } 2 7 : 4 1 5 W E L L M A N _ B { 1 9 7 9 } 8 4 : 1 2 1 W E L L M A N _ B { 1 9 9 } 9 6 : 5 5 8 A L B E R T _ R { 2 2 } 7 4 : 4 7 B O C C A L E T _ S { 2 6 } 4 2 4 : 1 7 5 B O G U N A _ M { 2 4 } 7 : 5 6 1 2 2 D A V I D S E N _ J { 2 2 } 8 8 : 1 2 8 7 1 G O N Z A L E Z _ M { 2 6 } 9 6 : 8 8 7 2 G O N Z A L E Z _ M { 2 6 } 2 2 4 : 1 3 7 G R O N L U N D _ A { 2 4 } 7 : 3 6 1 8 H O L M E _ P { 2 3 } 6 8 : 5 6 1 7 H O L M E _ P { 2 4 } 2 6 : 1 5 5 N E W M A N _ M { 2 2 } 9 9 : 2 5 6 6 N E W M A N _ M { 2 3 } 6 8 : 3 6 1 2 2 W A T T S _ D { 2 2 } 2 9 6 : 1 3 2 L I N D _ P { 2 7 } 9 : 2 2 8 B R A S S _ D { 2 4 } 4 7 : 7 9 5 T R A V E R S _ J { 1 9 6 9 } 3 2 : 4 2 5 B U R T _ R { 1 9 8 4 } 6 : 2 9 3 C U R T I S _ R { 1 9 9 5 } 1 7 : 2 2 9 M A R S D E N _ P { 1 9 9 3 } 1 5 : 3 9 9 N E A I G U S _ A { 1 9 9 4 } 3 8 : 6 7 R O M N E Y _ A { 1 9 8 4 } 6 : 5 9 R O T H E N B E _ R { 1 9 9 8 } 1 2 : 1 5 2 9 S U D M A N _ S { 1 9 8 5 } 7 : 1 2 7 A N D E R S O N _ C { 1 9 9 9 } 2 1 : 3 7 G O O D R E A U _ S { 2 7 } 2 9 : 2 3 1 W A S S E R M A _ S { 1 9 9 6 } 6 1 : 4 1 S A U L _ Z { 2 7 } 2 3 : 2 6 4 B R E I G E R _ R { 1 9 7 4 } 5 3 : 1 8 1 W H I T E _ H { 1 9 7 } : W H I T E _ H { 1 9 7 6 } 8 1 : 7 3 N E W M A N _ M { 2 } 1 1 : 8 1 9 R A V A S Z _ E { 2 3 } 6 7 : 2 6 1 1 2 S O N G _ C { 2 5 } 4 3 3 : 3 9 2 C A P O C C I _ A { 2 6 } 7 4 : 3 6 1 1 6 J E O N G _ H { 2 3 } 6 1 : 5 6 7 K O S S I N E T _ G { 2 6 } 3 1 1 : 8 8 T O I V O N E N _ R { 2 6 } 3 7 1 : 8 5 1 T O M A S S I N _ M { 2 7 } 3 8 5 : 7 5 G U L A T I _ R { 1 9 9 8 } 1 9 : 2 9 3 I B A R R A _ H { 1 9 9 3 } 3 6 : 4 7 1 H O L L A N D _ P { 1 9 8 3 } 5 : 1 9 L O R R A I N _ F { 1 9 7 1 } 1 : 4 9 G I R V A N _ M { 2 2 } 9 9 : 7 8 2 1 N E W M A N _ M { 2 4 } 6 9 : 2 6 1 1 3 W O N G _ L { 2 6 } 3 6 : 9 9 C A S T E L L O _ X { 2 7 } 7 9 : 6 6 6 K L O V D A H L _ A { 1 9 8 5 } 2 1 : 1 2 3 H O L L A N D _ P { 1 9 8 1 } 7 6 : 3 3 P A R K _ J { 2 4 } 7 : 6 6 1 1 7 L A T K I N _ C { 1 9 9 6 } 2 4 : 3 4 1 B O N A C I C H _ P { 1 9 7 2 } 2 : 1 1 3 B A R A B A S I _ A { 2 5 } 4 3 5 : 2 7 N E W M A N _ M { 2 3 } 6 7 : 2 6 1 2 6 S T R O G A T Z _ S { 2 1 } 4 1 : 2 6 8 C O S T A _ L { 2 7 } 5 6 : 1 6 7 P A L L A _ G { 2 7 } 4 4 6 : 6 6 4 W I L H E L M _ T { 2 7 } 3 8 5 : 3 8 5 B A T A G E L J _ V { 2 } 2 2 : 1 7 3 A R E N A S _ A { 2 4 } 3 8 : 3 7 3 C A L L A W A Y _ D { 2 } 8 5 : 5 4 6 8 G L E I S E R _ P { 2 3 } 6 : 5 6 5 G U I M E R A _ R { 2 3 } 6 8 : 6 5 1 3 N E W M A N _ M { 2 2 } 8 9 : 2 8 7 1 B U R T _ R { 2 } 2 2 : 1 M A R S D E N _ P { 1 9 9 } 1 6 : 4 3 5 G R A N O V E T _ M { 1 9 7 4 } : N E W M A N _ M { 2 4 } 3 8 : 3 2 1 F R I E D M A N _ S { 1 9 9 7 } 8 7 : 1 2 8 9 B U R T _ R { 1 9 8 7 } 9 2 : 1 2 8 7 C O L E M A N _ J { 1 9 6 6 } : D A V I S _ J { 1 9 6 7 } 2 : 1 8 1 M E Y E R S _ L { 2 3 } 9 : 2 4 N E W M A N _ M { 2 2 } 6 6 : 1 6 1 2 8 R O T H E N B E _ R { 1 9 9 5 } 1 7 : 2 7 3 G R A B O W S K _ A { 2 6 } 7 3 : 1 6 1 3 5 L I N D _ P { 2 7 } 7 6 : 3 6 1 1 7 N E W M A N _ M { 1 9 9 9 } 6 : 7 3 3 2 B U R T _ R { 2 } 1 1 : 1 2 3 D E S O T O _ C { 1 9 6 } 6 : 4 1 7 K A T Z _ E { 1 9 5 5 } : M I L G R A M _ S { 1 9 6 7 } 1 : 6 1 W A S S E R M A _ S { 1 9 8 } 7 5 : 2 8 G U L A T I _ R { 1 9 9 9 } 1 4 : 1 4 3 9 G O F F M A N _ E { 1 9 7 1 } : V A L E N T E _ T { 1 9 9 6 } 1 8 : 6 9 V A L E N T E _ T { 1 9 9 7 } 4 5 : 6 7 7 B U R T _ R { 2 } 2 2 : 3 4 5 H O L L A N D _ P { 1 9 7 3 } 3 : 8 5 I B A R R A _ H { 1 9 9 2 } 3 7 : 4 2 2 L I N _ N { 1 9 8 1 } 4 6 : 3 9 3 S I M M E L _ G { 1 9 5 5 } : W A T T S _ D { 2 4 } 3 : 2 4 3 P O O L _ I { 1 9 7 8 } 1 : 5 H E L L S T E N _ I { 2 7 } 7 2 : 4 6 9 H O L M E _ P { 2 6 } 7 4 : 5 6 1 8 N E W M A N _ M { 2 6 } 7 4 : 3 6 1 4 L A M B I O T T _ R { 2 7 } : P 8 2 6 B R E I G E R _ R { 1 9 7 9 } 4 2 : 2 6 2 J O H N S E N _ E { 1 9 8 6 } 8 : 2 5 7 M A R S D E N _ P { 1 9 8 7 } 5 2 : 1 2 2 E A M E S _ K { 2 2 } 9 9 : 1 3 3 3 R O T H E N B E _ R { 1 9 9 8 } 2 5 : 1 5 4 G H A N I _ A { 1 9 9 7 } 2 4 : 4 5 N E W M A N _ M { 2 4 } 6 9 : 6 6 1 3 3 H A M M E R _ M { 1 9 7 8 } 4 : 5 2 2 H A M M E R _ M { 1 9 8 } 2 : 1 6 5 C A M P B E L L _ K { 1 9 8 6 } 8 : 9 7 L A U M A N N _ E { 1 9 7 3 } 3 8 : 2 1 2 M O R E N O _ J { 1 9 5 3 } : K R A C K H A R _ D { 1 9 9 } 3 5 : 3 4 2 H A M M E R _ M { 1 9 8 2 } 1 6 : 2 9 1 R O T H E N B E _ R { 1 9 9 6 } 2 3 : 2 4 P O T T E R A T _ J { 1 9 9 9 } 1 5 : 1 3 3 1 P O T T E R A T _ J { 1 9 9 9 } 1 : 1 8 2 L I L J E R O S _ F { 2 3 } 5 : 1 8 9 K L O V D A H L _ A { 1 9 9 4 } 3 8 : 7 9 L I U _ X { 2 5 } 4 1 : 1 4 6 2 K I L L W O R T _ P { 1 9 7 6 } 3 5 : 2 6 9 P O R T E R _ M { 2 5 } 1 2 : 7 5 7 B U R T _ R { 1 9 7 8 } 7 : 1 8 9 F R I E D K I N _ N { 1 9 8 4 } 1 2 : 2 3 5 B U R T _ R { 1 9 7 6 } 5 5 : 9 3 D O R E I A N _ P { 1 9 9 6 } 1 8 : 1 4 9 S A M P S O N _ S { 1 9 6 9 } : B U L D U _ J { 2 7 } 9 : 1 7 2 M I L O _ R { 2 4 } 3 3 : 1 5 3 8 P O N C E L A _ J { 2 7 } 9 : 1 8 4 T H A D A K A M _ H { 2 7 } 9 : 1 9 D A V I S _ A { 1 9 4 1 } : K R U S K A L _ J { 1 9 6 4 } 2 9 : 1 R O E T H L I S _ F { 1 9 3 9 } : C A R T W R I G _ D { 1 9 5 6 } 6 3 : 2 7 7 H E I D E R _ F { 1 9 4 6 } 2 1 : 1 7 M A C R A E _ D { 1 9 6 } 2 3 : 3 6 S T E P H E N S _ K { 1 9 8 9 } 1 1 : 1 H O L L A N D _ P { 1 9 7 7 } 5 : 5 W A S S E R M A _ S { 1 9 8 8 } 5 3 : 2 6 1 H O M A N S _ G { 1 9 5 } : K I L D U F F _ M { 1 9 9 4 } 3 7 : 8 7 L A B I A N C A _ G { 1 9 9 8 } 4 1 : 5 5 K I L L W O R T _ P { 1 9 7 8 } 1 : 1 5 9 H A J R A _ K { 2 7 } : P 6 1 5 T H O I T S _ P { 1 9 8 2 } 2 3 : 1 4 5 S Z A B O _ G { 2 7 } 4 4 6 : 9 7 B U R T _ R { 1 9 9 5 } 7 : 2 5 5 A D A M I C _ L { 2 3 } 2 5 : 2 1 1 N E K O V E E _ M { 2 7 } 3 7 4 : 4 5 7 C A R B O N E _ A { 2 7 } 5 7 : 1 2 1 B U R K H A R D _ M { 1 9 9 } 3 5 : 1 4 B O T T _ E { 1 9 5 7 } : K U P E R M A N _ M { 2 6 } 7 3 : 4 6 1 3 9 R U Y U _ B { 2 7 } 1 4 3 : 2 9 E S T R A D A _ E { 2 5 } 7 1 : 5 6 1 3 E S T R A D A _ E { 2 5 } 7 2 : 4 6 1 5 E S T R A D A _ E { 2 6 } 6 : 3 5 E S T R A D A _ E { 2 7 } 4 : 4 8 B A L K U N D I _ P { 2 6 } 4 9 : 4 9 I B A R R A _ H { 2 5 } 1 6 : 3 5 9 G U L A T I _ R { 1 9 9 9 } 4 4 : 4 7 3 B E R N A R D _ H { 1 9 9 } 1 2 : 1 7 9 J O H N S E N _ E { 1 9 8 5 } 7 : 2 3 N E W M A N _ M { 2 2 } 1 4 7 : 4 H A M M E R _ M { 1 9 8 3 } 1 7 : 4 5 L A Z E G A _ E { 1 9 9 7 } 1 9 : 3 7 5 H A R A R Y _ F { 1 9 6 5 } : J O L L Y _ A { 2 1 } 7 8 : 4 3 3 M O R R I S _ M { 1 9 9 5 } 1 7 : 2 9 9 P O T T E R A T _ J { 2 } 2 7 : 6 4 4 W H I T E _ H { 1 9 6 3 } : H U N T E R _ D { 2 7 } 2 9 : 2 1 6 P A T T I S O N _ P { 1 9 9 9 } 5 2 : 1 6 9 R O B I N S _ G { 2 7 } 2 9 : 1 7 3 R O B I N S _ G { 2 7 } 2 9 : 1 9 2 R O B I N S _ G { 2 7 } 2 9 : 1 6 9 R O B I N S _ G { 2 5 } 1 1 : 8 9 4 S T R A U S S _ D { 1 9 9 } 8 5 : 2 4 B E R N A R D _ H { 1 9 8 2 } 1 1 : 3 B U R T _ R { 1 9 9 4 } 1 6 : 9 1 H A M M E R _ M { 1 9 8 4 } 6 : 3 4 1 M I L A R D O _ R { 1 9 8 9 } 5 1 : 1 6 5 M I L A R D O _ R { 1 9 9 2 } 9 : 4 4 7 M O R G A N _ D { 1 9 9 7 } 1 9 : 9 S U D M A N _ S { 1 9 8 8 } 1 : 9 3 W A S S E R M A _ S { 1 9 7 7 } 5 : 6 1 H E I D E R _ F { 1 9 5 8 } : M O O D Y _ J { 2 1 } 1 7 : 6 7 9 E A M E S _ K { 2 4 } 1 8 9 : 1 1 5 H O L M E _ P { 2 2 } 6 5 : 5 6 1 9 C H E N _ Y { 2 7 } 7 5 : 4 6 1 7 B R E I G E R _ R { 1 9 7 5 } 1 2 : 3 2 8 F A U S T _ K { 1 9 8 8 } 1 : 3 1 3 S N I J D E R S _ T { 1 9 9 1 } 5 6 : 3 9 7 W A S S E R M A _ S { 1 9 8 7 } 9 : 1 K R A C K H A R _ D { 1 9 8 8 } 1 : 3 5 9 F A U S T _ K { 1 9 9 2 } 1 4 : 5 K R A C K H A R _ D { 1 9 8 7 } 9 : 1 9 L A U M A N N _ E { 1 9 7 3 } : R O M N E Y _ A { 1 9 8 2 } 4 : 2 8 5 G U R E V I T C _ M { 1 9 6 1 } : F R E E M A N _ L { 1 9 9 1 } 1 3 : 1 4 1 B U R T _ R { 1 9 8 } 6 : 7 9 C L A U S E T _ A { 2 4 } 7 : 6 6 1 1 1 N E W M A N _ M { 2 2 } 6 6 : 3 5 1 1 Z A K H A R O V _ P { 2 7 } 3 7 8 : 5 5 K I M _ D { 2 5 } 3 5 1 : 6 7 1 X U A N _ Q { 2 6 } 7 3 : 3 6 1 5 X U A N _ Q { 2 7 } 3 7 8 : 5 6 1 G R A B O W S K _ A { 2 4 } 7 : 3 1 9 8 Y O O K _ S { 2 1 } 8 6 : 5 8 3 5 J E G E R _ M { 2 7 } 1 7 4 : 2 7 9 H A M M E R _ M { 1 9 8 1 } 7 : 4 5 W A L K E R _ M { 1 9 9 3 } 2 2 : 7 1 I B A R R A _ H { 1 9 9 3 } 3 8 : 2 7 7 F R I E D K I N _ N { 1 9 9 1 } 9 6 : 1 4 7 8 G O M E Z

A _ J { 2 7 } 9 8 : 1 8 1 3 H O L L A N D _ P { 1 9 7 } 7 6 : 4 9 2 N E W M A N _ M { 2 4 } 7 : 5 6 1 3 1 H U B B E L L _ C { 1 9 6 5 } 2 8 : 3 7 7 N E W C O M B _ T { 1 9 6 1 } : N E W M A N _ M { 2 5 } 2 7 : 3 9 N E W M A N _ M { 2 6 } 1 3 : 8 5 7 7 P A R K _ J { 2 3 } 6 8 : 2 6 1 1 2 B E R N A R D _ H { 1 9 8 } 2 : 1 9 1 W O O D H O U S _ D { 1 9 9 4 } 8 : 1 3 3 1 H O L L A N D _ P { 1 9 7 8 } 7 : 2 2 7 W H I T E _ H { 1 9 6 1 } 6 7 : 1 8 5 H U R L B E R T _ J { 2 } 6 5 : 5 9 8 R O T H E N B E _ R { 2 1 } 7 8 : 4 1 9 E S T R A D A _ E { 2 6 } 7 3 : 6 4 9 E S T R A D A _ E { 2 7 } 7 5 : 1 6 1 3 L A N D A U _ H { 1 9 5 1 } 1 3 : 1 L A N D A U _ H { 1 9 5 1 } 1 3 : 2 4 5 F O R T U N A T _ S { 2 7 } 1 4 : 3 6 F R A N K _ K { 1 9 9 6 } 1 8 : 9 3 K A D U S H I N _ C { 1 9 6 6 } 3 1 : 7 8 6 F R A N K _ K { 1 9 9 8 } 1 4 : 6 4 2 B A I L E Y _ S { 1 9 9 9 } 2 1 : 2 8 7 B A N K S _ D { 1 9 9 6 } 2 1 : 1 7 3 B R A N D E S _ U { 2 1 } 2 5 : 1 6 3 H A R T I G A N _ J { 1 9 7 2 } 6 7 : 1 2 3 F R E E M A N _ L { 1 9 8 4 } 1 : 3 4 3 N A D E L _ S { 1 9 5 7 } : G R O N L U N D _ A { 2 5 } 8 : 2 6 1 B U R T _ R { 1 9 9 7 } 1 9 : 3 5 5 E B E L _ H { 2 2 } 6 6 : 3 5 1 3 A L T M A N N _ M { 1 9 9 3 } 1 5 : 1 C O L E M A N _ J { 1 9 6 1 } : B A L K U N D I _ P { 2 5 } 1 6 : 9 4 1 F A R A R O _ T { 1 9 7 3 } : A L B A _ R { 1 9 7 6 } 5 : 7 7 F O R D _ L { 1 9 6 2 } : J O H N S O N _ S { 1 9 6 7 } 3 2 : 2 4 1 V A L E N T E _ T { 1 9 9 8 } 2 : 8 9 E H R H A R D T _ G { 2 6 } 7 4 : 3 6 1 6 T R A V I E S O _ G { 2 6 } 7 4 : 3 6 1 1 2 K I M _ D { 2 4 } 3 8 : 3 5 L U C E _ R { 1 9 5 } 1 5 : 1 6 9 B O O R M A N _ S { 1 9 7 6 } 8 1 : 1 3 8 4 F A U S T _ K { 1 9 8 5 } 7 : 7 7 M U E L L E R _ D { 1 9 8 } 1 4 : 1 4 7 B L O N D E L _ V { 2 6 } 3 4 1 : 2 3 1 R E E D _ D { 1 9 8 3 } 1 1 7 : 3 8 4 S A I L E R _ L { 1 9 7 8 } 1 : 7 3 W A R D _ J { 1 9 6 3 } 5 8 : 2 3 6 H O L L A N D _ P { 1 9 7 1 } 2 : 1 7 W H I T E _ H { 1 9 7 } 4 9 : 2 5 9 B U R T _ R { 1 9 8 } 2 5 : 5 5 7 B I A N C O N I _ G { 2 1 } 5 4 : 4 3 6 B O R G A T T I _ S { 1 9 8 9 } 1 1 : 6 5 C H A K R A B A _ D { 2 6 } 3 8 : A 1 N E W M A N _ M { 2 } 8 4 : 3 2 1 M O O R E _ C { 2 } 6 2 : 7 5 9 L A U M A N N _ E { 1 9 7 8 } 4 : 4 5 5 F R A N K _ K { 1 9 9 5 } 1 7 : 2 7 G R A B O W S K _ A { 2 5 } 3 6 : 1 5 7 9 K A D U S H I N _ C { 1 9 6 8 } 3 3 : 6 8 5 H O L M E _ P { 2 5 } 8 : H A R T I G A N _ J { 1 9 7 5 } : M A N D E L _ M { 1 9 8 3 } 4 8 : 3 7 6 R I C H A R D S _ W { 1 9 8 1 } 3 : 2 1 5 D O R E I A N _ P { 1 9 9 4 } 1 9 : 1 L E V I N E _ J { 1 9 7 2 } 3 7 : 1 4 L I N _ N { 1 9 8 1 } 7 : 7 3 B R E I G E R _ R { 1 9 7 8 } 7 : 2 1 3 B U R T _ R { 1 9 9 } 1 2 : 8 3 F E R G U S O N _ N { 2 } 2 7 : 6 H O L L A N D _ P { 1 9 7 2 } 7 7 : 1 2 5 F R A I G N I A _ P { 2 5 } 3 6 6 9 : 7 9 1 W A S S E R M A _ S { 1 9 8 4 } 6 : 1 7 7 S O K A L _ R { 1 9 5 8 } 3 8 : 1 4 9 F L A M E N T _ C { 1 9 6 3 } : H A L L I N A N _ M { 1 9 7 8 } 1 : 1 9 3 M A R S D E N _ P { 1 9 8 1 } 3 : 1 A L B A _ R { 1 9 7 3 } 3 : 1 1 3 L I P S E T _ S { 1 9 5 6 } : C S A N Y I _ G { 2 4 } 7 : 1 6 1 2 2 E R I C K S O N _ G { 1 9 8 4 } 2 3 : 1 8 7 D O R E I A N _ P { 1 9 8 } 2 : 2 3 5 K R U S K A L _ J { 1 9 6 4 } 2 9 : 1 1 5 L A N C E _ G { 1 9 6 7 } 1 : 2 7 1 S N E A T H _ P { 1 9 5 7 } 1 7 : 2 1 A N D E R S O N _ C { 1 9 9 2 } 1 4 : 1 3 7 B A T A G E L J _ V { 1 9 9 7 } 1 9 : 1 4 3 B R E I G E R _ R { 1 9 7 9 } 1 3 : 2 1 W H I T E _ D { 1 9 8 3 } 5 : 1 9 3 M A R S D E N _ P { 1 9 8 3 } 8 8 : 6 8 6 B U R T _ R { 1 9 8 } 8 5 : 8 9 2 H A N _ S { 1 9 9 6 } 1 8 : 4 7 B A T A G E L J _ V { 1 9 9 2 } 1 4 : 6 3 L A U M A N N _ E { 1 9 7 7 } 8 3 : 5 9 4 I S R A E L _ B { 1 9 8 7 } 1 4 : 4 6 1 O R N S T E I N _ M { 1 9 8 2 } 4 : 3 P A T T I S O N _ P { 1 9 8 2 } 2 5 : 8 7 F O S T E R _ C { 1 9 6 3 } 8 : 5 6 M C Q U I T T Y _ L { 1 9 6 8 } 3 : 4 6 5 I A M N I T C H _ A { 2 2 } 2 4 2 9 : 2 3 2 K I L L W O R T _ P { 1 9 7 9 } 2 : 1 9 M A C E _ M { 1 9 7 1 } : H O L L A N D _ P { 1 9 7 7 } 6 : 3 8 6 B U R T _ R { 1 9 7 8 } 1 : 1 5 B O N A C I C H _ P { 1 9 7 2 } : H I L D U M _ D { 1 9 8 6 } 8 : 7 9 T U R N E R _ C { 1 9 6 7 } 2 : 1 2 1 M C P H E R S O _ J { 1 9 8 2 } 3 : 2 2 5 P A T T I S O N _ P { 1 9 8 8 } 1 : 3 8 3 W I N S H I P _ C { 1 9 8 8 } 1 : 2 9 W H I T E _ H { 1 9 6 1 } 5 7 : 1 8 5 D O R E I A N _ P { 1 9 8 8 } 1 3 : 2 4 3 M I C H A E L S _ A { 1 9 9 3 } 1 5 : 2 1 7 C O O M B S _ C { 1 9 6 4 } : M O S T E L L E _ F { 1 9 6 8 } 6 3 : 1 R I C E _ R { 1 9 9 } 1 2 : 2 7 N E W C O M B _ T { 1 9 6 8 } : 2 8 N O R D L I E _ P { 1 9 5 8 } : B O Y D _ J { 1 9 6 9 } 6 : 1 3 9 K E M E N Y _ J { 1 9 6 } : M A R I O L I S _ P { 1 9 8 2 } 2 7 : 5 7 1 M I Z R U C H I _ M { 1 9 8 1 } 2 6 : 4 7 5 K A T Z _ L { 1 9 5 8 } 5 8 : 9 7 C O O L E Y _ C { 1 9 2 } : P A T T I S O N _ P { 1 9 9 5 } 3 9 : 5 7 S C H W A R T Z _ J { 1 9 8 4 } 6 : 1 3 B A T A G E L J _ V { 1 9 9 2 } 1 4 : 1 2 1 I A C O B U C C _ D { 1 9 8 9 } 1 1 : 3 1 5 W H I T E _ H { 1 9 7 7 } 1 6 : 1 2 1 A L L E N _ M { 1 9 8 2 } 4 : 3 4 9 I A C O B U C C _ D { 1 9 9 } 5 5 : 7 7 S C H W E I Z E _ T { 1 9 9 6 } 1 8 : 2 4 7 M A R S D E N _ P { 1 9 8 4 } 1 : 2 7 1 D O W _ M { 1 9 8 2 } 4 : 1 6 9 K A T Z _ L { 1 9 4 7 } 1 : 2 3 3 B O O R M A N _ S { 1 9 7 3 } 1 : 2 6 A R A B I E _ P { 1 9 8 4 } 6 : 3 7 3 P E R R U C C I _ R { 1 9 7 } 3 5 : 1 4 G A L A S K I E _ J { 1 9 8 1 } 4 6 : 4 7 5 B E R N A R D _ H { 1 9 8 7 } 9 : 4 9 G A L A S K I E _ J { 1 9 8 5 } 6 4 : 4 3 B U R T _ R { 1 9 8 1 } 3 : 7 1 D A V I S _ J { 1 9 6 8 } : B U R T _ R { 1 9 8 } 2 : 3 2 7 B R E I G E R _ R { 1 9 8 6 } 8 : 2 1 5 B U R T _ R { 1 9 8 8 } 1 : 1 S N I J D E R S _ T { 1 9 9 } 1 2 : 3 5 9 S O R O K I N _ P { 1 9 4 7 } : B J E R S T E D _ A { 1 9 5 6 } : J A R D I N E _ N { 1 9 7 1 } : B U R T _ R { 1 9 8 6 } 8 : 2 5 B U R T _ R { 1 9 7 7 } 5 6 : 1 6 B U R T _ R { 1 9 7 7 } 5 6 : 5 5 1 M I Z R U C H I _ M { 1 9 8 4 } 6 : 1 9 3 F O R T E S _ M { 1 9 4 5 } : B U R T _ R { 1 9 8 } 4 5 : 8 2 1 A R A B I E _ P { 1 9 9 } 1 2 : 9 9 B R E I G E R _ R { 1 9 8 1 } 7 6 : 5 1 L O R R A I N _ F { 1 9 7 5 } : B A R N E S _ J { 1 9 8 3 } 5 : 2 3 5 K A T Z _ L { 1 9 5 4 } 5 : 6 2 1 C A R R O L L _ J { 1 9 7 } 3 5 : 2 8 3 A B E L S O N _ R { 1 9 5 8 } 3 : 1 M C Q U I T T Y _ L { 1 9 6 8 } 2 8 : 2 1 1 A R A B I E _ P { 1 9 7 3 } 1 : 1 4 8 H U B E R T _ L { 1 9 7 4 } 6 9 : 6 9 8 B E R N A R D _ P { 1 9 7 4 } : K L A H R _ D { 1 9 6 9 } 3 4 : 3 1 9 W A L K E R _ G { 1 9 7 7 } 2 1 : 3 2 9 B R E I G E R _ R { 1 9 7 4 } : H E I L _ G { 1 9 7 4 } : M A R I O L I S _ P { 1 9 8 2 } 4 : 3 5 A R A B I E _ P { 1 9 7 3 } : A R A B I E _ P { 1 9 7 3 } 3 8 : 6 7 B E R N A R D _ P { } : U N P U B L I S H E D B E R N A R D _ P { 1 9 7 3 } 5 : 1 2 8 B O O R M A N _ S { 1 9 7 } : B O O R M A N _ S { 1 9 7 2 } 1 : 2 2 5 C A R R O L L _ J { 1 9 7 3 } : C L A R K _ J { 1 9 7 } 3 : 7 7 3 D A W E S _ R { 1 9 7 2 } : E D W A R D S _ A { 1 9 6 5 } 2 1 : 3 6 2 G L A N Z E R _ M { 1 9 5 9 } 5 6 : 3 1 7 G L E A S O N _ T { 1 9 6 9 } : G R I F F I T H _ B { } : U N P U B L I S H E D H A R T I G A N _ J { 1 9 7 3 } 2 : 8 1 H O L L A N D _ P { } : U N P U B L I S H E D H O L M A N _ E { 1 9 7 2 } 3 7 : 4 1 7 H O R A N _ C { 1 9 6 9 } 3 4 : 1 3 9 H U B E R T _ L { 1 9 7 3 } 3 8 : 4 7 H U B E R T _ L { 1 9 7 2 } 3 7 : 2 6 1 K R U S K A L _ J { 1 9 6 6 } 4 5 : 1 2 9 9 L A N C E _ G { 1 9 6 7 } 9 : 3 7 3 L A U M A N N _ E { 1 9 7 4 } 3 9 : 1 6 2 L I N G _ R { 1 9 7 1 } : L I N G _ R { 1 9 7 3 } 6 8 : 1 5 9 L O R R A I N _ F { 1 9 7 2 } : M I L L E R _ G { 1 9 5 5 } 2 7 : 3 3 8 N E E D H A M _ R { 1 9 6 5 } 8 : 1 1 3 R O B I N S O N _ A { 1 9 6 5 } : R O M N E Y _ A { 1 9 7 1 } : 1 9 1 S C H O E N F I _ J { 1 9 6 7 } : S H A F T O _ M { 1 9 7 2 } : S H E P A R D _ R { 1 9 6 2 } 2 7 : 1 2 5 S H E P A R D _ R { 1 9 6 2 } 2 7 : 2 1 9 S H E P A R D _ R { 1 9 6 9 } : S H E P A R D _ R { 1 9 7 2 } : 6 7 S H E P A R D _ R { 1 9 7 4 } 3 9 : 3 7 3 S O R E N S E N _ T { 1 9 4 8 } 5 : 1 S T E N S O N _ H { 1 9 6 9 } 7 1 : 1 2 2 S T R U H S A K _ T { 1 9 6 7 } 2 9 : 8 3 V O N W I E S E _ L { 1 9 4 1 } : W H I T E _ H { } : I N _ P R E S S W H I T E _ H { } : U N P U B L I S H E D W I N S H I P _ C { } : U N P U B L I S H E D W I S H _ M { 1 9 7 3 } 2 : B E A U C H A M _ M { 1 9 7 } : B A T A G E L J _ V { 1 9 9 9 } 1 7 3 1 : 9 J A C O B S O N _ D { 1 9 8 5 } 7 : 3 4 1 B U R T _ R { 1 9 7 9 } 6 : 2 1 1 B U R T _ R { 1 9 7 9 } 1 : 4 1 5 T U T Z A U E R _ F { 1 9 8 5 } 7 : 2 6 3 N I E M O L L E _ K { 1 9 8 } 1 4 : 1 1 L I E B E R S O _ S { 1 9 7 1 } 7 6 : 5 6 2 W H I T E _ H { 1 9 7 3 } 4 3 : 4 3 P A R K _ J { 2 7 } 1 4 : 1 7 9 1 6 N E W M A N _ M { 2 7 } 1 4 : 9 5 6 4 L E I C H T _ E { 2 7 } 5 9 : 7 5 G H O S H A L _ G { 2 7 } 5 8 : 1 7 5 W H I T E _ H { 1 9 7 4 } : R A P O P O R T _ A { 1 9 6 1 } 6 : 2 8 L A N D A U _ H { 1 9 5 3 } 1 5 : 1 4 3 D E U T S C H _ K { 1 9 5 3 } : H O W A R D _ L { } : U N P U B L I S H E D _ M A N U S C R I L O R R A I N _ F { 1 9 6 9 } : 6 1 6 L U C E _ R { 1 9 5 5 } 1 5 : 1 6 5 M I L G R A M _ S { } : I N _ P R E S S P O O L _ I { } : N O N M A T H E M A T I C A L _ I N T R $ H O W _ C O N S T R U C T _ S O C I O G { 1 9 4 7 } : D A V I S _ J { 1 9 7 } 2 : H A Y E S _ M { 1 9 5 3 } 2 2 : 1 9 H E M P E L _ C { 1 9 5 2 } 2 : H O L L A N D _ P { 1 9 7 } : K E N D A L L _ M { 1 9 3 9 } 3 1 : 3 2 4 L E I N H A R D _ S { 1 9 6 8 } : M O R A N _ P { 1 9 4 7 } 3 4 : 3 6 3 T A B A _ H { 1 9 5 } : T A B A _ H { 1 9 5 1 } : Z E L E N Y _ L { 1 9 4 7 } 1 : 3 9 6 Z E L E N Y _ L { 1 9 4 7 } 1 3 : 3 1 4 G U I M E R A _ R { 2 7 } 7 6 : 3 6 1 2 C R U C I T T I _ P { 2 6 } 7 3 : 3 6 1 2 5 L A T O R A _ V { 2 7 } 9 : 1 8 8 M A S O N _ O { 2 7 } 1 : 8 9 S M A L L _ H { 1 9 9 7 } 3 8 : 2 7 5 W H I T E _ H { } : U N P U B L I S H E D _ M A N U S C R I W H I T E _ H { } : U N P U B L I S H E D _ W O R K I N G W O L F F _ K { 1 9 5 9 } : S A L E S

A _ M { 2 7 } 1 4 : 1 5 2 2 4 A L V E S _ N { 2 7 } 7 6 : 3 6 1 1 V O L C H E N K _ D { 2 7 } 7 5 : 2 6 1 4 A D A M I C _ L { 2 7 } 9 : 2 3 1 = G O O D R E A U _ S { 2 7 } 2 9 : 2 3 1 = H U N T E R _ D { 2 7 } 2 9 : 2 1 6 = R O B I N S _ G { 2 7 } 2 9 : 1 9 2 = F A U S T _ K { 1 9 9 2 } 1 4 : 5 = A N D E R S O N _ C { 1 9 9 2 } 1 4 : 1 3 7 = W H I T E _ D { 1 9 8 3 } 5 : 1 9 3 = B A T A G E L J _ V { 1 9 9 2 } 1 4 : 6 3 = B A T A G E L J _ V { 1 9 9 2 } 1 4 : 1 2 1

Pajek

V. Batagelj

Large Networks

SLIDE 44

Large Networks

V. Batagelj

Pajek Network visualization Properties Important subnetworks Multiplication ESNA Pajek

Islands in authors’ citations network in Social networks

UNKNOWN BORGATTI_S ROGERS_E CARLEY_K GALASKIE_J GULATI_R BURT_R FREEMAN_L WASSERMA_S DOROGOVT_S HOLLAND_P LEINHARD_S NEWMAN_M KNOWLTON_A VLAHOV_D BARABASI_A BARTHELE_M COLEMAN_J LIN_N ROSS_N JENKINS_R LAUMANN_E ALBERT_R AMARAL_L BOCCALET_S GRONLUND_A HOLME_P WATTS_D BRASS_D MERTON_R THOMPSON_J WHITE_D CELENTAN_D CURTIS_R DESJARLA_D FRIEDMAN_S GRANOVET_M LATKIN_C MARSDEN_P NEAIGUS_A ROTHENBE_R VALENTE_T KELLY_J WEISNER_C ANDERSON_C JEONG_H SNIJDERS_T MILLER_M KASKUTAS_L BREIGER_R KRACKHAR_D WHITE_H BROWN_G KILDUFF_M COSTA_L MOLLOY_M IBARRA_H ADLER_P GIRVAN_M KLOVDAHL_A POTTERAT_J BRUGHA_T MACCARTH_B MAGLIANO_L WING_J COHEN_A PARK_J MANDELL_W DEROSA_C BONACICH_P OSTROM_E GRABOWSK_A STROGATZ_S BATAGELJ_V FAUST_K DISHION_T DOREIAN_P HUMMON_N MOORE_C WILLER_D ATRAN_S CAIRNS_R GEST_S VANDUIJN_M CRICK_N ESPELAGE_D FARMER_T KINDERMA_T LEUNG_M XIE_H MIZRUCHI_M HENDERSO_S COOK_K HUNT_J BOORMAN_S PATTISON_P MORRIS_M MORENO_Y SCHWARTZ_N FRIEDKIN_N LAZEGA_E MAGNUSSO_D LAI_G CARPENTE_S PEARL_R VANACKER_R RODKIN_P PELLEGRI_A COIE_J HYMEL_S AMIRKHAN_Y KRETZSCH_M BEBBINGT_P ROBINS_G SKVORETZ_J JANSSEN_M BREWIN_C MASUDA_N KIM_D OLSSON_P FOLKE_C HAHN_T ADGER_W BERKES_F GUNDERSO_L HOLLING_C SCHEFFER_M WESTLEY_F BALKUNDI_P FARRELL_M STRAUSS_D EVERETT_M FERLIGOJ_A FARARO_T HURLBERT_J MUTH_S SOLOMON_P SEIKKULA_J FIENBERG_S HIGGINS_C GAMBOA_G BIENENST_E ESTELL_D CAIRNS_B DARROW_W WOODHOUS_D GERGEN_K MATZGER_H DAPPORTO_L PALAGI_E JEANNE_R RAU_P REEVE_H ROSELER_P STARKS_P STRASSMA_J TURILLAZ_S WESTEBER_M WALKER_B MELTZER_H FIORILLO_A MALANGON_C MAJ_M MARKOVSK_B MAHADEVA_R SCHILLIN_C MAY_P MUSSAT_M CORP_E DELALAUR_L DEPOMPER_M DEYRIS_E FRANTZ_P LEBEAU_E LEMOIGNE_M LEMOY_A LEVOT_P MAILLARD_J MARECHAL_M KILIC_C AYDIN_I TASKINTU_N OZCURUME_G KURT_G EREN_E LALE_T OZEL_S ZILELI_L BASOGLU_M MCGORRY_P LEWIS_G CADWALLA_T AALTONEN_J ALAKARE_B ALANEN_Y ANDERSEN_T ANDERSON_H FADDEN_G SELVINIP SHOTTER_J DELUCCHI_K FEDORA_P HELD_T LESAGE_A IACOBUCC_D MEDIN_D GOFORTH_J CLEMMER_J SABORNIE_E ABEL_E LYNCH_E MARASCO_C GUARNERI_M GOSSAGE_J WHITE-CO_M GOODHART_K DECOTEAU_S TRUJILLO_P KALBERG_W VILJOEN_D HOYME_H NIELSEN_R NECKERMA_H MORGAN_Z VAPNARSK_V EK_E COLEY_J TIMURA_C BARAN_M LESBAUPI_I ARRUDA_M BENJAMIN_C BIONDI_A BOFF_C GONCALVE_R MATTOSO_J PINAUD_J STEDILE_J TRINDADE_H D’AMIA_G AMATI_C ANNONI_A ARRIGONI_P ASPARI_D BECCARIA_G BELGIOJO_A BELTRAMI_L BIANCONI_C CASSIRAM_A CATTANEO_C CHIZZOLI_G DALLAJ_A FRANCHET_G GATTIPER_M GIULINI_G GOLDOLI_E GOZZOLI_M GUILINI_G HONEGGER_A KANNES_G LATUADA_S LUCCHELL_G MERIGGI_M MEZZANOT_G MEZZANOT_P MONTALTO_R PAPAGNA_P PATETTA_L PIZZAGAL_F REGGIORI_F RICCI_G ROMUSSI_C ROSSI_M SANDRI_M SCOTTI_A VACANI_C VALLI_F VERCELLO_V ZOTTI_S BUCHANAN_L HOLLOWEL_J GARIEPY_J BROADBEL_L MAVROVOU_M BURGARD_A FAMILI_I VANDIEN_S PFAENDTN_J KLINKE_D SUMATHI_R

Pajek

V. Batagelj

Large Networks

SLIDE 45

Large Networks

V. Batagelj

Pajek Network visualization Properties Important subnetworks Multiplication ESNA Pajek

ESNA Pajek

Pajek – program for analysis and visualization of large networks is freely available, for noncommercial use, at its web site. http://pajek.imfm.si/ An introduction to social network analysis with Pajek is available in the book ESNA (de Nooy, Mrvar, Batagelj 2005; second, extended edition 2011). ESNA in Japanese was published by Tokyo Denki University Press in 2010.

V. Batagelj

Large Networks