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Temporal networks: slowing down diffusion by long lasting interactions.

Naoki Masuda1, Konstantin Klemm, Víctor M Eguíluz

  • 1Department of Mathematical Informatics, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-8656, Japan.

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|November 19, 2013
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Summary
This summary is machine-generated.

Temporal networks exhibit slower dynamics than aggregate networks due to the noncommutability of interactions. The Laplacian spectrum of temporal networks shows smaller eigenvalues but identical eigenmodes compared to aggregate networks.

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Area of Science:

  • Complex systems analysis
  • Network science
  • Dynamical processes

Background:

  • Interactions in complex systems follow a sequence, impacting information flow and disease spread.
  • Temporal networks capture the time-ordered nature of these interactions, unlike static aggregate networks.

Purpose of the Study:

  • To investigate the Laplacian spectrum of temporal networks.
  • To compare the spectral properties of temporal networks with their aggregate counterparts.
  • To understand how temporal ordering affects dynamical processes.

Main Methods:

  • Analysis of the Laplacian spectrum for temporal networks and their aggregate representations.
  • Comparison of eigenvalues and eigenmodes between temporal and aggregate network spectra.
  • Illustration using temporal motifs, larger network models, and real-world temporal data.

Main Results:

  • The ensemble average spectrum of temporal networks shares eigenmodes with aggregate networks but has smaller eigenvalues.
  • In large networks, temporal dynamics are a time-rescaled version of aggregate dynamics.
  • Diffusive dynamics are consistently slower in temporal networks due to interaction noncommutability.

Conclusions:

  • The noncommutability of interactions in temporal networks fundamentally alters their spectral properties and dynamics compared to aggregate networks.
  • Temporal network structure leads to slower diffusion and information propagation.
  • Findings are validated across theoretical models and empirical data.