Controllability of Indu-Bala product networks

Area of Science:

• Complex systems analysis
• Graph theory
• Network science

Background:

• Composite networks, formed by factor networks, offer a novel approach to modeling complex systems with diverse agents and relationships.
• The Indu-Bala product is a graph operation that facilitates the creation of co-spectral graphs and simplifies network analysis.

Purpose of the Study:

• To investigate the controllability of composite networks constructed using factor networks and the Indu-Bala product.
• To develop efficient methods for analyzing the controllability of these complex network structures.

Main Methods:

• Utilizing Laplacian dynamics to model the composite networks.
• Leveraging the spectral properties of Indu-Bala product networks (IBPNs) for computational efficiency.
• Applying the PBH test to derive algebraic criteria for controllability.

Main Results:

• Eigenvalues and eigenvectors of IBPNs are derived from their factor networks, reducing computational complexity.
• Sufficient and necessary algebraic conditions for the controllability of IBPNs were established.
• The study reveals the direct relationship between the controllability of the entire network and its constituent factors.

Conclusions:

• The developed criteria simplify the analysis and construction of controllable composite networks.
• This research provides insights into the synergistic mechanisms governing complex networks.
• The findings aid in the design and improvement of complex network models.