Degree Distribution of Evolution Networks with Acceleration of Edge Attachment

Recent studies show that the topologies of complex networks can be categorised into three catalogues: random graph model, small-world model, and scale-free model. The main reasons for the emergence of the three different models are the differences of edges' connectivity and vertexes' increasing modes in the evolution of the complex networks. According to the measured data of the real-world complex networks, the range of power-law exponent of those networks is [2, 3]. However, the range of the theoretical results that have been obtained is [2, +∞). A new edges' connectivity mode with the acceleration of edge preferential attachment is proposed in this article. And using the master equation approach, the exponent of power law in the mode is presented. Theoretical analyses and simulation results indicate that the exponent of power law is adjusted in the range from 2 to 3 with the proper connectivity acceleration.