Sustainability of Scale-Free Properties in Synchronizations of Dynamic Scale-Free Networks

Scale-free networks are ubiquitous in social, biological and technological networked systems. Dynamic Scale-free networks and their synchronizations are important to understand and predict the behavior of social, biological and technological networked systems. In this research, computational experiments have been conducted to understand the sustainability of scale-free properties during the time of synchronizations in dynamic scale-free networks. Two synchronization phenomena which are synchronization based on states of nodes with coupling configuration matrix and synchronization based on states of nodes with network centralities have been implemented for the synchronization in dynamic scale-free networks. In experiments, dynamic scale-free networks have been generated with a network generation algorithm and analyzed to understand the fluctuation from the scale-free properties in their phases during the time of synchronizations.