Real-world networks are dynamical complex network systems. The dynamics of a network system is a coupling of the local dynamics with the global dynamics. The local dynamics is the time-varying behaviors of ensembles at the local level. The global dynamics is the collective behavior of the ensembles following specific laws at the global level. These laws include basic physical principles and constraints. Complex networks have inherent resilience that offsets disturbance and maintains the state of the system. However, when disturbance is potent enough, network dynamics can be perturbed to a level that ensembles no longer follow the constraint conditions. As a result, the collective behavior of a complex network diminishes and the network collapses. The characteristic of a complex network is the response of the system which is time-dependent. Therefore, complex networks need to account for time-dependency and obey physical laws and constraints. Statistical mechanics is viable for the study of multi-body dynamic systems having uncertain states such as complex network systems. Statistical entropy can be used to define the distribution of the states of ensembles. The difference between the states of ensembles define the interaction between them. This interaction is known as the collective behavior. In other words statistical entropy defines the dynamics of a complex network. Variation of entropy corresponds to the variation of network dynamics and vice versa. Therefore, entropy can serve as an indicator of network dynamics. A stable network is characterized by a specific entropy while a network on the verge of collapse is characterized by another. As the collective behavior of a complex network can be described by entropy, the correlation between the statistical entropy and network dynamics is investigated.
An Almost-Solvable Model of Complex Network Dynamics
