Modelling Multi-Trait Scale-free Networks by Optimization

Recently, one paper in Nature(Papadopoulos, 2012) raised an old debate on the origin of the scale-free property of complex networks, which focuses on whether the scale-free property origins from the optimization or not. Because the real-world complex networks often have multiple traits, any explanation on the scale-free property of complex networks should be capable of explaining the other traits as well. This paper proposed a framework which can model multi-trait scale-free networks based on optimization, and used three examples to demonstrate its effectiveness. The results suggested that the optimization is a more generalized explanation because it can not only explain the origin of the scale-free property, but also the origin of the other traits in a uniform way. This paper provides a universal method to get ideal networks for the researches such as epidemic spreading and synchronization on complex networks. PACS numbers: 89.75.Da, 89.75.Fb, 89.20.Hh