A General Framework for Dynamic Complex Networks

A general framework applicable for characterizing dynamic complex networks is presented. The framework 1) incorporates a revised Kuramoto model to define constituent dynamics, 2) explores information entropy for the description of global ensemble behaviors, 3) defines the variation of the state of connected constituents using energy, and 4) introduces two new time-dependent parameters, i.e., degrees of coupling, to delineate the extent to which the state of one constituent impacts the other. Information entropy which defines the randomness of constituent energy at the microscopic level provides a definitive measure for the ensemble dynamics at the macroscopic level. Whether a dynamic complex network is evolving toward synchronization or deteriorating and collapsing can be determined by tracking ensemble entropy in time. Two popular topological network structures are examined under the framework for their respective network responses. It is found that, in addition to misrepresenting the true network dynamics, static network structures do not differentiate themselves in resolving network properties such as average path length and degree distribution, thus rendering similar interpretations for the underlying network.