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Vulnerability and power on networks

Published online by Cambridge University Press:  16 February 2015

ENRICO BOZZO ,
MASSIMO FRANCESCHET  and
FRANCA RINALDI
ENRICO BOZZO
Affiliation:
Department of Mathematics and Computer Science, University of Udine, Udine, Italy (e-mail: enrico.bozzo@uniud.it, massimo.franceschet@uniud.it, franca.rinaldi@uniud.it)
MASSIMO FRANCESCHET
Affiliation:
Department of Mathematics and Computer Science, University of Udine, Udine, Italy (e-mail: enrico.bozzo@uniud.it, massimo.franceschet@uniud.it, franca.rinaldi@uniud.it)
FRANCA RINALDI
Affiliation:
Department of Mathematics and Computer Science, University of Udine, Udine, Italy (e-mail: enrico.bozzo@uniud.it, massimo.franceschet@uniud.it, franca.rinaldi@uniud.it)
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Abstract

Inspired by socio-political scenarios, like dictatorships, in which a minority of people exercise control over a majority of weakly interconnected individuals, we propose vulnerability and power measures defined on groups of actors of networks. We establish an unexpected connection between network vulnerability and graph regularizability. We use the Shapley value of coalition games to introduce fresh notions of vulnerability and power at node level defined in terms of the corresponding measures at group level. We investigate the computational complexity of computing the defined measures, both at group and node levels, and provide effective methods to quantify them. Finally we test vulnerability and power on both artificial and real networks.

Keywords

centrality measuresrobustnessregularizable graphs2-vertex cover2-matchinginteger linear programmingcoalitional gamesShapley value
Type
Research Article
Information
Network Science , Volume 3 , Issue 2 , June 2015 , pp. 196 - 226
Copyright
Copyright © Cambridge University Press 2015 

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