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Summary
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This study introduces a data-driven method to identify collective variables (CVs) in complex network dynamics. The approach reveals low-dimensional collective variables even in theoretically unexplained systems.

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Area of Science:

  • Complex Systems
  • Network Science
  • Data Science

Background:

  • Collective variables (CVs) simplify high-dimensional system states for analyzing emergent dynamics on networks.
  • Understanding the link between CVs and network measures is challenging, often requiring deep knowledge of system dynamics and network topology.

Purpose of the Study:

  • To develop a data-driven method for algorithmically learning and understanding CVs in binary-state spreading processes on networks.
  • To explore the relationship between CVs and network properties across diverse network structures.

Main Methods:

  • A novel data-driven methodology was employed to identify and analyze CVs.
  • The method was applied to binary-state spreading processes on various network topologies, including stochastic block models, ring graphs, random regular graphs, and scale-free networks (Albert-Barabási model).

Main Results:

  • The study successfully demonstrated the algorithmic learning of CVs for spreading processes on networks of arbitrary topology.
  • Evidence for the existence of low-dimensional CVs was found, even in network configurations lacking prior theoretical understanding.

Conclusions:

  • The developed data-driven method effectively identifies collective variables in complex network dynamics.
  • This approach advances the understanding of emergent behaviors in networked systems and highlights the prevalence of low-dimensional collective variables.