Betweenness Centrality: Extremal Values and Structural Properties

R. Grassi (), R. Scapellato (), S. Stefani () and A. Torriero ()
Additional contact information
R. Grassi: Dipartimento di Metodi Quantitativi per le Scienze Economiche ed Aziendali Università degli Studi di Milano — Bicocca
R. Scapellato: Politecnico di Milano
S. Stefani: Dipartimento di Metodi Quantitativi per le Scienze Economiche ed Aziendali Università degli Studi di Milano — Bicocca
A. Torriero: Finanza matematica e Econometria Università Cattolica del Sacro Cuore di Milano

A chapter in Networks, Topology and Dynamics, 2009, pp 161-175 from Springer

Abstract: In this paper we investigate the structural properties of betweenness cen-trality 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 on cutvertex properties.

Keywords: Betweenness Centrality; Closeness Centrality; Eigenvector Centrality; Star Graph; Span Subgraph (search for similar items in EconPapers)
Date: 2009
References: Add references at CitEc
Citations: View citations in EconPapers (4)

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:lnechp:978-3-540-68409-1_8

Ordering information: This item can be ordered from
http://www.springer.com/9783540684091

DOI: 10.1007/978-3-540-68409-1_8

Access Statistics for this chapter

More chapters in Lecture Notes in Economics and Mathematical Systems from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().