Abstract: The effects of inner edge addition on the structure of the Barabasi-Albert(BA)scale-free network are analyzed, with the linear and non-linear preferential attachment. Based on the extended rate-equation approach, considering the changing rates of the existing nodes’ degrees caused by the addition of new nodes and edges, the exact expressions for the degree distributions are obtained. When the preferential attachment is linear, the degree distributions follow the power-law form. For the sub-linear preferential attachment, the degree distributions follow the form of stretched exponential; for the sup-linear preferential attachment, the double-end-point preferential attachment can lead to an extremely low number of “gel” nodes connecting to nearly every other node in the network. The results obtained provide references for further researches on other properties of inner evolving networks.

Key words: rate-equation, degree distribution, inner evolving