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Structural controllability of complex networks based on preferential matching.

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Minimum driver node sets (MDSs) can include high-degree nodes, challenging previous assumptions. Network edge direction influences whether driver nodes are high-degree.

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Area of Science:

  • Network Science
  • Control Theory
  • Computer Science

Background:

  • Minimum driver node sets (MDSs) are crucial for analyzing the structural controllability of complex networks.
  • Previous studies suggested MDSs avoid high-degree nodes, but this was based on limited enumeration due to the #P-complete nature of MDS calculation.
  • A lack of comprehensive analysis has prevented definitive conclusions on the degree properties of MDSs.

Purpose of the Study:

  • To develop a method for finding MDSs with specific degree properties.
  • To investigate the degree distribution of MDSs, particularly concerning high- and medium-degree nodes.
  • To explore the relationship between network edge direction and the degree of driver nodes.

Main Methods:

  • Proposed a preferential matching algorithm to identify MDSs with desired degree characteristics.
  • Conducted experimental analysis on various networks to evaluate the degree properties of obtained MDSs.
  • Analyzed the influence of network edge direction on the degree distribution of driver nodes.

Main Results:

  • The preferential matching algorithm successfully generated MDSs composed of high- and medium-degree nodes.
  • Experimental results indicate that the average degree of MDSs can exceed the overall network average.
  • The tendency for driver nodes to be high-degree is strongly correlated with the network's edge direction.

Conclusions:

  • Contrary to prior limited observations, MDSs can comprise high-degree nodes.
  • The preferential matching approach offers a way to find MDSs with specific degree profiles.
  • Network topology, specifically edge direction, is a key factor determining driver node degree characteristics.