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Edge orientation for optimizing controllability of complex networks.

Yan-Dong Xiao1, Song-Yang Lao1, Lv-Lin Hou1

  • 1College of Information Systems and Management, National University of Defense Technology, Changsha 410073, China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 7, 2014
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Summary
This summary is machine-generated.

Optimizing complex network controllability involves assigning edge directions, a problem termed edge orientation for optimal controllability (EOOC). This study introduces a novel method to solve EOOC by transforming it into a maximum independent set problem.

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Area of Science:

  • Network Science
  • Control Theory
  • Graph Theory

Background:

  • Controllability of complex networks is a critical area of research.
  • Previous optimization methods often focused on structural perturbations, neglecting the impact of edge direction.
  • Network synchronizability and controllability are distinct properties, requiring different optimization strategies.

Purpose of the Study:

  • To systematically define and address the edge orientation for optimal controllability (EOOC) problem.
  • To develop a method for optimizing network controllability by assigning directions to edges.
  • To investigate the influence of degree-degree correlations on EOOC.

Main Methods:

  • Defined the edge orientation for optimal controllability (EOOC) problem.
  • Constructed a switching network to transform EOOC into a maximum independent set problem.
  • Analyzed the relationship between degree-degree correlations and EOOC through experiments.

Main Results:

  • The proposed method for EOOC is proven to be unambiguous and optimal.
  • Disassortativity in network structure weakens the effectiveness of edge orientation for optimal controllability.
  • Assortativity patterns were found to have no significant correlation with EOOC.

Conclusions:

  • Network structure fundamentally dictates network controllability and the potential for optimization.
  • Assigning edge directions is a viable and effective strategy for enhancing network controllability.
  • The developed method provides a rigorous approach to optimizing network control through edge orientation.