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Calculating the minimum control counts (MCCs) for complex networks is challenging. This study provides analytic estimates for expected MCCs in random network models, offering insights into network structures influencing control requirements.

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Area of Science:

  • Complex networks
  • Network controllability
  • Graph theory

Background:

  • The minimum number of controls required for full controllability is a key network measure.
  • Computing minimum control counts (MCCs) is computationally intensive.
  • Assessing MCCs in real networks requires computationally expensive null models.

Purpose of the Study:

  • To derive analytic estimates for expected minimum control counts (MCCs) in common random network models.
  • To reduce the computational cost of evaluating MCCs.
  • To understand the structural properties of random networks that necessitate specific control counts.

Main Methods:

  • Derivation of analytic estimates for expected MCCs.
  • Comparison of analytic estimates with exact control counts.
  • Analysis of random network models including Erdős–Rényi and Barabási–Albert models.

Main Results:

  • Analytic estimates show good agreement with exact MCCs for random network models.
  • The derived expressions provide insights into the structural drivers of control requirements.
  • The study establishes a more efficient method for estimating MCCs.

Conclusions:

  • Analytic estimates offer a computationally feasible alternative to exact calculations for MCCs.
  • Understanding network structure through MCCs is crucial for network control.
  • This work facilitates the analysis of controllability in large-scale complex networks.