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Xin-Dong Gao1, Wen-Xu Wang1,2, Ying-Cheng Lai3,4

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Understanding network control efficacy is crucial. This study introduces a framework to determine how many nodes are controllable from a given set, revealing that hub nodes often have lower control centrality in undirected networks.

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Area of Science:

  • Network Science
  • Complex Systems Engineering

Background:

  • Controlling complex networks is a key research area.
  • Theoretical frameworks exist for full network control via driver nodes.
  • Realistic constraints limit externally driven nodes, necessitating control efficacy assessment.

Purpose of the Study:

  • To develop a framework for determining control efficacy in undirected networks.
  • To identify controllable nodes for any given set of driver nodes.
  • To provide a mathematical and physical understanding of network control.

Main Methods:

  • Mathematical framework based on non-singular transformation.
  • Development of a diffusion-based physical model for control signal propagation.
  • Application to model and empirical complex networks.

Main Results:

  • A rigorous theorem to determine network control efficacy.
  • Identification of controllable nodes based on driver node selection.
  • Demonstration that hub nodes generally have lower control centrality in undirected networks.

Conclusions:

  • The developed framework accurately assesses network control efficacy.
  • The diffusion model offers physical intuition for control processes.
  • Findings challenge assumptions about hub node importance in control centrality.