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Trade-offs between robustness and small-world effect in complex networks.

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Robustness and the small-world effect in complex networks have a conflicting relationship. Optimizing for one feature weakens the other, necessitating a trade-off optimization model for balanced network topology.

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Area of Science:

  • Network science
  • Complex systems analysis
  • Graph theory

Background:

  • Robustness and small-world effects are key properties of complex networks.
  • The interplay between these two crucial features remains largely unexplored.
  • Understanding this relationship is vital for designing resilient and efficient networks.

Purpose of the Study:

  • To investigate the relationship between network robustness and the small-world effect.
  • To develop a model for optimizing the trade-off between robustness and small-world properties.
  • To analyze the structural characteristics of networks optimized for this trade-off.

Main Methods:

  • Demonstration of a conflicting relationship between robustness and small-world effect for a fixed degree sequence.
  • Proposal of a multi-objective trade-off optimization model.
  • Development of a heuristic algorithm to find optimal trade-off network topologies.

Main Results:

  • Robustness-oriented optimization diminishes the small-world effect, and vice versa.
  • The optimized network topology exhibits a distinct core-periphery structure.
  • Detailed investigation into the structural properties of these optimized networks.

Conclusions:

  • A trade-off exists between network robustness and the small-world effect.
  • A core-periphery structure emerges in networks optimized for this balance.
  • The proposed model and algorithm provide a method for achieving optimal network designs balancing these critical features.