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Networks evolve complex structures under pressures for modularity and robustness. Our models reveal how these combined forces create diverse patterns, sometimes helping, sometimes hindering each other, shaping network organization.

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Area of Science:

  • Network Science
  • Complex Systems
  • Theoretical Ecology

Background:

  • Emerging network structures are shaped by selective pressures.
  • Understanding simultaneous optimization of modularity and robustness is crucial.
  • Previous models often isolate evolutionary dynamics from structural optimization.

Purpose of the Study:

  • To investigate network structures optimized for both modularity and robustness.
  • To isolate the effects of joint optimization using maximum-entropy null models.
  • To analyze the interplay between synergistic and antagonistic selective pressures.

Main Methods:

  • Construction of maximum-entropy null models.
  • Analysis of network structures under simultaneous optimization criteria.
  • Identification of phase diagrams for optimized network patterns.

Main Results:

  • A rich phase diagram of optimized network structures was revealed.
  • Combinations of modular, core-periphery, and bipartite patterns were observed.
  • Parameter regions showed synergistic and antagonistic effects between optimization criteria.

Conclusions:

  • Interactions between selective pressures are pivotal in determining network structure.
  • Simple network models can capture these complex interactions.
  • The study provides insights into the formation of robust and modular systems.