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Using the network reliability polynomial to characterize and design networks.

Stephen Eubank1, Mina Youssef2, Yasamin Khorramzadeh3

  • 1Network Dynamics and Simulation Science Laboratory, Virginia Bioinformatics Institute ; Department of Population Health Sciences, Virginia-Maryland Regional College of Veterinary Medicine.

Journal of Complex Networks
|June 19, 2015
PubMed
Summary
This summary is machine-generated.

This study introduces the network reliability polynomial for analyzing large networks in epidemiology. A new centrality measure, criticality, helps target interventions for disease outbreaks and other network dynamics.

Keywords:
complex networksgraph theorygraphical modelsnetwork reliabilitynetwork theorynetwork topology

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Area of Science:

  • Network epidemiology
  • Complex systems analysis
  • Mathematical modeling

Background:

  • Network characterization and design are crucial for understanding disease spread.
  • Existing methods may not adequately capture dynamic properties of large, complex networks.
  • The network reliability polynomial offers a potential framework for network analysis.

Purpose of the Study:

  • To apply the network reliability polynomial to characterize and distinguish large networks in epidemiology.
  • To introduce a novel centrality measure, 'criticality,' for network analysis.
  • To demonstrate the utility of criticality in targeting interventions for infectious disease outbreaks.

Main Methods:

  • Utilizing the network reliability polynomial for network characterization.
  • Developing efficient estimation techniques for the polynomial.
  • Generalizing network flow and cut concepts to reliability structures.
  • Defining and calculating the criticality measure for network nodes and edges.

Main Results:

  • Efficient estimation of the network reliability polynomial enables dynamic characterization of large networks.
  • The criticality measure is introduced as a novel centrality metric.
  • Criticality is shown to be related to betweenness centrality.
  • Application of criticality to targeting interventions for infectious disease control is illustrated.

Conclusions:

  • The network reliability polynomial provides a powerful framework for network epidemiology.
  • Criticality offers a new, effective measure for identifying key network components.
  • The developed methods are broadly applicable to diffusive dynamical systems on complex networks.