ANALYSIS AND VISUALIZATION OF LARGE NETWORKS
Vladimir Batagelj, Andrej Mrvar · 2003
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].