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Triadic percolation induces dynamical topological patterns in higher-order networks.

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Triadic interactions in spatial networks create complex, time-varying patterns in the giant component. This study reveals new topological patterns and dynamics, crucial for understanding systems like neural networks.

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Area of Science:

  • Complex Systems
  • Network Science
  • Mathematical Biology

Background:

  • Triadic interactions, where a third node influences a pair, are key in biological and ecological systems.
  • Previous work showed triadic percolation on random graphs leads to chaotic dynamics.
  • Real-world networks often feature local, spatially embedded triadic interactions.

Purpose of the Study:

  • To investigate the impact of local triadic interactions on spatial networks.
  • To characterize the resulting spatio-temporal modulation of the giant component.
  • To analyze the topological patterns and information content of triadic percolation.

Main Methods:

  • Simulations of triadic interactions on spatially embedded networks.
  • Topological data analysis for pattern classification (stripes, octopus, small clusters).
  • Assessment of information content using entropy and complexity measures.

Main Results:

  • Spatial triadic interactions induce complex spatio-temporal modulations of the giant component.
  • Distinct topological patterns (stripes, octopus, small clusters) emerge.
  • Multistability of dynamics and a comprehensive phase diagram were identified.

Conclusions:

  • Triadic interactions in spatial networks lead to novel, time-varying giant component topologies.
  • This framework is applicable to dynamic systems, particularly in neuroscience.
  • The study expands the understanding of percolation theory in realistic network settings.