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Controllability limit of edge dynamics in complex networks.

Shao-Peng Pang1, Wen-Xu Wang2,3, Fei Hao4

  • 1School of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Science), Jinan, Shandong Province 250353, China.

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This study reveals that controlling edge dynamics in complex networks is influenced by degree correlations. Adjusting these correlations can achieve desired network controllability within specific limits.

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Area of Science:

  • Network Science
  • Control Theory
  • Complex Systems

Background:

  • Edge dynamics are crucial in complex networks with intricate topological features.
  • Controllability of edge dynamical systems depends on driving initial states to desired states via control inputs.

Purpose of the Study:

  • To investigate how the correlation between in- and out-degrees impacts edge dynamics control in complex networks.
  • To establish a framework for analyzing the effects of degree correlation on network controllability.

Main Methods:

  • Utilized maximum matching and direct acquisition methods to define controllability limits.
  • Analyzed the impact of adjusting degree correlation on edge controllability.

Main Results:

  • Controllability limits were found to be ubiquitous across various model and real-world networks.
  • Arbitrary edge controllability is achievable by tuning degree correlation within identified limits.
  • Observed nonsmooth phenomena at upper limits and widespread exponential/power-law scaling behaviors.

Conclusions:

  • Degree correlation is a key factor in managing edge dynamics controllability.
  • The proposed framework provides insights into network control by adjusting topological correlations.
  • Understanding these limits and behaviors is essential for designing and controlling complex network systems.