Using the network reliability polynomial to characterize and design networks
We consider methods for solving certain network characterization and design problems that arise in network epidemiology. We argue that the network reliability polynomial introduced by Moore and Shannon is a useful framework in which to reason about these problems. Specifically, we show how efficient... Full description
Journal Title:  Journal of Complex Networks 2014, Vol. 2(4), pp.356372 
Main Author:  Eubank, Stephen 
Other Authors:  Youssef, Mina , Khorramzadeh, Yasamin 
Format:  Electronic Article 
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ID:  ISSN: 20511310 ; EISSN: 20511329 ; DOI: 10.1093/comnet/cnu037 
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recordid:  oxford10.1093/comnet/cnu037 
title:  Using the network reliability polynomial to characterize and design networks 
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ispartof:  Journal of Complex Networks, 2014, Vol. 2(4), pp.356372 
description:  We consider methods for solving certain network characterization and design problems that arise in network epidemiology. We argue that the network reliability polynomial introduced by Moore and Shannon is a useful framework in which to reason about these problems. Specifically, we show how efficient estimation of the polynomial permits characterizing and distinguishing very large networks in ways that are dynamically relevant. Furthermore, a generalization of flows and cuts to structures that determine the reliability suggests a new measure of edge or vertex centrality that we call criticality . We describe how criticality is related to the more common notion of betweenness and illustrate its application to targeting interventions to control outbreaks of infectious disease. Although our applications are to infectious disease outbreaks, the methods we develop are applicable to many other diffusive dynamical systems over complex networks. 
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identifier:  ISSN: 20511310 ; EISSN: 20511329 ; DOI: 10.1093/comnet/cnu037 
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