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Cross-linked structure of network evolution.

Danielle S Bassett1, Nicholas F Wymbs2, Mason A Porter3

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This study introduces a hypergraph approach to analyze temporal network co-evolution. It reveals how cross-link structures uncover hidden dynamics in coupled oscillators and brain networks during learning.

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Area of Science:

  • Network Science
  • Dynamical Systems
  • Computational Neuroscience

Background:

  • Temporal networks exhibit complex co-evolutionary dynamics.
  • Understanding these dynamics is crucial for fields like neuroscience and systems biology.
  • Existing methods may not fully capture the intricate interplay within evolving networks.

Purpose of the Study:

  • To develop a novel method for analyzing temporal network co-evolution.
  • To apply this method to real-world and synthetic network data.
  • To demonstrate the utility of cross-link structures in uncovering network dynamics.

Main Methods:

  • Utilizing hypergraph formalism to represent cross-link structures in temporal networks.
  • Analyzing temporal network data from coupled nonlinear oscillators.
  • Investigating human brain activity networks during learning.

Main Results:

  • Hyperedges in oscillator networks reveal co-evolution patterns within and between communities.
  • Brain networks show initial co-evolution during learning that stabilizes with practice.
  • Decreasing hyperedge size indicates the emergence of autonomous subgraphs.

Conclusions:

  • Cross-link structure analysis effectively uncovers unexpected co-evolutionary attributes.
  • This approach enhances the investigation of temporal network structures.
  • The findings are applicable to both synthetic and real-world dynamical systems.