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Optimal cost for strengthening or destroying a given network.

Amikam Patron1, Reuven Cohen2, Daqing Li3,4

  • 1Department of Physics, Bar-Ilan University, Ramat-Gan 5290002, Israel.

Physical Review. E
|June 17, 2017
PubMed
Summary

This study presents a cost-effective method to strengthen or destroy random networks by prioritizing node degrees. The priority list is universal across network types, aiding in resilient network design and attack planning.

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Area of Science:

  • Network Science
  • Complex Systems Analysis
  • Graph Theory

Background:

  • Network resilience and vulnerability are critical in diverse applications, from infrastructure design to disease control.
  • Understanding node importance based on connectivity is key to efficient network manipulation.
  • Existing methods often lack a cost-optimization framework for targeted node interventions.

Purpose of the Study:

  • To develop a universally applicable, cost-minimal method for strengthening or destroying random networks.
  • To identify a degree-based priority list for node selection in network interventions.
  • To analyze the impact of node cost-degree correlation on network manipulation strategies.

Main Methods:

  • Defining a cost function c(k) based on node degree k.
  • Developing a degree-priority list derived from the cost function.
  • Applying the priority list to select nodes for strengthening or destruction to minimize total cost.
  • Analyzing the universality of the priority list across different random network types.

Main Results:

  • A universal, degree-based priority list for node strengthening or destruction was identified.
  • This priority list is independent of the network's specific degree distribution.
  • The optimal strategy for minimum cost strengthening or destruction is consistent across various random networks.
  • A difference in the critical fraction of nodes (p_c) for giant component existence was observed between strengthening and destruction.

Conclusions:

  • The developed method provides an efficient, cost-minimal approach to network strengthening and destruction.
  • The universality of the degree-priority list simplifies network intervention strategies.
  • While the node selection priority is similar for strengthening and destruction, the network's robustness (p_c) differs, highlighting distinct implications for resilience and vulnerability.