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Betweenness Centrality: Extremal Values and Structural Properties

In: Networks, Topology and Dynamics

Author

Listed:
  • 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)

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.

Suggested Citation

  • R. Grassi & R. Scapellato & S. Stefani & A. Torriero, 2009. "Betweenness Centrality: Extremal Values and Structural Properties," Lecture Notes in Economics and Mathematical Systems, in: Ahmad K. Naimzada & Silvana Stefani & Anna Torriero (ed.), Networks, Topology and Dynamics, pages 161-175, Springer.
    • Handle: RePEc:spr:lnechp:978-3-540-68409-1_8
    DOI: 10.1007/978-3-540-68409-1_8
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    Citations

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    Cited by:

    1. Marco D’Errico & Silvana Stefani & Anna Torriero, 2014. "Informal ties in organizations: a case study," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(4), pages 1929-1943, July.
    2. Anna D’Arcangelis & Giulia Rotundo, 2015. "Mutual funds relationships and performance analysis," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(4), pages 1573-1584, July.
    3. Giulia Rotundo & Anna D’Arcangelis, 2014. "Network of companies: an analysis of market concentration in the Italian stock market," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(4), pages 1893-1910, July.
    4. Ettore Croci & Rosanna Grassi, 2014. "The economic effect of interlocking directorates in Italy: new evidence using centrality measures," Computational and Mathematical Organization Theory, Springer, vol. 20(1), pages 89-112, March.

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