ANALYSIS AND VISUALIZATION OF LARGE NETWORKS

abstractAmerican Library Association /ALA/American Library Directorybibliographic recordbibliographybindingblanket orderbookbook sizeBooks in Print /BIP/call numbercatalogchargecollationcolophonconditioncopyrightcoverdummydust jacketeditioneditorendpaperentryfictionfixed locationfoliofrequencyfront matterhalf-titlehomepageimprintindexInternational Standard Book Number /ISBN/invoiceissuejournal layoutlibrarianlibrarylibrary bindingLibrary Literaturenew bookOak Knollpageparts of a bookperiodicalplateprintingpublicationpublished pricepublisherpublishingreviewround tableserialseriessuggestion boxtable of contents /TOC/texttitletitle pagetransaction logvendorwork Pajek Fig.8. Edge-cut at level 11 of transitive network of ODLIS dictionary graph v i A(T i 1 ) \ A(T i ) 6= ;, i = 2;:::s holds; such sequence is called an arccyclic triangular chain.Again, we can introduce two types of cyclic triangular connectivity:A pair of vertices u;v 2 V is (vertex) cyclic triangularly connected i u = v, or there exists a cyclic triangular chain that connects u to v.A pair of vertices u;v 2 V is arc cyclic triangularly connected i u = v,or there exists an arc cyclic triangular chain that connects u to v.Cyclic triangular connectivity is an equivalence relation on the set ofvertices V; and the arc cyclic triangular connectivity components determinean equivalence relation on the set of arcs A.There exists also a parallel to unilateral connectivity. The vertex v 2 Vis transitively triangularly reachable from the vertex u 2 V i u = v, or thereexists a walk from u to v in which each arc is transitive { is a base of sometransitive triangle.Transitive arcs are essentially reinforced arcs. If we remove from a graphG = (V;A) a transitive arc the reachability relation in V does not change.In Figure 8 the edge-cut at level 11 of transitive network of ODLIS dic-tionary graph [45] is presented.These notions can be generalized to short cycle connectivity [20].

[1]  Eugene Garfield,et al.  THE USE OF CITATION DATA IN WRITING THE HISTORY OF SCIENCE , 1964 .

[2]  Stephen B. Seidman,et al.  Network structure and minimum degree , 1983 .

[3]  Robert E. Tarjan,et al.  Data structures and network algorithms , 1983, CBMS-NSF regional conference series in applied mathematics.

[4]  A. Gibbons.  Algorithmic Graph Theory , 1985 .

[5]  Fionn Murtagh,et al.  Multidimensional clustering algorithms , 1985 .

[6]  Norman P. Hummon,et al.  Connectivity in a citation network: The development of DNA theory☆ , 1989 .

[7]  Robin Wilson,et al.  Graphs an Introductory Approach , 1990, The Mathematical Gazette.

[8]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[9]  John Scott.  Social Network Analysis , 1988 .

[10]  A. Ferligoj,et al.  An optimizational approach to regular equivalence , 1992 .

[11]  Stanley Wasserman,et al.  Social Network Analysis: Methods and Applications , 1994 .

[12]  P. Doreian,et al.  A partitioning approach to structural balance , 1996 .

[13]  S. Wasserman,et al.  Logit models and logistic regressions for social networks: I. An introduction to Markov graphs andp , 1996 .

[14]  V. Batagelj.  Notes on blockmodeling , 1997 .

[15]  Jon Kleinberg,et al.  Authoritative sources in a hyperlinked environment , 1998, SODA '98.

[16]  Anthropology: Analyzing large kinship and marriage networks with Pgraph and Pajek , 1999 .

[17]  Vladimir Batagelj,et al.  Partitioning Approach to Visualization of Large Graphs , 1999, GD.

[18]  Vladimir Batagelj,et al.  Some analyses of Erdős collaboration graph , 2000, Soc. Networks.

[19]  Vladimir Batagelj,et al.  Symmetric-Acyclic Decompositions of Networks , 2000, J. Classif..

[20]  Vladimir Batagelj,et al.  Pajek - Analysis and Visualization of Large Networks , 2004, Graph Drawing Software.

[21]  Vladimir Batagelj,et al.  A subquadratic triad census algorithm for large sparse networks with small maximum degree , 2001, Soc. Networks.

[22]  Ronald L. Rivest,et al.  Introduction to Algorithms, Second Edition , 2001 .

[23]  Gary D Bader,et al.  Systematic identification of protein complexes in Saccharomyces cerevisiae by mass spectrometry , 2002, Nature.

[24]  Vladimir Batagelj,et al.  Generalized Cores , 2002, ArXiv.

[25]  David M. Pennock,et al.  Winners don't take all: Characterizing the competition for links on the web , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[26]  Vladimir Batagelj,et al.  An O(m) Algorithm for Cores Decomposition of Networks , 2003, ArXiv.

[27]  Vladimir Batagelj,et al.  Short Cycles Connectivity , 2003, ArXiv.

[28]  Vladimir Batagelj,et al.  Relinking marriages in genealogies , 2004, Advances in Methodology and Statistics.

[29]  Vladimir Batagelj,et al.  Exploratory Social Network Analysis with Pajek , 2005 .