Betweenness centrality: extremal values and structural properties

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

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

Betweenness centrality: extremal values and structural properties

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

Università Cattolica del Sacro Cuore

Research output: Chapter in Book/Report/Conference proceeding › Chapter

11 Citations (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.

Original language	English
Title of host publication	TOPOLOGY AND DYNAMICS: THEORY AND APPLICATIONS TO ECONOMIC AND SOCIAL SYSTEMS, Lectures Notes in Economics and Mathematical Systems
Editors	STEFANI Silvana, TORRIERO Anna NAIMZADA Ahmad
Pages	161-175
Number of pages	15
DOIs	https://doi.org/10.1007/978-3-540-68409-1_8
Publication status	Published - 2009

Publication series

Name	LECTURE NOTES IN ECONOMICS AND MATHEMATICAL SYSTEMS

Keywords

betweenness
graphs
trees

Access to Document

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

Cite this

Grassi, R., Scapellato, R., Scapellato, R., Stefani, S., Stefani, S., Grassi, R., & Torriero, A. (2009). Betweenness centrality: extremal values and structural properties. In STEFANI. S. TORRIERO. A. NAIMZADA Ahmad (Ed.), TOPOLOGY AND DYNAMICS: THEORY AND APPLICATIONS TO ECONOMIC AND SOCIAL SYSTEMS, Lectures Notes in Economics and Mathematical Systems (pp. 161-175). (LECTURE NOTES IN ECONOMICS AND MATHEMATICAL SYSTEMS). https://doi.org/10.1007/978-3-540-68409-1_8

Grassi, R. ; Scapellato, Raffaele ; Scapellato, R. et al. / Betweenness centrality: extremal values and structural properties. TOPOLOGY AND DYNAMICS: THEORY AND APPLICATIONS TO ECONOMIC AND SOCIAL SYSTEMS, Lectures Notes in Economics and Mathematical Systems. editor / STEFANI Silvana, TORRIERO Anna NAIMZADA Ahmad. 2009. pp. 161-175 (LECTURE NOTES IN ECONOMICS AND MATHEMATICAL SYSTEMS).

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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.",

keywords = "betweenness, graphs, trees, betweenness, graphs, trees",

author = "R. Grassi and Raffaele Scapellato and R. Scapellato and Silvana Stefani and S. Stefani and Rosanna Grassi and Anna Torriero",

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editor = "{NAIMZADA Ahmad}, {STEFANI Silvana, TORRIERO Anna}",

booktitle = "TOPOLOGY AND DYNAMICS: THEORY AND APPLICATIONS TO ECONOMIC AND SOCIAL SYSTEMS, Lectures Notes in Economics and Mathematical Systems",

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Grassi, R, Scapellato, R, Scapellato, R, Stefani, S, Stefani, S, Grassi, R & Torriero, A 2009, Betweenness centrality: extremal values and structural properties. in STEFANISTORRIEROA NAIMZADA Ahmad (ed.), TOPOLOGY AND DYNAMICS: THEORY AND APPLICATIONS TO ECONOMIC AND SOCIAL SYSTEMS, Lectures Notes in Economics and Mathematical Systems. LECTURE NOTES IN ECONOMICS AND MATHEMATICAL SYSTEMS, pp. 161-175. https://doi.org/10.1007/978-3-540-68409-1_8

Betweenness centrality: extremal values and structural properties. / Grassi, R.; Scapellato, Raffaele; Scapellato, R. et al.
TOPOLOGY AND DYNAMICS: THEORY AND APPLICATIONS TO ECONOMIC AND SOCIAL SYSTEMS, Lectures Notes in Economics and Mathematical Systems. ed. / STEFANI Silvana, TORRIERO Anna NAIMZADA Ahmad. 2009. p. 161-175 (LECTURE NOTES IN ECONOMICS AND MATHEMATICAL SYSTEMS).

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Betweenness centrality: extremal values and structural properties

AU - Grassi, R.

AU - Scapellato, Raffaele

AU - Scapellato, R.

AU - Stefani, Silvana

AU - Stefani, S.

AU - Grassi, Rosanna

AU - Torriero, Anna

PY - 2009

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AB - 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.

KW - betweenness

KW - graphs

KW - trees

KW - betweenness

KW - graphs

KW - trees

UR - http://hdl.handle.net/10807/14122

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M3 - Chapter

SN - 978-3-540-68407-7

T3 - LECTURE NOTES IN ECONOMICS AND MATHEMATICAL SYSTEMS

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EP - 175

BT - TOPOLOGY AND DYNAMICS: THEORY AND APPLICATIONS TO ECONOMIC AND SOCIAL SYSTEMS, Lectures Notes in Economics and Mathematical Systems

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ER -

Grassi R, Scapellato R, Scapellato R, Stefani S, Stefani S, Grassi R et al. Betweenness centrality: extremal values and structural properties. In NAIMZADA Ahmad STEFANISTORRIEROA, editor, TOPOLOGY AND DYNAMICS: THEORY AND APPLICATIONS TO ECONOMIC AND SOCIAL SYSTEMS, Lectures Notes in Economics and Mathematical Systems. 2009. p. 161-175. (LECTURE NOTES IN ECONOMICS AND MATHEMATICAL SYSTEMS). doi: 10.1007/978-3-540-68409-1_8

Betweenness centrality: extremal values and structural properties

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