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 on Information Retrieval 29 Aug - 02 Sep 2011, Koblenz, Germany V. Batagelj Large Networks
Outline Large Networks V. Batagelj Pajek 1 Pajek Network visualization 2 Network visualization Properties 3 Properties Important 4 Important subnetworks subnetworks 5 Multiplication Multiplication ESNA Pajek 6 ESNA Pajek V. Batagelj Large Networks
Pajek and large networks Large Networks Pajek is a program for analysis and visu- V. Batagelj alization of large networks. large ≡ the network can be stored in the Pajek computer memory. Network visualization Network = Graph + Data Properties Pajek is mostly a two men (A. Mrvar and V. Batagelj) project. Important We started to develop Pajek in 1996. It was assembled from subnetworks experiences and code from my projects on graph algorithms in Multiplication eighties and first half of nineties, and Andrej’s master thesis on graph ESNA Pajek 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. V. Batagelj Large Networks
Pajek ’s backround Large Networks The main goals in the design of V. Batagelj Pajek are: • to support abstraction by Pajek (recursive) decomposition of Network visualization a large network into several global Properties smaller networks that can be hierarchy treated further using more Important subnetworks sophisticated methods; Multiplication local • to provide the user with some reduction ESNA Pajek powerful visualization tools; • to implement a selection of inter-links efficient subquadratic cut-out context algorithms for analysis of large networks. V. Batagelj Large Networks
New algorithms Large Networks V. Batagelj • vertex and line cuts, Pajek • vertex and line islands, Network visualization • (generalized) cores, Properties • triadic spectrum; 3-rings and 4-rings weights, Important subnetworks • fragment (motif) searching, Multiplication • hierarchical clustering with relational constraints, ESNA Pajek • Doreian & Hummon weights in acyclic networks, • multiplication of networks, • fast Pathfinder algorithm, . . . V. Batagelj Large Networks
Pajek is a network ’calculator’ In Pajek analysis and visualization are Large Networks performed using 6 data types: V. Batagelj • network (graph), • partition (nominal or ordinal Pajek properties of vertices), Network visualization • vector (numerical properties of Properties vertices), Important • cluster (subset of vertices), subnetworks Multiplication • permutation (reordering of ESNA Pajek 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. V. Batagelj Large Networks
Pajek ’s network description language Multi-relational temporal network – KEDS/WEIS Large Networks % Recoded by WEISmonths, Sun Nov 28 21:57:00 2004 V. Batagelj % from http://www.ku.edu/~keds/data.dir/balk.html *vertices 325 1 "AFG" [1-*] 2 "AFR" [1-*] Pajek 3 "ALB" [1-*] 4 "ALBMED" [1-*] Network 5 "ALG" [1-*] ... visualization 318 "YUGGOV" [1-*] 319 "YUGMAC" [1-*] Properties 320 "YUGMED" [1-*] 321 "YUGMTN" [1-*] 322 "YUGSER" [1-*] Important 323 "ZAI" [1-*] subnetworks 324 "ZAM" [1-*] 325 "ZIM" [1-*] *arcs :0 "*** ABANDONED" Multiplication *arcs :10 "YIELD" *arcs :11 "SURRENDER" ESNA Pajek *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 V. Batagelj Large Networks
Network visualization Large Networks Standard network visualization methods can produce readable results for V. Batagelj not too large and relatively sparse networks. For denser networks the matrix representation is usually the right choice. Pajek In network analysis it is very important to support also visualization of Network visualization additional data. It seems that interactive layouts are the future of network visualization. Properties In Pajek the following visualization tools are available: Important subnetworks • spring embedders: Kamada Kawai, Fruchterman Reingold Multiplication • eigen vectors ESNA Pajek • acyclic • manual improvements • matrix representation In nineties we won several first prizes at the Graph Drawing competitions. V. Batagelj Large Networks
Network = Graph + Data Large Networks V. Batagelj Display of properties – school (Moody) Pajek Network visualization Properties Important subnetworks Multiplication ESNA Pajek V. Batagelj Large Networks
Analysis of Countries.net To obtain picture in which the Large Networks stronger lines cover weaker lines Kazakhstan Afghanistan V. Batagelj Japan we have to sort them Azerbaijan Georgia Morocco Liechtenstein Ecuador Net/Transform/Sort India Pajek Iceland Uzbekistan Belarus Tunisia lines/Line values/Ascending Jordan Lebanon Network For dense (sub)networks we get visualization Armenia Canada France Algeria United Kingdom better visualization by using Italia Russian F. The Netherlands Properties Finland China Malta Moldavia Turkey matrix display. In this case we Greece Thailand Germany Portugal Spain Important Switzerland Israel also recoded values (2,10,50). subnetworks Turkmenistan Sweden Denmark Austria Cyprus Estonia Serbia-Montenegro Slovakia To determine clusters we used Ukraine Norway USA Multiplication Belgium Macedonia Poland Slovenia Ward’s clustering procedure with Croatia Hungary ESNA Pajek Luxembourg Ireland Latvia Romania dissimilarity measure d 5 (corrected Bulgaria Czech R. Lithuania Albania 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. V. Batagelj Large Networks
Matrix display Pajek - shadow [0.00,4.00] Large Ecuador Networks Thailand Armenia Turkmenist Uzbekistan V. Batagelj Moldavia Japan Kazakhstan Azerbaijan India Macedonia Pajek Albania Liechtenst Serbia-Mon Iceland Network Canada Estonia China visualization Belarus Georgia Afghanista Morocco Properties Malta Tunisia Lebanon Jordan Important Algeria Pajek - Ward [0.00,4785.14] Croatia subnetworks Latvia Lithuania Luxembourg Cyprus Ecuador Thailand Turkey Multiplication Armenia Turkmenist Bulgaria Uzbekistan Ukraine Moldavia Japan Slovenia Kazakhstan Azerbaijan Romania India ESNA Pajek Macedonia Slovakia Albania Liechtenst USA Serbia-Mon Russian F. Iceland Canada Israel Estonia China Hungary Belarus Georgia Ireland Tunisia Czech R. Lebanon Jordan Norway Algeria Malta Poland Morocco Afghanista Finland Luxembourg Croatia Portugal Latvia Denmark Lithuania Cyprus Switzerlan Turkey Bulgaria Austria Ukraine Slovenia Sweden Romania Slovakia Greece USA Belgium Portugal Denmark Spain Poland The Nether Finland Switzerlan Italia Austria Czech R. France Ireland Norway United Kin Hungary Germany Israel Russian F. Sweden Greece Belgium Luxembourg Spain Turkmenist Uzbekistan Kazakhstan Macedonia Serbia-Mon The Nether Azerbaijan Liechtenst Afghanista Russian F. Switzerlan United Kin The Nether Moldavia Lithuania Romania Czech R. Denmark Germany France Ecuador Thailand Armenia Morocco Lebanon Bulgaria Slovenia Slovakia Hungary Portugal Sweden Belgium Albania Iceland Canada Estonia Belarus Georgia Tunisia Croatia Cyprus Ukraine Norway Finland Greece United Kin Japan Jordan Algeria Turkey Ireland Poland Austria France China Malta Latvia Israel Spain Germany India USA Italia Italia V. Batagelj Large Networks
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