Controllability and observability analysis for vertex domination centrality in directed networks

Area of Science:

• Network Science
• Systems Biology
• Control Theory

Background:

• Topological centrality measures node importance in complex networks.
• Existing measures are insufficient for directed networks modeling dynamic processes.
• Quantifying a vertex's ability to control or observe other vertices is crucial.

Purpose of the Study:

• Introduce a novel direction-specific index, domination centrality.
• Assess the intervention capabilities of vertices in directed networks.
• Analyze vertex interactions and functional dependencies for network domination.

Main Methods:

• Determine controllable and observable subspaces under global minimum-cost conditions.
• Define and calculate domination centrality for directed networks.
• Employ clustering analysis to detect functional modules using domination similarity.

Main Results:

• Domination centrality is largely determined by the network's degree distribution.
• High-domination centrality nodes, not necessarily hubs, are key for system intervention.
• Significant functional modules were detected in glossary and metabolic networks.

Conclusions:

• Domination centrality effectively assesses vertex intervention capabilities in directed networks.
• The index provides practical insights into network structure and dynamics.
• Domination centrality offers a more nuanced understanding of node importance than traditional centrality measures.