Betweenness centrality: extremal values and structural properties

Anna Torriero, Raffaele Scapellato, Silvana Stefani, Rosanna Grassi, R. Grassi, R. Scapellato, S. Stefani

Risultato della ricerca: Contributo in libroChapter

11 Citazioni (Scopus)

Abstract

In this paper we investigate the structural properties of betweenness centrality and determine some cases in which betweenness reaches its extremal values. Special attention is paid to Star(G), the set of vertices adjacent to all other vertices in a graph and we prove several results about the betweenness of the elements of this set. We introduce the new concept of total betweenness and relate it to group betweenness. We prove a necessary and sufficient condition for the two measures to coincide. Next we consider cutsets and cutvertices and we find a lower bound for their betweenness; in particular for a cutvertex this lower bound is the cutting number. Finally we apply the previous results to trees, proving an alternative formula for betweenness based oil cutvertex properties.
Lingua originaleEnglish
Titolo della pubblicazione ospiteTOPOLOGY AND DYNAMICS: THEORY AND APPLICATIONS TO ECONOMIC AND SOCIAL SYSTEMS, Lectures Notes in Economics and Mathematical Systems
EditorSTEFANI Silvana, TORRIERO Anna NAIMZADA Ahmad
Pagine161-175
Numero di pagine15
DOI
Stato di pubblicazionePubblicato - 2009

Serie di pubblicazioni

NomeLECTURE NOTES IN ECONOMICS AND MATHEMATICAL SYSTEMS

Keywords

  • betweenness
  • graphs
  • trees

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