More general discussions on information transfer of the centralized network system with coupled oscillations and random matrices

In this study, a centralized information network is generalized to an n-dimensional agent model. In addition, the random matrix theory can also be employed to investigate the fluctuating properties of their eigenvalues and evaluate their physical interpretations as a property of sparse matrices. The nature of the eigenvectors for the extended network provides the same context as coupled oscillations because the undirected network model is exactly the same as a coupled oscillating system with free ends. Moreover, the spectra of the eigenvalues also provide characteristic properties to be interpreted. This work then provides general rules for such a network and discusses the validity of the method.