Controllability of Indu-Bala product networks

A composite network formed by factor networks is a new type of complex network model that can describe different types of agents and multiple complicated relationships in complex systems. "Indu-Bala product" of graphs is a new graph operation with symmetry properties and good mathematical expression, which enables one to construct many pairs of respective co-spectral graphs. This work studies the controllability of a composite network formed by factor networks via Indu-Bala product based on Laplacian dynamics. The eigenvalues and eigenvectors of Indu-Bala product networks (IBPNs) can be represented by factors' eigenvalues and eigenvectors, which can reduce the computational complexity and analytical burden. Based on the PBH test, sufficient and necessary algebraic criterions for controllability of IBPNs are established, which reveal the controllability relationship between entire network and its factors. This work will help one to construct, understand and improve the composite complex network models, and gain insight into the synergistic mechanisms of the networks.