Highly nonlinear complexity of interaction dynamics in scale-free networks

Interaction dynamics induced by finite-capacity effect is a typical diffusion model on networks. Although several significant properties of it like condensation have been well studied, the origin of its highly nonlinear complexity, influenced by complex structure and interactive behavior, is still missing. Aimed at filling this gap, we propose entropy to quantify the complexity and exhibit its strong dependence on two coupled crucial elements of nodes, the local topology and the finite capacity. Further, the performance of interaction dynamics, efficiency function is also analyzed in terms of entropy rate and relatively promoted through routing strategy arguments supported by maximum entropy theory studies. This will play a crucial role for inference problems emerging in the field of interaction dynamics on complex networks.