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 given 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 cutvertices and cutsets and find a lower bound for their betweenness. In particular for a cutvertex this lower bound is the cutting number. Finally we apply these results to trees, proving an alternative formula for betweenness based on cutvertex properties.
Grassi, R., Scapellato, R., Stefani, S., & Torriero, A. (2009). Betweenness Centrality: Extremal Values and Structural Properties. In A. Naimzada, S. Stefani, & A. Torriero (a cura di), Networks, Topology and Dynamics. Theory and Applications to Economics and Social Systems (pp. 161-176). Heidelberg : Springer.
Citazione: | Grassi, R., Scapellato, R., Stefani, S., & Torriero, A. (2009). Betweenness Centrality: Extremal Values and Structural Properties. In A. Naimzada, S. Stefani, & A. Torriero (a cura di), Networks, Topology and Dynamics. Theory and Applications to Economics and Social Systems (pp. 161-176). Heidelberg : Springer. |
Titolo: | Betweenness Centrality: Extremal Values and Structural Properties |
Autori: | Grassi, R; Scapellato, R; Stefani, S; Torriero, A |
Autori: | |
Tipo: | Capitolo o saggio |
Carattere della pubblicazione: | Scientifica |
Data di pubblicazione: | 2009 |
Lingua: | English |
Titolo del libro: | Networks, Topology and Dynamics. Theory and Applications to Economics and Social Systems |
ISBN: | 978-3-540-68407-7 |
Appare nelle tipologie: | 03 - Contributo in libro |
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