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From networks to time series.

Yutaka Shimada1, Tohru Ikeguchi, Takaomi Shigehara

  • 1Graduate School of Science and Engineering, Saitama University, Sakura-ku, Saitama-shi, Saitama, Japan. yshimada@sat.t.u-tokyo.ac.jp

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Summary
This summary is machine-generated.

This study introduces a framework to convert complex networks into time series using multidimensional scaling. Different network types, like ring and random networks, transform into distinct time series patterns, offering new analytical insights.

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Area of Science:

  • Complex networks analysis
  • Time series generation
  • Network science

Background:

  • Complex networks are ubiquitous in nature and technology.
  • Analyzing network dynamics often requires time series representations.
  • Existing methods for network-to-time-series transformation are limited.

Purpose of the Study:

  • To propose a novel framework for transforming complex networks into time series.
  • To analyze the time series characteristics resulting from different network structures.
  • To provide analytical validation for the proposed transformation method.

Main Methods:

  • Utilized classical multidimensional scaling (MDS) for network transformation.
  • Applied the framework to the Watts and Strogatz network model.
  • Employed circulant-matrix theory and perturbation theory for analytical verification.

Main Results:

  • Ring lattices transform into periodic time series.
  • Small-world networks yield noisy periodic time series.
  • Random networks generate random time series.
  • Analytical results confirmed for high-dimensional lattices.

Conclusions:

  • The proposed framework effectively translates network topology into distinct time series patterns.
  • This method offers a new perspective for analyzing complex systems dynamics.
  • The analytical framework provides robust validation for the observed transformations.