Centrality and Betweenness: Vertex and Edge Decomposition of the Wiener Index
Giles Caporossi, Marcia Helena Moreira Paiva, Damir Vukičević, Segatto Marcelo · match Communications in Mathematical and in Computer Chemistry · 2011
Abstract Inthispaper,wepresentanedgeandvertexdecompositionoftheWienerindex( W )thatisrelatedtotheconceptofbetweennesscentralityusedinsocialnetworksstudies. Someclassicalmethodstocom-pute W couldeasilybederivedfromthisformulationandnovelinvariantsmaybedefinedbythismean.Another vertex decomposition of W is the transmission. If transmission and centrality are both vertexdecompositionsof W itseemsthattheyarerepresentoppositeconcepts, howeverthenatureofthisre-lationisnotalwayssoclear. SomepropertiesobtainedwiththeAutoGraphiXsoftwareonbetweenness,centralityandtheirrelationtotransmissionarepresentedandproved. Resume Dans cet article, nous presentons une decomposition par aretes et sommets de l’indice de Wiener ( W )reliee au concept de «betweenness centrality» utilisee dans les etudes de reseaux sociaux. Certainesmethodesclassiquesdecalculde W peuventfacilementetrededuitesdecetteformulationetdenouveauxinvariantspeuventetreconstruitsdecettefacon.Uneautredecompositionde W ,estlatransmission.Silatransmissionetlacentralitesontdeuxdecompositionsde